id sid tid token lemma pos american_scientific_journal-522 1 1 american american PROPN american_scientific_journal-522 1 2 scientific scientific ADJ american_scientific_journal-522 1 3 research research NOUN american_scientific_journal-522 1 4 journal journal NOUN american_scientific_journal-522 1 5 for for ADP american_scientific_journal-522 1 6 engineering engineering NOUN american_scientific_journal-522 1 7 , , PUNCT american_scientific_journal-522 1 8 technology technology NOUN american_scientific_journal-522 1 9 , , PUNCT american_scientific_journal-522 1 10 and and CCONJ american_scientific_journal-522 1 11 sciences science NOUN american_scientific_journal-522 1 12 ( ( PUNCT american_scientific_journal-522 1 13 asrjets asrjet NOUN american_scientific_journal-522 1 14 ) ) PUNCT american_scientific_journal-522 1 15 issn issn PROPN american_scientific_journal-522 1 16 ( ( PUNCT american_scientific_journal-522 1 17 print print NOUN american_scientific_journal-522 1 18 ) ) PUNCT american_scientific_journal-522 1 19 2313 2313 NUM american_scientific_journal-522 1 20 - - SYM american_scientific_journal-522 1 21 4410 4410 NUM american_scientific_journal-522 1 22 , , PUNCT american_scientific_journal-522 1 23 issn issn PROPN american_scientific_journal-522 1 24 ( ( PUNCT american_scientific_journal-522 1 25 online online ADJ american_scientific_journal-522 1 26 ) ) PUNCT american_scientific_journal-522 1 27 2313 2313 NUM american_scientific_journal-522 1 28 - - SYM american_scientific_journal-522 1 29 4402 4402 NUM american_scientific_journal-522 1 30 © © PROPN american_scientific_journal-522 1 31 global global ADJ american_scientific_journal-522 1 32 society society NOUN american_scientific_journal-522 1 33 of of ADP american_scientific_journal-522 1 34 scientific scientific ADJ american_scientific_journal-522 1 35 research research NOUN american_scientific_journal-522 1 36 and and CCONJ american_scientific_journal-522 1 37 researchers researcher NOUN american_scientific_journal-522 1 38 http://asrjetsjournal.org/ http://asrjetsjournal.org/ VERB american_scientific_journal-522 1 39 free free ADJ american_scientific_journal-522 1 40 vibration vibration NOUN american_scientific_journal-522 1 41 analysis analysis NOUN american_scientific_journal-522 1 42 of of ADP american_scientific_journal-522 1 43 isotropic isotropic ADJ american_scientific_journal-522 1 44 plates plate NOUN american_scientific_journal-522 1 45 by by ADP american_scientific_journal-522 1 46 alternative alternative ADJ american_scientific_journal-522 1 47 hierarchical hierarchical ADJ american_scientific_journal-522 1 48 finite finite ADJ american_scientific_journal-522 1 49 element element NOUN american_scientific_journal-522 1 50 method method NOUN american_scientific_journal-522 1 51 based base VERB american_scientific_journal-522 1 52 on on ADP american_scientific_journal-522 1 53 reddy reddy PROPN american_scientific_journal-522 1 54 ’s ’s PART american_scientific_journal-522 1 55 c1 c1 PROPN american_scientific_journal-522 1 56 hsdt hsdt PROPN american_scientific_journal-522 1 57 s. s. PROPN american_scientific_journal-522 1 58 m. m. PROPN american_scientific_journal-522 1 59 n. n. PROPN american_scientific_journal-522 1 60 serdouna serdouna PROPN american_scientific_journal-522 1 61 * * PROPN american_scientific_journal-522 1 62 , , PUNCT american_scientific_journal-522 1 63 s. s. PROPN american_scientific_journal-522 1 64 m. m. PROPN american_scientific_journal-522 1 65 hamza hamza PROPN american_scientific_journal-522 1 66 - - PUNCT american_scientific_journal-522 1 67 cherifb cherifb PROPN american_scientific_journal-522 1 68 a a PRON american_scientific_journal-522 1 69 , , PUNCT american_scientific_journal-522 1 70 bfaculty bfaculty NOUN american_scientific_journal-522 1 71 of of ADP american_scientific_journal-522 1 72 engineering engineering NOUN american_scientific_journal-522 1 73 , , PUNCT american_scientific_journal-522 1 74 department department NOUN american_scientific_journal-522 1 75 of of ADP american_scientific_journal-522 1 76 mechanical mechanical ADJ american_scientific_journal-522 1 77 engineering engineering NOUN american_scientific_journal-522 1 78 , , PUNCT american_scientific_journal-522 1 79 university university NOUN american_scientific_journal-522 1 80 of of ADP american_scientific_journal-522 1 81 tlemcen tlemcen PROPN american_scientific_journal-522 1 82 , , PUNCT american_scientific_journal-522 1 83 b.p b.p PROPN american_scientific_journal-522 1 84 . . PROPN american_scientific_journal-522 1 85 230 230 NUM american_scientific_journal-522 1 86 , , PUNCT american_scientific_journal-522 1 87 tlemcen tlemcen NOUN american_scientific_journal-522 1 88 13000 13000 NUM american_scientific_journal-522 1 89 , , PUNCT american_scientific_journal-522 1 90 algeria algeria PROPN american_scientific_journal-522 1 91 a a DET american_scientific_journal-522 1 92 serdounn2006 serdounn2006 PROPN american_scientific_journal-522 1 93 @hotmail.com @hotmail.com X american_scientific_journal-522 1 94 bsmhamzacherif@yahoo.fr bsmhamzacherif@yahoo.fr PROPN american_scientific_journal-522 1 95 abstract abstract ADJ american_scientific_journal-522 1 96 this this DET american_scientific_journal-522 1 97 paper paper NOUN american_scientific_journal-522 1 98 presents present VERB american_scientific_journal-522 1 99 the the DET american_scientific_journal-522 1 100 free free ADJ american_scientific_journal-522 1 101 vibration vibration NOUN american_scientific_journal-522 1 102 analysis analysis NOUN american_scientific_journal-522 1 103 of of ADP american_scientific_journal-522 1 104 isotropic isotropic NOUN american_scientific_journal-522 1 105 thick thick ADJ american_scientific_journal-522 1 106 rectangular rectangular ADJ american_scientific_journal-522 1 107 plates plate NOUN american_scientific_journal-522 1 108 , , PUNCT american_scientific_journal-522 1 109 based base VERB american_scientific_journal-522 1 110 on on ADP american_scientific_journal-522 1 111 higher high ADJ american_scientific_journal-522 1 112 order order NOUN american_scientific_journal-522 1 113 shear shear NOUN american_scientific_journal-522 1 114 deformation deformation NOUN american_scientific_journal-522 1 115 theory theory NOUN american_scientific_journal-522 1 116 ( ( PUNCT american_scientific_journal-522 1 117 hsdt hsdt NOUN american_scientific_journal-522 1 118 ) ) PUNCT american_scientific_journal-522 1 119 . . PUNCT american_scientific_journal-522 2 1 the the DET american_scientific_journal-522 2 2 plate plate NOUN american_scientific_journal-522 2 3 theory theory NOUN american_scientific_journal-522 2 4 ensures ensure VERB american_scientific_journal-522 2 5 a a DET american_scientific_journal-522 2 6 zero zero NUM american_scientific_journal-522 2 7 shear shear NOUN american_scientific_journal-522 2 8 - - PUNCT american_scientific_journal-522 2 9 stress stress NOUN american_scientific_journal-522 2 10 condition condition NOUN american_scientific_journal-522 2 11 at at ADP american_scientific_journal-522 2 12 the the DET american_scientific_journal-522 2 13 top top ADJ american_scientific_journal-522 2 14 and and CCONJ american_scientific_journal-522 2 15 bottom bottom ADJ american_scientific_journal-522 2 16 surfaces surface NOUN american_scientific_journal-522 2 17 of of ADP american_scientific_journal-522 2 18 the the DET american_scientific_journal-522 2 19 plate plate NOUN american_scientific_journal-522 2 20 , , PUNCT american_scientific_journal-522 2 21 and and CCONJ american_scientific_journal-522 2 22 do do AUX american_scientific_journal-522 2 23 not not PART american_scientific_journal-522 2 24 requires require VERB american_scientific_journal-522 2 25 a a DET american_scientific_journal-522 2 26 shear shear NOUN american_scientific_journal-522 2 27 correction correction NOUN american_scientific_journal-522 2 28 factor factor NOUN american_scientific_journal-522 2 29 . . PUNCT american_scientific_journal-522 3 1 the the DET american_scientific_journal-522 3 2 model model NOUN american_scientific_journal-522 3 3 requires require VERB american_scientific_journal-522 3 4 inter inter ADJ american_scientific_journal-522 3 5 - - ADJ american_scientific_journal-522 3 6 element element ADJ american_scientific_journal-522 3 7 c1 c1 NOUN american_scientific_journal-522 3 8 continuity continuity NOUN american_scientific_journal-522 3 9 for for ADP american_scientific_journal-522 3 10 the the DET american_scientific_journal-522 3 11 transverse transverse NOUN american_scientific_journal-522 3 12 displacement displacement NOUN american_scientific_journal-522 3 13 . . PUNCT american_scientific_journal-522 4 1 to to PART american_scientific_journal-522 4 2 overcome overcome VERB american_scientific_journal-522 4 3 this this DET american_scientific_journal-522 4 4 hindrance hindrance NOUN american_scientific_journal-522 4 5 , , PUNCT american_scientific_journal-522 4 6 a a DET american_scientific_journal-522 4 7 new new ADJ american_scientific_journal-522 4 8 hierarchical hierarchical ADJ american_scientific_journal-522 4 9 p p NOUN american_scientific_journal-522 4 10 - - PUNCT american_scientific_journal-522 4 11 element element NOUN american_scientific_journal-522 4 12 with with ADP american_scientific_journal-522 4 13 six six NUM american_scientific_journal-522 4 14 degrees degree NOUN american_scientific_journal-522 4 15 of of ADP american_scientific_journal-522 4 16 freedom freedom NOUN american_scientific_journal-522 4 17 per per ADP american_scientific_journal-522 4 18 node node NOUN american_scientific_journal-522 4 19 is be AUX american_scientific_journal-522 4 20 developed develop VERB american_scientific_journal-522 4 21 and and CCONJ american_scientific_journal-522 4 22 used use VERB american_scientific_journal-522 4 23 to to PART american_scientific_journal-522 4 24 find find VERB american_scientific_journal-522 4 25 natural natural ADJ american_scientific_journal-522 4 26 frequencies frequency NOUN american_scientific_journal-522 4 27 of of ADP american_scientific_journal-522 4 28 thick thick ADJ american_scientific_journal-522 4 29 plates plate NOUN american_scientific_journal-522 4 30 . . PUNCT american_scientific_journal-522 5 1 convergence convergence NOUN american_scientific_journal-522 5 2 studies study NOUN american_scientific_journal-522 5 3 and and CCONJ american_scientific_journal-522 5 4 comparison comparison NOUN american_scientific_journal-522 5 5 have have AUX american_scientific_journal-522 5 6 been be AUX american_scientific_journal-522 5 7 carried carry VERB american_scientific_journal-522 5 8 out out ADP american_scientific_journal-522 5 9 for for ADP american_scientific_journal-522 5 10 with with ADP american_scientific_journal-522 5 11 different different ADJ american_scientific_journal-522 5 12 boundaries boundary NOUN american_scientific_journal-522 5 13 conditions condition NOUN american_scientific_journal-522 5 14 . . PUNCT american_scientific_journal-522 6 1 it it PRON american_scientific_journal-522 6 2 is be AUX american_scientific_journal-522 6 3 shown show VERB american_scientific_journal-522 6 4 that that SCONJ american_scientific_journal-522 6 5 the the DET american_scientific_journal-522 6 6 present present ADJ american_scientific_journal-522 6 7 element element NOUN american_scientific_journal-522 6 8 enables enable VERB american_scientific_journal-522 6 9 rapid rapid ADJ american_scientific_journal-522 6 10 convergence convergence NOUN american_scientific_journal-522 6 11 . . PUNCT american_scientific_journal-522 7 1 keywords keyword NOUN american_scientific_journal-522 7 2 : : PUNCT american_scientific_journal-522 7 3 free free ADJ american_scientific_journal-522 7 4 vibration vibration NOUN american_scientific_journal-522 7 5 ; ; PUNCT american_scientific_journal-522 7 6 thick thick ADJ american_scientific_journal-522 7 7 isotropic isotropic NOUN american_scientific_journal-522 7 8 plates plate NOUN american_scientific_journal-522 7 9 ; ; PUNCT american_scientific_journal-522 7 10 hierarchical hierarchical ADJ american_scientific_journal-522 7 11 finite finite PROPN american_scientific_journal-522 7 12 element element NOUN american_scientific_journal-522 7 13 method method NOUN american_scientific_journal-522 7 14 ; ; PUNCT american_scientific_journal-522 7 15 third third ADJ american_scientific_journal-522 7 16 order order NOUN american_scientific_journal-522 7 17 c1 c1 PROPN american_scientific_journal-522 7 18 hsdt hsdt NOUN american_scientific_journal-522 7 19 . . PUNCT american_scientific_journal-522 8 1 1 1 X american_scientific_journal-522 8 2 . . X american_scientific_journal-522 8 3 introduction introduction NOUN american_scientific_journal-522 8 4 thick thick ADJ american_scientific_journal-522 8 5 plates plate NOUN american_scientific_journal-522 8 6 are be AUX american_scientific_journal-522 8 7 extensively extensively ADV american_scientific_journal-522 8 8 used use VERB american_scientific_journal-522 8 9 in in ADP american_scientific_journal-522 8 10 many many ADJ american_scientific_journal-522 8 11 fields field NOUN american_scientific_journal-522 8 12 of of ADP american_scientific_journal-522 8 13 engineering engineering NOUN american_scientific_journal-522 8 14 , , PUNCT american_scientific_journal-522 8 15 including include VERB american_scientific_journal-522 8 16 aerospace aerospace NOUN american_scientific_journal-522 8 17 , , PUNCT american_scientific_journal-522 8 18 civil civil ADJ american_scientific_journal-522 8 19 structures structure NOUN american_scientific_journal-522 8 20 , , PUNCT american_scientific_journal-522 8 21 hydraulic hydraulic ADJ american_scientific_journal-522 8 22 structures structure NOUN american_scientific_journal-522 8 23 , , PUNCT american_scientific_journal-522 8 24 etc etc X american_scientific_journal-522 8 25 . . X american_scientific_journal-522 8 26 for for ADP american_scientific_journal-522 8 27 plates plate NOUN american_scientific_journal-522 8 28 analysis analysis VERB american_scientific_journal-522 8 29 different different ADJ american_scientific_journal-522 8 30 theories theory NOUN american_scientific_journal-522 8 31 exists exist VERB american_scientific_journal-522 8 32 , , PUNCT american_scientific_journal-522 8 33 the the DET american_scientific_journal-522 8 34 classical classical ADJ american_scientific_journal-522 8 35 plates plate NOUN american_scientific_journal-522 8 36 theory theory NOUN american_scientific_journal-522 8 37 ( ( PUNCT american_scientific_journal-522 8 38 cpt cpt NOUN american_scientific_journal-522 8 39 ) ) PUNCT american_scientific_journal-522 8 40 is be AUX american_scientific_journal-522 8 41 adopted adopt VERB american_scientific_journal-522 8 42 for for ADP american_scientific_journal-522 8 43 thin thin ADJ american_scientific_journal-522 8 44 plates plate NOUN american_scientific_journal-522 8 45 , , PUNCT american_scientific_journal-522 8 46 where where SCONJ american_scientific_journal-522 8 47 the the DET american_scientific_journal-522 8 48 effect effect NOUN american_scientific_journal-522 8 49 of of ADP american_scientific_journal-522 8 50 shear shear ADJ american_scientific_journal-522 8 51 deformation deformation NOUN american_scientific_journal-522 8 52 is be AUX american_scientific_journal-522 8 53 neglected neglect VERB american_scientific_journal-522 8 54 [ [ X american_scientific_journal-522 8 55 1 1 NUM american_scientific_journal-522 8 56 ] ] PUNCT american_scientific_journal-522 8 57 . . PUNCT american_scientific_journal-522 9 1 the the DET american_scientific_journal-522 9 2 reissner reissner NOUN american_scientific_journal-522 9 3 . . PUNCT american_scientific_journal-522 10 1 mindlin mindlin PROPN american_scientific_journal-522 10 2 plate plate NOUN american_scientific_journal-522 10 3 theory theory NOUN american_scientific_journal-522 10 4 is be AUX american_scientific_journal-522 10 5 used use VERB american_scientific_journal-522 10 6 for for ADP american_scientific_journal-522 10 7 moderately moderately ADV american_scientific_journal-522 10 8 thick thick ADJ american_scientific_journal-522 10 9 plates plate NOUN american_scientific_journal-522 10 10 , , PUNCT american_scientific_journal-522 10 11 known know VERB american_scientific_journal-522 10 12 as as ADP american_scientific_journal-522 10 13 the the DET american_scientific_journal-522 10 14 first first ADJ american_scientific_journal-522 10 15 order order NOUN american_scientific_journal-522 10 16 shear shear NOUN american_scientific_journal-522 10 17 deformation deformation NOUN american_scientific_journal-522 10 18 theory theory NOUN american_scientific_journal-522 10 19 ( ( PUNCT american_scientific_journal-522 10 20 fsdt fsdt NOUN american_scientific_journal-522 10 21 ) ) PUNCT american_scientific_journal-522 10 22 , , PUNCT american_scientific_journal-522 10 23 in in ADP american_scientific_journal-522 10 24 which which PRON american_scientific_journal-522 10 25 the the DET american_scientific_journal-522 10 26 effect effect NOUN american_scientific_journal-522 10 27 of of ADP american_scientific_journal-522 10 28 shear shear ADJ american_scientific_journal-522 10 29 deformation deformation NOUN american_scientific_journal-522 10 30 is be AUX american_scientific_journal-522 10 31 considered consider VERB american_scientific_journal-522 10 32 by by ADP american_scientific_journal-522 10 33 using use VERB american_scientific_journal-522 10 34 a a DET american_scientific_journal-522 10 35 proper proper ADJ american_scientific_journal-522 10 36 choice choice NOUN american_scientific_journal-522 10 37 of of ADP american_scientific_journal-522 10 38 a a DET american_scientific_journal-522 10 39 shear shear NOUN american_scientific_journal-522 10 40 correction correction NOUN american_scientific_journal-522 10 41 factor factor NOUN american_scientific_journal-522 10 42 which which PRON american_scientific_journal-522 10 43 depend depend VERB american_scientific_journal-522 10 44 on on ADP american_scientific_journal-522 10 45 loading loading NOUN american_scientific_journal-522 10 46 and and CCONJ american_scientific_journal-522 10 47 boundary boundary ADJ american_scientific_journal-522 10 48 conditions condition NOUN american_scientific_journal-522 10 49 [ [ X american_scientific_journal-522 10 50 2 2 NUM american_scientific_journal-522 10 51 ] ] PUNCT american_scientific_journal-522 10 52 . . PUNCT american_scientific_journal-522 11 1 the the DET american_scientific_journal-522 11 2 simplifying simplifying NOUN american_scientific_journal-522 11 3 assumptions assumption NOUN american_scientific_journal-522 11 4 made make VERB american_scientific_journal-522 11 5 in in ADP american_scientific_journal-522 11 6 cpt cpt PROPN american_scientific_journal-522 11 7 and and CCONJ american_scientific_journal-522 11 8 fsdt fsdt NOUN american_scientific_journal-522 11 9 are be AUX american_scientific_journal-522 11 10 reflected reflect VERB american_scientific_journal-522 11 11 by by ADP american_scientific_journal-522 11 12 the the DET american_scientific_journal-522 11 13 high high ADJ american_scientific_journal-522 11 14 percentage percentage NOUN american_scientific_journal-522 11 15 errors error NOUN american_scientific_journal-522 11 16 in in ADP american_scientific_journal-522 11 17 the the DET american_scientific_journal-522 11 18 results result NOUN american_scientific_journal-522 11 19 of of ADP american_scientific_journal-522 11 20 thick thick ADJ american_scientific_journal-522 11 21 plates plate NOUN american_scientific_journal-522 11 22 analysis analysis NOUN american_scientific_journal-522 11 23 . . PUNCT american_scientific_journal-522 12 1 for for ADP american_scientific_journal-522 12 2 these these DET american_scientific_journal-522 12 3 plates plate NOUN american_scientific_journal-522 12 4 , , PUNCT american_scientific_journal-522 12 5 higher high ADJ american_scientific_journal-522 12 6 - - PUNCT american_scientific_journal-522 12 7 order order NOUN american_scientific_journal-522 12 8 shear shear NOUN american_scientific_journal-522 12 9 deformation deformation NOUN american_scientific_journal-522 12 10 theories theory NOUN american_scientific_journal-522 12 11 ( ( PUNCT american_scientific_journal-522 12 12 hsdt hsdt NOUN american_scientific_journal-522 12 13 ) ) PUNCT american_scientific_journal-522 12 14 are be AUX american_scientific_journal-522 12 15 required require VERB american_scientific_journal-522 12 16 . . PUNCT american_scientific_journal-522 13 1 the the DET american_scientific_journal-522 13 2 hsdt hsdt NOUN american_scientific_journal-522 13 3 ensure ensure VERB american_scientific_journal-522 13 4 a a DET american_scientific_journal-522 13 5 zero zero NUM american_scientific_journal-522 13 6 shear shear NOUN american_scientific_journal-522 13 7 - - PUNCT american_scientific_journal-522 13 8 stress stress NOUN american_scientific_journal-522 13 9 condition condition NOUN american_scientific_journal-522 13 10 on on ADP american_scientific_journal-522 13 11 the the DET american_scientific_journal-522 13 12 top top ADJ american_scientific_journal-522 13 13 and and CCONJ american_scientific_journal-522 13 14 bottom bottom ADJ american_scientific_journal-522 13 15 surfaces surface NOUN american_scientific_journal-522 13 16 of of ADP american_scientific_journal-522 13 17 the the DET american_scientific_journal-522 13 18 plate plate NOUN american_scientific_journal-522 13 19 , , PUNCT american_scientific_journal-522 13 20 and and CCONJ american_scientific_journal-522 13 21 do do AUX american_scientific_journal-522 13 22 not not PART american_scientific_journal-522 13 23 require require VERB american_scientific_journal-522 13 24 a a DET american_scientific_journal-522 13 25 shear shear NOUN american_scientific_journal-522 13 26 correction correction NOUN american_scientific_journal-522 13 27 factor factor NOUN american_scientific_journal-522 13 28 , , PUNCT american_scientific_journal-522 13 29 which which PRON american_scientific_journal-522 13 30 is be AUX american_scientific_journal-522 13 31 a a DET american_scientific_journal-522 13 32 major major ADJ american_scientific_journal-522 13 33 feature feature NOUN american_scientific_journal-522 13 34 of of ADP american_scientific_journal-522 13 35 these these DET american_scientific_journal-522 13 36 theories theory NOUN american_scientific_journal-522 13 37 . . PUNCT american_scientific_journal-522 14 1 * * PUNCT american_scientific_journal-522 14 2 corresponding correspond VERB american_scientific_journal-522 14 3 author author NOUN american_scientific_journal-522 14 4 . . PUNCT american_scientific_journal-522 15 1 1 1 NUM american_scientific_journal-522 15 2 http://asrjetsjournal.org/ http://asrjetsjournal.org/ PROPN american_scientific_journal-522 15 3 american american ADJ american_scientific_journal-522 15 4 scientific scientific ADJ american_scientific_journal-522 15 5 research research NOUN american_scientific_journal-522 15 6 journal journal NOUN american_scientific_journal-522 15 7 for for ADP american_scientific_journal-522 15 8 engineering engineering NOUN american_scientific_journal-522 15 9 , , PUNCT american_scientific_journal-522 15 10 technology technology NOUN american_scientific_journal-522 15 11 , , PUNCT american_scientific_journal-522 15 12 and and CCONJ american_scientific_journal-522 15 13 sciences science NOUN american_scientific_journal-522 15 14 ( ( PUNCT american_scientific_journal-522 15 15 asrjets asrjet NOUN american_scientific_journal-522 15 16 ) ) PUNCT american_scientific_journal-522 15 17 ( ( PUNCT american_scientific_journal-522 15 18 2014 2014 NUM american_scientific_journal-522 15 19 ) ) PUNCT american_scientific_journal-522 15 20 volume volume NOUN american_scientific_journal-522 15 21 9 9 NUM american_scientific_journal-522 15 22 , , PUNCT american_scientific_journal-522 15 23 no no DET american_scientific_journal-522 15 24 1 1 NUM american_scientific_journal-522 15 25 , , PUNCT american_scientific_journal-522 15 26 pp pp ADV american_scientific_journal-522 15 27 1 1 NUM american_scientific_journal-522 15 28 - - SYM american_scientific_journal-522 15 29 19 19 NUM american_scientific_journal-522 15 30 nelson nelson NOUN american_scientific_journal-522 15 31 and and CCONJ american_scientific_journal-522 15 32 lorch lorch VERB american_scientific_journal-522 15 33 [ [ X american_scientific_journal-522 15 34 3 3 NUM american_scientific_journal-522 15 35 ] ] PUNCT american_scientific_journal-522 15 36 , , PUNCT american_scientific_journal-522 15 37 the the DET american_scientific_journal-522 15 38 authors author NOUN american_scientific_journal-522 15 39 in in ADP american_scientific_journal-522 15 40 [ [ X american_scientific_journal-522 15 41 4 4 NUM american_scientific_journal-522 15 42 ] ] PUNCT american_scientific_journal-522 15 43 presented present VERB american_scientific_journal-522 15 44 a a DET american_scientific_journal-522 15 45 hsdt hsdt NOUN american_scientific_journal-522 15 46 for for ADP american_scientific_journal-522 15 47 laminated laminated ADJ american_scientific_journal-522 15 48 plates plate NOUN american_scientific_journal-522 15 49 however however ADV american_scientific_journal-522 15 50 the the DET american_scientific_journal-522 15 51 displacement displacement ADJ american_scientific_journal-522 15 52 field field NOUN american_scientific_journal-522 15 53 does do AUX american_scientific_journal-522 15 54 satisfy satisfy VERB american_scientific_journal-522 15 55 the the DET american_scientific_journal-522 15 56 shear shear NOUN american_scientific_journal-522 15 57 - - PUNCT american_scientific_journal-522 15 58 stress stress NOUN american_scientific_journal-522 15 59 free free ADJ american_scientific_journal-522 15 60 condition condition NOUN american_scientific_journal-522 15 61 on on ADP american_scientific_journal-522 15 62 the the DET american_scientific_journal-522 15 63 top top ADJ american_scientific_journal-522 15 64 and and CCONJ american_scientific_journal-522 15 65 bottom bottom ADJ american_scientific_journal-522 15 66 surfaces surface NOUN american_scientific_journal-522 15 67 of of ADP american_scientific_journal-522 15 68 the the DET american_scientific_journal-522 15 69 plate plate NOUN american_scientific_journal-522 15 70 . . PUNCT american_scientific_journal-522 16 1 lewinson lewinson NOUN american_scientific_journal-522 17 1 [ [ X american_scientific_journal-522 17 2 5 5 NUM american_scientific_journal-522 17 3 ] ] PUNCT american_scientific_journal-522 17 4 , , PUNCT american_scientific_journal-522 17 5 murthy murthy ADJ american_scientific_journal-522 18 1 [ [ X american_scientific_journal-522 18 2 6 6 NUM american_scientific_journal-522 18 3 ] ] PUNCT american_scientific_journal-522 18 4 , , PUNCT american_scientific_journal-522 18 5 and and CCONJ american_scientific_journal-522 18 6 reddy reddy PROPN american_scientific_journal-522 18 7 [ [ X american_scientific_journal-522 18 8 7 7 NUM american_scientific_journal-522 18 9 ] ] PUNCT american_scientific_journal-522 18 10 presented present VERB american_scientific_journal-522 18 11 a a DET american_scientific_journal-522 18 12 new new ADJ american_scientific_journal-522 18 13 higher high ADJ american_scientific_journal-522 18 14 order order NOUN american_scientific_journal-522 18 15 shear shear NOUN american_scientific_journal-522 18 16 deformation deformation NOUN american_scientific_journal-522 18 17 theories theory NOUN american_scientific_journal-522 18 18 considered consider VERB american_scientific_journal-522 18 19 as as ADP american_scientific_journal-522 18 20 an an DET american_scientific_journal-522 18 21 extension extension NOUN american_scientific_journal-522 18 22 of of ADP american_scientific_journal-522 18 23 hencky hencky PROPN american_scientific_journal-522 18 24 ’s ’s PART american_scientific_journal-522 18 25 theory theory NOUN american_scientific_journal-522 18 26 , , PUNCT american_scientific_journal-522 18 27 which which PRON american_scientific_journal-522 18 28 include include VERB american_scientific_journal-522 18 29 a a DET american_scientific_journal-522 18 30 realistic realistic ADJ american_scientific_journal-522 18 31 displacement displacement ADJ american_scientific_journal-522 18 32 field field NOUN american_scientific_journal-522 18 33 satisfying satisfy VERB american_scientific_journal-522 18 34 the the DET american_scientific_journal-522 18 35 conditions condition NOUN american_scientific_journal-522 18 36 of of ADP american_scientific_journal-522 18 37 zero zero NUM american_scientific_journal-522 18 38 transverse transverse NOUN american_scientific_journal-522 18 39 shearstress shearstress NOUN american_scientific_journal-522 18 40 and/or and/or CCONJ american_scientific_journal-522 18 41 strains strain NOUN american_scientific_journal-522 18 42 , , PUNCT american_scientific_journal-522 18 43 known know VERB american_scientific_journal-522 18 44 as as ADP american_scientific_journal-522 18 45 reddy reddy PROPN american_scientific_journal-522 18 46 ’s ’s PART american_scientific_journal-522 18 47 third third ADJ american_scientific_journal-522 18 48 - - PUNCT american_scientific_journal-522 18 49 order order NOUN american_scientific_journal-522 18 50 theory theory NOUN american_scientific_journal-522 18 51 . . PUNCT american_scientific_journal-522 19 1 this this DET american_scientific_journal-522 19 2 model model NOUN american_scientific_journal-522 19 3 requires require VERB american_scientific_journal-522 19 4 c1 c1 PROPN american_scientific_journal-522 19 5 inter inter PROPN american_scientific_journal-522 19 6 element element PROPN american_scientific_journal-522 19 7 continuity continuity NOUN american_scientific_journal-522 19 8 requirement requirement NOUN american_scientific_journal-522 19 9 . . PUNCT american_scientific_journal-522 20 1 phan phan PROPN american_scientific_journal-522 20 2 and and CCONJ american_scientific_journal-522 20 3 reddy reddy PROPN american_scientific_journal-522 20 4 developed develop VERB american_scientific_journal-522 20 5 a a DET american_scientific_journal-522 20 6 non non ADJ american_scientific_journal-522 20 7 conforming conform VERB american_scientific_journal-522 20 8 rectangular rectangular ADJ american_scientific_journal-522 20 9 element element NOUN american_scientific_journal-522 20 10 with with ADP american_scientific_journal-522 20 11 seven seven NUM american_scientific_journal-522 20 12 degrees degree NOUN american_scientific_journal-522 20 13 of of ADP american_scientific_journal-522 20 14 freedom freedom NOUN american_scientific_journal-522 20 15 per per ADP american_scientific_journal-522 20 16 node node NOUN american_scientific_journal-522 20 17 , , PUNCT american_scientific_journal-522 20 18 based base VERB american_scientific_journal-522 20 19 on on ADP american_scientific_journal-522 20 20 c1 c1 PROPN american_scientific_journal-522 20 21 reddy reddy PROPN american_scientific_journal-522 20 22 ’s ’s PART american_scientific_journal-522 20 23 third third ADJ american_scientific_journal-522 20 24 order order NOUN american_scientific_journal-522 20 25 theory theory NOUN american_scientific_journal-522 20 26 to to PART american_scientific_journal-522 20 27 analyze analyze VERB american_scientific_journal-522 20 28 laminated laminated ADJ american_scientific_journal-522 20 29 composites composite NOUN american_scientific_journal-522 20 30 plates plate NOUN american_scientific_journal-522 20 31 . . PUNCT american_scientific_journal-522 21 1 kant kant PROPN american_scientific_journal-522 21 2 and and CCONJ american_scientific_journal-522 21 3 his his PRON american_scientific_journal-522 21 4 colleagues colleague NOUN american_scientific_journal-522 22 1 [ [ X american_scientific_journal-522 22 2 8 8 NUM american_scientific_journal-522 22 3 ] ] PUNCT american_scientific_journal-522 22 4 investigate investigate VERB american_scientific_journal-522 22 5 the the DET american_scientific_journal-522 22 6 free free ADJ american_scientific_journal-522 22 7 and and CCONJ american_scientific_journal-522 22 8 transient transient ADJ american_scientific_journal-522 22 9 vibration vibration NOUN american_scientific_journal-522 22 10 analysis analysis NOUN american_scientific_journal-522 22 11 of of ADP american_scientific_journal-522 22 12 composites composite NOUN american_scientific_journal-522 22 13 and and CCONJ american_scientific_journal-522 22 14 sandwich sandwich NOUN american_scientific_journal-522 22 15 plates plate NOUN american_scientific_journal-522 22 16 based base VERB american_scientific_journal-522 22 17 on on ADP american_scientific_journal-522 22 18 a a DET american_scientific_journal-522 22 19 refined refined ADJ american_scientific_journal-522 22 20 theory theory NOUN american_scientific_journal-522 22 21 by by ADP american_scientific_journal-522 22 22 using use VERB american_scientific_journal-522 22 23 the the DET american_scientific_journal-522 22 24 finite finite ADJ american_scientific_journal-522 22 25 element element NOUN american_scientific_journal-522 22 26 method method NOUN american_scientific_journal-522 22 27 and and CCONJ american_scientific_journal-522 22 28 analytical analytical ADJ american_scientific_journal-522 22 29 solution solution NOUN american_scientific_journal-522 22 30 . . PUNCT american_scientific_journal-522 23 1 the the DET american_scientific_journal-522 23 2 authors author NOUN american_scientific_journal-522 23 3 in in ADP american_scientific_journal-522 23 4 [ [ X american_scientific_journal-522 23 5 9,10 9,10 NUM american_scientific_journal-522 23 6 ] ] PUNCT american_scientific_journal-522 23 7 investigate investigate VERB american_scientific_journal-522 23 8 the the DET american_scientific_journal-522 23 9 free free ADJ american_scientific_journal-522 23 10 vibration vibration NOUN american_scientific_journal-522 23 11 and and CCONJ american_scientific_journal-522 23 12 transient transient ADJ american_scientific_journal-522 23 13 response response NOUN american_scientific_journal-522 23 14 of of ADP american_scientific_journal-522 23 15 composite composite ADJ american_scientific_journal-522 23 16 sandwich sandwich NOUN american_scientific_journal-522 23 17 plates plate NOUN american_scientific_journal-522 23 18 by by ADP american_scientific_journal-522 23 19 using use VERB american_scientific_journal-522 23 20 two two NUM american_scientific_journal-522 23 21 c0 c0 NOUN american_scientific_journal-522 23 22 assumed assume VERB american_scientific_journal-522 23 23 strain strain PROPN american_scientific_journal-522 23 24 finite finite PROPN american_scientific_journal-522 23 25 element element NOUN american_scientific_journal-522 23 26 based base VERB american_scientific_journal-522 23 27 on on ADP american_scientific_journal-522 23 28 reddy reddy PROPN american_scientific_journal-522 23 29 ’s ’s PART american_scientific_journal-522 23 30 third third ADJ american_scientific_journal-522 23 31 - - PUNCT american_scientific_journal-522 23 32 order order NOUN american_scientific_journal-522 23 33 theory theory NOUN american_scientific_journal-522 23 34 . . PUNCT american_scientific_journal-522 24 1 sheikh sheikh NOUN american_scientific_journal-522 24 2 and and CCONJ american_scientific_journal-522 24 3 chakrabarti chakrabarti PROPN american_scientific_journal-522 25 1 [ [ X american_scientific_journal-522 25 2 11 11 NUM american_scientific_journal-522 25 3 ] ] PUNCT american_scientific_journal-522 25 4 used use VERB american_scientific_journal-522 25 5 a a DET american_scientific_journal-522 25 6 triangular triangular NOUN american_scientific_journal-522 25 7 element element NOUN american_scientific_journal-522 25 8 based base VERB american_scientific_journal-522 25 9 on on ADP american_scientific_journal-522 25 10 reddy reddy PROPN american_scientific_journal-522 25 11 ’s ’s PART american_scientific_journal-522 25 12 higher high ADJ american_scientific_journal-522 25 13 order order NOUN american_scientific_journal-522 25 14 shear shear ADJ american_scientific_journal-522 25 15 deformation deformation NOUN american_scientific_journal-522 25 16 plate plate NOUN american_scientific_journal-522 25 17 theory theory NOUN american_scientific_journal-522 25 18 . . PUNCT american_scientific_journal-522 26 1 batra batra PROPN american_scientific_journal-522 26 2 and and CCONJ american_scientific_journal-522 26 3 his his PRON american_scientific_journal-522 26 4 colleagues colleague NOUN american_scientific_journal-522 26 5 . . PUNCT american_scientific_journal-522 27 1 [ [ X american_scientific_journal-522 27 2 12 12 NUM american_scientific_journal-522 27 3 ] ] PUNCT american_scientific_journal-522 27 4 used use VERB american_scientific_journal-522 27 5 a a DET american_scientific_journal-522 27 6 hsdt hsdt NOUN american_scientific_journal-522 27 7 and and CCONJ american_scientific_journal-522 27 8 the the DET american_scientific_journal-522 27 9 finite finite ADJ american_scientific_journal-522 27 10 element element NOUN american_scientific_journal-522 27 11 method method NOUN american_scientific_journal-522 27 12 to to PART american_scientific_journal-522 27 13 analyze analyze VERB american_scientific_journal-522 27 14 free free ADJ american_scientific_journal-522 27 15 vibrations vibration NOUN american_scientific_journal-522 27 16 and and CCONJ american_scientific_journal-522 27 17 stress stress NOUN american_scientific_journal-522 27 18 distribution distribution NOUN american_scientific_journal-522 27 19 in in ADP american_scientific_journal-522 27 20 tick tick NOUN american_scientific_journal-522 27 21 isotropic isotropic NOUN american_scientific_journal-522 27 22 plate plate NOUN american_scientific_journal-522 27 23 . . PUNCT american_scientific_journal-522 28 1 kulkarni kulkarni PROPN american_scientific_journal-522 28 2 and and CCONJ american_scientific_journal-522 28 3 kapuria kapuria PROPN american_scientific_journal-522 29 1 [ [ X american_scientific_journal-522 29 2 13 13 NUM american_scientific_journal-522 29 3 ] ] PUNCT american_scientific_journal-522 29 4 used use VERB american_scientific_journal-522 29 5 a a DET american_scientific_journal-522 29 6 discrete discrete ADJ american_scientific_journal-522 29 7 kirchoff kirchoff NOUN american_scientific_journal-522 29 8 quadrilateral quadrilateral ADJ american_scientific_journal-522 29 9 element element NOUN american_scientific_journal-522 29 10 based base VERB american_scientific_journal-522 29 11 on on ADP american_scientific_journal-522 29 12 the the DET american_scientific_journal-522 29 13 third third ADJ american_scientific_journal-522 29 14 order order NOUN american_scientific_journal-522 29 15 theory theory NOUN american_scientific_journal-522 29 16 for for ADP american_scientific_journal-522 29 17 composite composite ADJ american_scientific_journal-522 29 18 plates plate NOUN american_scientific_journal-522 29 19 . . PUNCT american_scientific_journal-522 30 1 because because SCONJ american_scientific_journal-522 30 2 reddy reddy PROPN american_scientific_journal-522 30 3 ’s ’s PART american_scientific_journal-522 30 4 third third ADJ american_scientific_journal-522 30 5 - - PUNCT american_scientific_journal-522 30 6 order order NOUN american_scientific_journal-522 30 7 theory theory NOUN american_scientific_journal-522 30 8 requires require VERB american_scientific_journal-522 30 9 inter inter ADJ american_scientific_journal-522 30 10 element element NOUN american_scientific_journal-522 30 11 c1 c1 PROPN american_scientific_journal-522 30 12 continuity continuity NOUN american_scientific_journal-522 30 13 on on ADP american_scientific_journal-522 30 14 the the DET american_scientific_journal-522 30 15 transverse transverse NOUN american_scientific_journal-522 30 16 displacement displacement NOUN american_scientific_journal-522 30 17 . . PUNCT american_scientific_journal-522 31 1 the the DET american_scientific_journal-522 31 2 conclusion conclusion NOUN american_scientific_journal-522 31 3 can can AUX american_scientific_journal-522 31 4 be be AUX american_scientific_journal-522 31 5 made make VERB american_scientific_journal-522 31 6 from from ADP american_scientific_journal-522 31 7 the the DET american_scientific_journal-522 31 8 literature literature NOUN american_scientific_journal-522 31 9 review review NOUN american_scientific_journal-522 31 10 , , PUNCT american_scientific_journal-522 31 11 that that SCONJ american_scientific_journal-522 31 12 a a DET american_scientific_journal-522 31 13 very very ADV american_scientific_journal-522 31 14 few few ADJ american_scientific_journal-522 31 15 conforming conforming NOUN american_scientific_journal-522 31 16 element element NOUN american_scientific_journal-522 31 17 based base VERB american_scientific_journal-522 31 18 on on ADP american_scientific_journal-522 31 19 this this DET american_scientific_journal-522 31 20 plate plate NOUN american_scientific_journal-522 31 21 theory theory NOUN american_scientific_journal-522 31 22 are be AUX american_scientific_journal-522 31 23 developed develop VERB american_scientific_journal-522 31 24 . . PUNCT american_scientific_journal-522 32 1 to to PART american_scientific_journal-522 32 2 overcome overcome VERB american_scientific_journal-522 32 3 this this DET american_scientific_journal-522 32 4 hindrance hindrance NOUN american_scientific_journal-522 32 5 , , PUNCT american_scientific_journal-522 32 6 the the DET american_scientific_journal-522 32 7 hierarchical hierarchical ADJ american_scientific_journal-522 32 8 finite finite ADJ american_scientific_journal-522 32 9 element element NOUN american_scientific_journal-522 32 10 method method NOUN american_scientific_journal-522 32 11 can can AUX american_scientific_journal-522 32 12 be be AUX american_scientific_journal-522 32 13 used use VERB american_scientific_journal-522 32 14 . . PUNCT american_scientific_journal-522 33 1 in in ADP american_scientific_journal-522 33 2 the the DET american_scientific_journal-522 33 3 hierarchical hierarchical ADJ american_scientific_journal-522 33 4 finite finite NOUN american_scientific_journal-522 33 5 element element NOUN american_scientific_journal-522 33 6 method method NOUN american_scientific_journal-522 33 7 the the DET american_scientific_journal-522 33 8 mesh mesh NOUN american_scientific_journal-522 33 9 keeps keep VERB american_scientific_journal-522 33 10 unchanged unchanged ADJ american_scientific_journal-522 33 11 and and CCONJ american_scientific_journal-522 33 12 the the DET american_scientific_journal-522 33 13 polynomial polynomial ADJ american_scientific_journal-522 33 14 degree degree NOUN american_scientific_journal-522 33 15 of of ADP american_scientific_journal-522 33 16 the the DET american_scientific_journal-522 33 17 shape shape NOUN american_scientific_journal-522 33 18 functions function NOUN american_scientific_journal-522 33 19 is be AUX american_scientific_journal-522 33 20 increased increase VERB american_scientific_journal-522 33 21 . . PUNCT american_scientific_journal-522 34 1 see see VERB american_scientific_journal-522 34 2 for for ADP american_scientific_journal-522 34 3 instance instance NOUN american_scientific_journal-522 34 4 szabo szabo PROPN american_scientific_journal-522 34 5 and and CCONJ american_scientific_journal-522 34 6 sahrmann sahrmann NOUN american_scientific_journal-522 35 1 [ [ X american_scientific_journal-522 35 2 14 14 NUM american_scientific_journal-522 35 3 ] ] PUNCT american_scientific_journal-522 35 4 , , PUNCT american_scientific_journal-522 35 5 szabo szabo PROPN american_scientific_journal-522 35 6 and and CCONJ american_scientific_journal-522 35 7 babuska babuska PROPN american_scientific_journal-522 36 1 [ [ X american_scientific_journal-522 36 2 15 15 NUM american_scientific_journal-522 36 3 ] ] PUNCT american_scientific_journal-522 36 4 and and CCONJ american_scientific_journal-522 36 5 hamza hamza PROPN american_scientific_journal-522 36 6 - - PUNCT american_scientific_journal-522 36 7 cherif cherif PROPN american_scientific_journal-522 36 8 [ [ X american_scientific_journal-522 36 9 16 16 NUM american_scientific_journal-522 36 10 ] ] PUNCT american_scientific_journal-522 36 11 . . PUNCT american_scientific_journal-522 37 1 in in ADP american_scientific_journal-522 37 2 this this DET american_scientific_journal-522 37 3 paper paper NOUN american_scientific_journal-522 37 4 we we PRON american_scientific_journal-522 37 5 address address VERB american_scientific_journal-522 37 6 these these DET american_scientific_journal-522 37 7 above above ADV american_scientific_journal-522 37 8 - - PUNCT american_scientific_journal-522 37 9 mentioned mention VERB american_scientific_journal-522 37 10 points point NOUN american_scientific_journal-522 37 11 . . PUNCT american_scientific_journal-522 38 1 the the DET american_scientific_journal-522 38 2 new new ADJ american_scientific_journal-522 38 3 approach approach NOUN american_scientific_journal-522 38 4 with with ADP american_scientific_journal-522 38 5 hierarchical hierarchical ADJ american_scientific_journal-522 38 6 finite finite ADJ american_scientific_journal-522 38 7 element element NOUN american_scientific_journal-522 38 8 method method NOUN american_scientific_journal-522 38 9 is be AUX american_scientific_journal-522 38 10 formulated formulate VERB american_scientific_journal-522 38 11 for for ADP american_scientific_journal-522 38 12 thick thick ADJ american_scientific_journal-522 38 13 plates plate NOUN american_scientific_journal-522 38 14 vibration vibration NOUN american_scientific_journal-522 38 15 analysis analysis NOUN american_scientific_journal-522 38 16 . . PUNCT american_scientific_journal-522 39 1 a a DET american_scientific_journal-522 39 2 new new ADJ american_scientific_journal-522 39 3 hierarchical hierarchical ADJ american_scientific_journal-522 39 4 p p NOUN american_scientific_journal-522 39 5 - - PUNCT american_scientific_journal-522 39 6 element element NOUN american_scientific_journal-522 39 7 with with ADP american_scientific_journal-522 39 8 six six NUM american_scientific_journal-522 39 9 degrees degree NOUN american_scientific_journal-522 39 10 of of ADP american_scientific_journal-522 39 11 freedom freedom NOUN american_scientific_journal-522 39 12 per per ADP american_scientific_journal-522 39 13 node node NOUN american_scientific_journal-522 39 14 is be AUX american_scientific_journal-522 39 15 developed develop VERB american_scientific_journal-522 39 16 , , PUNCT american_scientific_journal-522 39 17 based base VERB american_scientific_journal-522 39 18 on on ADP american_scientific_journal-522 39 19 the the DET american_scientific_journal-522 39 20 c1 c1 PROPN american_scientific_journal-522 39 21 higher high ADJ american_scientific_journal-522 39 22 order order NOUN american_scientific_journal-522 39 23 shear shear ADJ american_scientific_journal-522 39 24 deformation deformation NOUN american_scientific_journal-522 39 25 theory theory NOUN american_scientific_journal-522 39 26 . . PUNCT american_scientific_journal-522 40 1 the the DET american_scientific_journal-522 40 2 continuity continuity NOUN american_scientific_journal-522 40 3 along along ADP american_scientific_journal-522 40 4 the the DET american_scientific_journal-522 40 5 inter inter ADJ american_scientific_journal-522 40 6 - - ADJ american_scientific_journal-522 40 7 element element ADJ american_scientific_journal-522 40 8 boundary boundary NOUN american_scientific_journal-522 40 9 is be AUX american_scientific_journal-522 40 10 not not PART american_scientific_journal-522 40 11 required require VERB american_scientific_journal-522 40 12 in in ADP american_scientific_journal-522 40 13 the the DET american_scientific_journal-522 40 14 model model NOUN american_scientific_journal-522 40 15 . . PUNCT american_scientific_journal-522 41 1 to to PART american_scientific_journal-522 41 2 demonstrate demonstrate VERB american_scientific_journal-522 41 3 the the DET american_scientific_journal-522 41 4 convergence convergence NOUN american_scientific_journal-522 41 5 and and CCONJ american_scientific_journal-522 41 6 accuracy accuracy NOUN american_scientific_journal-522 41 7 of of ADP american_scientific_journal-522 41 8 the the DET american_scientific_journal-522 41 9 proposed propose VERB american_scientific_journal-522 41 10 method method NOUN american_scientific_journal-522 41 11 , , PUNCT american_scientific_journal-522 41 12 present present ADJ american_scientific_journal-522 41 13 results result NOUN american_scientific_journal-522 41 14 are be AUX american_scientific_journal-522 41 15 compared compare VERB american_scientific_journal-522 41 16 with with ADP american_scientific_journal-522 41 17 existing exist VERB american_scientific_journal-522 41 18 data datum NOUN american_scientific_journal-522 41 19 available available ADJ american_scientific_journal-522 41 20 from from ADP american_scientific_journal-522 41 21 other other ADJ american_scientific_journal-522 41 22 analytical analytical ADJ american_scientific_journal-522 41 23 and and CCONJ american_scientific_journal-522 41 24 numerical numerical ADJ american_scientific_journal-522 41 25 methods method NOUN american_scientific_journal-522 41 26 . . PUNCT american_scientific_journal-522 42 1 then then ADV american_scientific_journal-522 42 2 , , PUNCT american_scientific_journal-522 42 3 natural natural ADJ american_scientific_journal-522 42 4 frequencies frequency NOUN american_scientific_journal-522 42 5 of of ADP american_scientific_journal-522 42 6 rectangular rectangular ADJ american_scientific_journal-522 42 7 plates plate NOUN american_scientific_journal-522 42 8 under under ADP american_scientific_journal-522 42 9 different different ADJ american_scientific_journal-522 42 10 boundary boundary ADJ american_scientific_journal-522 42 11 conditions condition NOUN american_scientific_journal-522 42 12 are be AUX american_scientific_journal-522 42 13 tabulated tabulate VERB american_scientific_journal-522 42 14 for for ADP american_scientific_journal-522 42 15 a a DET american_scientific_journal-522 42 16 wide wide ADJ american_scientific_journal-522 42 17 range range NOUN american_scientific_journal-522 42 18 of of ADP american_scientific_journal-522 42 19 aspect aspect NOUN american_scientific_journal-522 42 20 ratios ratio NOUN american_scientific_journal-522 42 21 and and CCONJ american_scientific_journal-522 42 22 thickness thickness NOUN american_scientific_journal-522 42 23 to to PART american_scientific_journal-522 42 24 length length NOUN american_scientific_journal-522 42 25 ratios ratio NOUN american_scientific_journal-522 42 26 . . PUNCT american_scientific_journal-522 43 1 2 2 X american_scientific_journal-522 43 2 . . X american_scientific_journal-522 43 3 formulation formulation NOUN american_scientific_journal-522 43 4 1.1 1.1 NUM american_scientific_journal-522 43 5 . . PUNCT american_scientific_journal-522 44 1 energy energy NOUN american_scientific_journal-522 44 2 formulation formulation NOUN american_scientific_journal-522 44 3 consider consider VERB american_scientific_journal-522 44 4 an an DET american_scientific_journal-522 44 5 homogeneous homogeneous ADJ american_scientific_journal-522 44 6 , , PUNCT american_scientific_journal-522 44 7 isotropic isotropic ADJ american_scientific_journal-522 44 8 , , PUNCT american_scientific_journal-522 44 9 thick thick ADJ american_scientific_journal-522 44 10 plate plate NOUN american_scientific_journal-522 44 11 bounded bound VERB american_scientific_journal-522 44 12 by by ADP american_scientific_journal-522 44 13 0 0 NUM american_scientific_journal-522 44 14 ≤ ≤ NUM american_scientific_journal-522 44 15 x x PUNCT american_scientific_journal-522 44 16 ≤ ≤ NUM american_scientific_journal-522 44 17 a a PRON american_scientific_journal-522 44 18 , , PUNCT american_scientific_journal-522 44 19 0 0 NUM american_scientific_journal-522 44 20 ≤ ≤ NUM american_scientific_journal-522 44 21 y y PROPN american_scientific_journal-522 44 22 ≤ ≤ NUM american_scientific_journal-522 44 23 b b NOUN american_scientific_journal-522 44 24 , , PUNCT american_scientific_journal-522 44 25 and and CCONJ american_scientific_journal-522 44 26 −h/2 −h/2 PROPN american_scientific_journal-522 44 27 ≤ ≤ PROPN american_scientific_journal-522 44 28 z z NOUN american_scientific_journal-522 44 29 ≤ ≤ NOUN american_scientific_journal-522 44 30 h/2 h/2 NUM american_scientific_journal-522 44 31 , , PUNCT american_scientific_journal-522 44 32 as as ADP american_scientific_journal-522 44 33 show show NOUN american_scientific_journal-522 44 34 in in ADP american_scientific_journal-522 44 35 fig fig NOUN american_scientific_journal-522 44 36 . . PUNCT american_scientific_journal-522 45 1 1 1 X american_scientific_journal-522 45 2 . . X american_scientific_journal-522 45 3 the the DET american_scientific_journal-522 45 4 displacement displacement NOUN american_scientific_journal-522 45 5 of of ADP american_scientific_journal-522 45 6 the the DET american_scientific_journal-522 45 7 plate plate NOUN american_scientific_journal-522 45 8 are be AUX american_scientific_journal-522 45 9 decomposed decompose VERB american_scientific_journal-522 45 10 into into ADP american_scientific_journal-522 45 11 three three NUM american_scientific_journal-522 45 12 orthogonal orthogonal ADJ american_scientific_journal-522 45 13 components component NOUN american_scientific_journal-522 45 14 , , PUNCT american_scientific_journal-522 45 15 u u NOUN american_scientific_journal-522 45 16 , , PUNCT american_scientific_journal-522 45 17 v v NOUN american_scientific_journal-522 45 18 and and CCONJ american_scientific_journal-522 45 19 w w NOUN american_scientific_journal-522 45 20 parallel parallel NOUN american_scientific_journal-522 45 21 to to ADP american_scientific_journal-522 45 22 the the DET american_scientific_journal-522 45 23 xaxis xaxis PROPN american_scientific_journal-522 45 24 , , PUNCT american_scientific_journal-522 45 25 y y NOUN american_scientific_journal-522 45 26 - - PUNCT american_scientific_journal-522 45 27 axis axis NOUN american_scientific_journal-522 45 28 and and CCONJ american_scientific_journal-522 45 29 z z NOUN american_scientific_journal-522 45 30 - - PUNCT american_scientific_journal-522 45 31 axis axis ADJ american_scientific_journal-522 45 32 , , PUNCT american_scientific_journal-522 45 33 respectively respectively ADV american_scientific_journal-522 45 34 . . PUNCT american_scientific_journal-522 46 1 in in ADP american_scientific_journal-522 46 2 accordance accordance NOUN american_scientific_journal-522 46 3 with with ADP american_scientific_journal-522 46 4 the the DET american_scientific_journal-522 46 5 higher high ADJ american_scientific_journal-522 46 6 - - PUNCT american_scientific_journal-522 46 7 order order NOUN american_scientific_journal-522 46 8 shear shear NOUN american_scientific_journal-522 46 9 deformable deformable ADJ american_scientific_journal-522 46 10 theory theory NOUN american_scientific_journal-522 46 11 [ [ X american_scientific_journal-522 46 12 10,11 10,11 NOUN american_scientific_journal-522 46 13 ] ] PUNCT american_scientific_journal-522 46 14 , , PUNCT american_scientific_journal-522 46 15 the the DET american_scientific_journal-522 46 16 displacements displacement NOUN american_scientific_journal-522 46 17 can can AUX american_scientific_journal-522 46 18 be be AUX american_scientific_journal-522 46 19 expressed express VERB american_scientific_journal-522 46 20 as as ADP american_scientific_journal-522 46 21 2 2 NUM american_scientific_journal-522 46 22 american american ADJ american_scientific_journal-522 46 23 scientific scientific ADJ american_scientific_journal-522 46 24 research research NOUN american_scientific_journal-522 46 25 journal journal NOUN american_scientific_journal-522 46 26 for for ADP american_scientific_journal-522 46 27 engineering engineering NOUN american_scientific_journal-522 46 28 , , PUNCT american_scientific_journal-522 46 29 technology technology NOUN american_scientific_journal-522 46 30 , , PUNCT american_scientific_journal-522 46 31 and and CCONJ american_scientific_journal-522 46 32 sciences science NOUN american_scientific_journal-522 46 33 ( ( PUNCT american_scientific_journal-522 46 34 asrjets asrjet NOUN american_scientific_journal-522 46 35 ) ) PUNCT american_scientific_journal-522 46 36 ( ( PUNCT american_scientific_journal-522 46 37 2014 2014 NUM american_scientific_journal-522 46 38 ) ) PUNCT american_scientific_journal-522 46 39 volume volume NOUN american_scientific_journal-522 46 40 9 9 NUM american_scientific_journal-522 46 41 , , PUNCT american_scientific_journal-522 46 42 no no DET american_scientific_journal-522 46 43 1 1 NUM american_scientific_journal-522 46 44 , , PUNCT american_scientific_journal-522 46 45 pp pp ADV american_scientific_journal-522 46 46 1 1 NUM american_scientific_journal-522 46 47 - - SYM american_scientific_journal-522 46 48 19 19 NUM american_scientific_journal-522 46 49 ( ( PUNCT american_scientific_journal-522 46 50 ) ) PUNCT american_scientific_journal-522 46 51 0 0 NUM american_scientific_journal-522 47 1 x x SYM american_scientific_journal-522 47 2 x x X american_scientific_journal-522 47 3 wu wu PROPN american_scientific_journal-522 47 4 z z PROPN american_scientific_journal-522 47 5 θ θ PROPN american_scientific_journal-522 47 6     SPACE american_scientific_journal-522 47 7 θ θ X american_scientific_journal-522 47 8 x x PUNCT american_scientific_journal-522 47 9 f f PROPN american_scientific_journal-522 47 10 z z PROPN american_scientific_journal-522 47 11 ∂ ∂ PROPN american_scientific_journal-522 47 12 = = X american_scientific_journal-522 48 1 − − PROPN american_scientific_journal-522 48 2 + + NOUN american_scientific_journal-522 48 3   NOUN american_scientific_journal-522 48 4 ∂ ∂ NOUN american_scientific_journal-522 48 5   PUNCT american_scientific_journal-522 49 1 ( ( PUNCT american_scientific_journal-522 49 2 ) ) PUNCT american_scientific_journal-522 49 3 0 0 PUNCT american_scientific_journal-522 50 1 y y PROPN american_scientific_journal-522 50 2 wv wv PROPN american_scientific_journal-522 50 3 z z PROPN american_scientific_journal-522 50 4 θ θ PROPN american_scientific_journal-522 50 5     SPACE american_scientific_journal-522 50 6 θyy θyy VERB american_scientific_journal-522 50 7 f f PROPN american_scientific_journal-522 50 8 z z NOUN american_scientific_journal-522 50 9   PROPN american_scientific_journal-522 50 10 ∂ ∂ PROPN american_scientific_journal-522 50 11 = = PUNCT american_scientific_journal-522 51 1 − − PROPN american_scientific_journal-522 52 1 + + NOUN american_scientific_journal-522 52 2   NOUN american_scientific_journal-522 52 3 ∂ ∂ NOUN american_scientific_journal-522 52 4   PUNCT american_scientific_journal-522 53 1 0w= 0w= PROPN american_scientific_journal-522 53 2 w w VERB american_scientific_journal-522 53 3 in in ADP american_scientific_journal-522 53 4 which which PRON american_scientific_journal-522 53 5 ( ( PUNCT american_scientific_journal-522 53 6 ) ) PUNCT american_scientific_journal-522 53 7 3 3 NUM american_scientific_journal-522 53 8 2 2 NUM american_scientific_journal-522 53 9 4 4 NUM american_scientific_journal-522 53 10 3 3 NUM american_scientific_journal-522 53 11 zf zf PROPN american_scientific_journal-522 53 12 z z NOUN american_scientific_journal-522 53 13 h h NOUN american_scientific_journal-522 53 14 = = PUNCT american_scientific_journal-522 53 15 ( ( PUNCT american_scientific_journal-522 53 16 2 2 NUM american_scientific_journal-522 53 17 ) ) PUNCT american_scientific_journal-522 53 18 where where SCONJ american_scientific_journal-522 53 19 w0 w0 PROPN american_scientific_journal-522 53 20 is be AUX american_scientific_journal-522 53 21 the the DET american_scientific_journal-522 53 22 transverse transverse ADJ american_scientific_journal-522 53 23 displacement displacement NOUN american_scientific_journal-522 53 24 of of ADP american_scientific_journal-522 53 25 middle middle ADJ american_scientific_journal-522 53 26 plate plate NOUN american_scientific_journal-522 53 27 components component NOUN american_scientific_journal-522 53 28 and and CCONJ american_scientific_journal-522 53 29 θx θx INTJ american_scientific_journal-522 53 30 , , PUNCT american_scientific_journal-522 53 31 θy θy INTJ american_scientific_journal-522 53 32 are be AUX american_scientific_journal-522 53 33 the the DET american_scientific_journal-522 53 34 rotations rotation NOUN american_scientific_journal-522 53 35 of of ADP american_scientific_journal-522 53 36 the the DET american_scientific_journal-522 53 37 normal normal ADJ american_scientific_journal-522 53 38 to to ADP american_scientific_journal-522 53 39 the the DET american_scientific_journal-522 53 40 middle middle ADJ american_scientific_journal-522 53 41 plane plane NOUN american_scientific_journal-522 53 42 about about ADP american_scientific_journal-522 53 43 the the DET american_scientific_journal-522 53 44 x x NOUN american_scientific_journal-522 53 45 - - NOUN american_scientific_journal-522 53 46 axis axis ADJ american_scientific_journal-522 53 47 and and CCONJ american_scientific_journal-522 53 48 y y NOUN american_scientific_journal-522 53 49 - - PUNCT american_scientific_journal-522 53 50 axis axis NOUN american_scientific_journal-522 53 51 respectively respectively ADV american_scientific_journal-522 53 52 . . PUNCT american_scientific_journal-522 54 1 the the DET american_scientific_journal-522 54 2 linear linear ADJ american_scientific_journal-522 54 3 strain strain NOUN american_scientific_journal-522 54 4 - - PUNCT american_scientific_journal-522 54 5 displacement displacement NOUN american_scientific_journal-522 54 6 relationships relationship NOUN american_scientific_journal-522 54 7 . . PUNCT american_scientific_journal-522 55 1 { { PUNCT american_scientific_journal-522 55 2 } } PUNCT american_scientific_journal-522 55 3 ( ( PUNCT american_scientific_journal-522 55 4 ) ) PUNCT american_scientific_journal-522 55 5 ( ( PUNCT american_scientific_journal-522 55 6 ) ) PUNCT american_scientific_journal-522 55 7 2 2 NUM american_scientific_journal-522 55 8 0 0 NUM american_scientific_journal-522 55 9 2 2 NUM american_scientific_journal-522 55 10 2 2 NUM american_scientific_journal-522 55 11 0 0 NUM american_scientific_journal-522 55 12 20 20 NUM american_scientific_journal-522 55 13 0 0 NUM american_scientific_journal-522 55 14 0 0 NUM american_scientific_journal-522 55 15 0 0 NUM american_scientific_journal-522 55 16 0 0 NUM american_scientific_journal-522 55 17 0 0 NUM american_scientific_journal-522 55 18 0 0 NUM american_scientific_journal-522 55 19 0 0 NUM american_scientific_journal-522 55 20 0 0 NUM american_scientific_journal-522 55 21 00 00 NUM american_scientific_journal-522 55 22 0 0 NUM american_scientific_journal-522 56 1 x x SYM american_scientific_journal-522 56 2 x x X american_scientific_journal-522 57 1 xx xx NUM american_scientific_journal-522 58 1 y y PROPN american_scientific_journal-522 58 2 yy yy INTJ american_scientific_journal-522 58 3 y y PROPN american_scientific_journal-522 58 4 y y PROPN american_scientific_journal-522 58 5 yz yz PROPN american_scientific_journal-522 58 6 xz xz PROPN american_scientific_journal-522 58 7 x x PUNCT american_scientific_journal-522 59 1 x x PUNCT american_scientific_journal-522 59 2 xy xy NOUN american_scientific_journal-522 59 3 y y PROPN american_scientific_journal-522 59 4 x x SYM american_scientific_journal-522 59 5 θ θ NOUN american_scientific_journal-522 59 6 w w PROPN american_scientific_journal-522 59 7 θ θ NOUN american_scientific_journal-522 59 8 x x PUNCT american_scientific_journal-522 59 9 x x NOUN american_scientific_journal-522 59 10 xε xε NUM american_scientific_journal-522 59 11 θ θ PROPN american_scientific_journal-522 59 12 w w PROPN american_scientific_journal-522 59 13 ε ε PROPN american_scientific_journal-522 59 14 w w PROPN american_scientific_journal-522 59 15 wy wy PROPN american_scientific_journal-522 59 16 yθ yθ PROPN american_scientific_journal-522 59 17 θγε θγε NOUN american_scientific_journal-522 59 18 z z PROPN american_scientific_journal-522 59 19     SPACE american_scientific_journal-522 60 1 y y PROPN american_scientific_journal-522 60 2 y y PROPN american_scientific_journal-522 60 3 zγ zγ PROPN american_scientific_journal-522 60 4 w w VERB american_scientific_journal-522 60 5 wθ wθ PROPN american_scientific_journal-522 60 6 θ θ PROPN american_scientific_journal-522 60 7 γ γ X american_scientific_journal-522 60 8 x x PROPN american_scientific_journal-522 60 9 xθ xθ PROPN american_scientific_journal-522 61 1 θ θ PROPN american_scientific_journal-522 61 2 f f PROPN american_scientific_journal-522 61 3 x x SYM american_scientific_journal-522 61 4 y y PROPN american_scientific_journal-522 61 5 z z PROPN american_scientific_journal-522 61 6 f f PROPN american_scientific_journal-522 61 7 z z PROPN american_scientific_journal-522 61 8 ∂ ∂ NOUN american_scientific_journal-522 61 9 ∂ ∂ NUM american_scientific_journal-522 61 10 ∂ ∂ NOUN american_scientific_journal-522 61 11   VERB american_scientific_journal-522 61 12 + + NOUN american_scientific_journal-522 61 13   NOUN american_scientific_journal-522 61 14   NOUN american_scientific_journal-522 61 15   PROPN american_scientific_journal-522 61 16   PROPN american_scientific_journal-522 61 17 ∂ ∂ NOUN american_scientific_journal-522 61 18 ∂ ∂ ADJ american_scientific_journal-522 62 1 ∂ ∂ PROPN american_scientific_journal-522 62 2   VERB american_scientific_journal-522 62 3   ADJ american_scientific_journal-522 62 4   PROPN american_scientific_journal-522 62 5   PUNCT american_scientific_journal-522 62 6   PROPN american_scientific_journal-522 63 1 ∂ ∂ PROPN american_scientific_journal-522 63 2   PROPN american_scientific_journal-522 63 3   ADJ american_scientific_journal-522 63 4   NOUN american_scientific_journal-522 64 1 ∂ ∂ PROPN american_scientific_journal-522 64 2   PROPN american_scientific_journal-522 64 3   PROPN american_scientific_journal-522 64 4   PROPN american_scientific_journal-522 64 5   PROPN american_scientific_journal-522 64 6   PROPN american_scientific_journal-522 64 7 ∂ ∂ AUX american_scientific_journal-522 65 1 ∂ ∂ PROPN american_scientific_journal-522 65 2   PROPN american_scientific_journal-522 65 3   PROPN american_scientific_journal-522 65 4 ∂ ∂ ADJ american_scientific_journal-522 65 5 ∂∂+ ∂∂+ NOUN american_scientific_journal-522 65 6 + + PROPN american_scientific_journal-522 65 7   PROPN american_scientific_journal-522 65 8   PROPN american_scientific_journal-522 65 9   PROPN american_scientific_journal-522 65 10   PROPN american_scientific_journal-522 65 11   PROPN american_scientific_journal-522 65 12   PROPN american_scientific_journal-522 65 13   PROPN american_scientific_journal-522 65 14 = = X american_scientific_journal-522 66 1 = = PUNCT american_scientific_journal-522 67 1 + + CCONJ american_scientific_journal-522 67 2 − − PROPN american_scientific_journal-522 67 3 −∂ −∂ PRON american_scientific_journal-522 67 4 ∂ ∂ VERB american_scientific_journal-522 67 5   PROPN american_scientific_journal-522 67 6   ADP american_scientific_journal-522 67 7   PROPN american_scientific_journal-522 67 8   ADJ american_scientific_journal-522 67 9   PROPN american_scientific_journal-522 67 10   NOUN american_scientific_journal-522 67 11 ∂ ∂ ADJ american_scientific_journal-522 67 12   ADJ american_scientific_journal-522 67 13   ADJ american_scientific_journal-522 67 14   PROPN american_scientific_journal-522 67 15   PROPN american_scientific_journal-522 67 16   PROPN american_scientific_journal-522 67 17   PROPN american_scientific_journal-522 67 18 ∂ ∂ NOUN american_scientific_journal-522 68 1 ∂ ∂ PROPN american_scientific_journal-522 68 2   PROPN american_scientific_journal-522 68 3   PROPN american_scientific_journal-522 68 4   PROPN american_scientific_journal-522 68 5   PROPN american_scientific_journal-522 68 6   PROPN american_scientific_journal-522 68 7   PROPN american_scientific_journal-522 68 8 + + NOUN american_scientific_journal-522 68 9 + + PUNCT american_scientific_journal-522 68 10 ∂ ∂ NUM american_scientific_journal-522 68 11 ∂ ∂ PROPN american_scientific_journal-522 68 12   NOUN american_scientific_journal-522 68 13   PROPN american_scientific_journal-522 68 14   PROPN american_scientific_journal-522 68 15   PROPN american_scientific_journal-522 68 16   PROPN american_scientific_journal-522 68 17   ADJ american_scientific_journal-522 68 18   PUNCT american_scientific_journal-522 68 19   NOUN american_scientific_journal-522 68 20 ∂ ∂ NOUN american_scientific_journal-522 68 21 ∂ ∂ PROPN american_scientific_journal-522 68 22   PROPN american_scientific_journal-522 68 23   PROPN american_scientific_journal-522 68 24   PROPN american_scientific_journal-522 68 25   PROPN american_scientific_journal-522 68 26 + + PROPN american_scientific_journal-522 68 27   NOUN american_scientific_journal-522 68 28   NOUN american_scientific_journal-522 68 29   PROPN american_scientific_journal-522 68 30 ∂ ∂ NOUN american_scientific_journal-522 68 31 ∂ ∂ X american_scientific_journal-522 68 32   PROPN american_scientific_journal-522 68 33 2 2 NUM american_scientific_journal-522 68 34 0 0 NUM american_scientific_journal-522 68 35 0 0 NUM american_scientific_journal-522 68 36 0 0 NUM american_scientific_journal-522 68 37 2y 2y PROPN american_scientific_journal-522 68 38 x x X american_scientific_journal-522 68 39 yθ yθ NOUN american_scientific_journal-522 68 40 y y PROPN american_scientific_journal-522 68 41 θ θ PROPN american_scientific_journal-522 69 1 θ θ X american_scientific_journal-522 69 2 w w X american_scientific_journal-522 69 3 x x PUNCT american_scientific_journal-522 69 4 y y NOUN american_scientific_journal-522 69 5 xy xy NOUN american_scientific_journal-522 69 6   PROPN american_scientific_journal-522 69 7   PROPN american_scientific_journal-522 69 8   PROPN american_scientific_journal-522 69 9   PROPN american_scientific_journal-522 69 10   PROPN american_scientific_journal-522 69 11   PROPN american_scientific_journal-522 69 12 ∂ ∂ PROPN american_scientific_journal-522 69 13   VERB american_scientific_journal-522 69 14 + + ADJ american_scientific_journal-522 69 15   ADJ american_scientific_journal-522 69 16 ∂ ∂ NOUN american_scientific_journal-522 69 17   VERB american_scientific_journal-522 69 18   ADP american_scientific_journal-522 69 19   PROPN american_scientific_journal-522 69 20   ADJ american_scientific_journal-522 69 21   PROPN american_scientific_journal-522 69 22   PROPN american_scientific_journal-522 69 23   PROPN american_scientific_journal-522 69 24   PROPN american_scientific_journal-522 69 25   PROPN american_scientific_journal-522 69 26 ∂ ∂ NOUN american_scientific_journal-522 69 27 ∂ ∂ NUM american_scientific_journal-522 70 1 ∂ ∂ PROPN american_scientific_journal-522 70 2 + + PRON american_scientific_journal-522 70 3 + + ADJ american_scientific_journal-522 70 4   PROPN american_scientific_journal-522 70 5 ∂ ∂ X american_scientific_journal-522 70 6 ∂ ∂ NUM american_scientific_journal-522 70 7 ∂ ∂ DET american_scientific_journal-522 70 8   PROPN american_scientific_journal-522 70 9 ( ( PUNCT american_scientific_journal-522 70 10 3 3 NUM american_scientific_journal-522 70 11 ) ) PUNCT american_scientific_journal-522 70 12 the the DET american_scientific_journal-522 70 13 constitutive constitutive ADJ american_scientific_journal-522 70 14 equations equation NOUN american_scientific_journal-522 70 15 for for ADP american_scientific_journal-522 70 16 linear linear ADJ american_scientific_journal-522 70 17 elastic elastic ADJ american_scientific_journal-522 70 18 isotropic isotropic NOUN american_scientific_journal-522 70 19 material material NOUN american_scientific_journal-522 70 20 are be AUX american_scientific_journal-522 70 21 { { PUNCT american_scientific_journal-522 70 22 σ σ NOUN american_scientific_journal-522 70 23 } } PUNCT american_scientific_journal-522 70 24 = = NOUN american_scientific_journal-522 71 1 [ [ X american_scientific_journal-522 71 2 c]{ε c]{ε PROPN american_scientific_journal-522 71 3 } } PUNCT american_scientific_journal-522 71 4 ( ( PUNCT american_scientific_journal-522 71 5 4 4 NUM american_scientific_journal-522 71 6 ) ) PUNCT american_scientific_journal-522 71 7 in in ADP american_scientific_journal-522 71 8 the the DET american_scientific_journal-522 71 9 case case NOUN american_scientific_journal-522 71 10 of of ADP american_scientific_journal-522 71 11 plane plane NOUN american_scientific_journal-522 71 12 stress stress VERB american_scientific_journal-522 71 13 the the DET american_scientific_journal-522 71 14 stress stress NOUN american_scientific_journal-522 71 15 vector vector NOUN american_scientific_journal-522 71 16 can can AUX american_scientific_journal-522 71 17 be be AUX american_scientific_journal-522 71 18 written write VERB american_scientific_journal-522 71 19 as as ADP american_scientific_journal-522 71 20 { { PUNCT american_scientific_journal-522 71 21 σ σ NOUN american_scientific_journal-522 71 22 } } PUNCT american_scientific_journal-522 71 23 = = PUNCT american_scientific_journal-522 71 24 { { PUNCT american_scientific_journal-522 71 25 σxx σxx NOUN american_scientific_journal-522 71 26 σxx σxx VERB american_scientific_journal-522 71 27 τyz τyz PROPN american_scientific_journal-522 71 28 τxz τxz PROPN american_scientific_journal-522 71 29 τxy τxy PROPN american_scientific_journal-522 71 30 } } PUNCT american_scientific_journal-522 71 31 ( ( PUNCT american_scientific_journal-522 71 32 5 5 NUM american_scientific_journal-522 71 33 ) ) PUNCT american_scientific_journal-522 72 1 where where SCONJ american_scientific_journal-522 72 2 [ [ X american_scientific_journal-522 72 3 c c X american_scientific_journal-522 72 4 ] ] X american_scientific_journal-522 72 5 = = PUNCT american_scientific_journal-522 72 6 ⎣ ⎣ ADJ american_scientific_journal-522 72 7 ⎢ ⎢ NOUN american_scientific_journal-522 72 8 ⎢ ⎢ NOUN american_scientific_journal-522 72 9 ⎢ ⎢ NOUN american_scientific_journal-522 72 10 ⎢ ⎢ NOUN american_scientific_journal-522 72 11 ⎢ ⎢ NOUN american_scientific_journal-522 72 12 ⎢ ⎢ NOUN american_scientific_journal-522 72 13 ⎡ ⎡ NOUN american_scientific_journal-522 72 14 e e NOUN american_scientific_journal-522 72 15 1−ν2 1−ν2 NUM american_scientific_journal-522 72 16 ν ν X american_scientific_journal-522 72 17 e e X american_scientific_journal-522 72 18 1−ν2 1−ν2 NUM american_scientific_journal-522 72 19 0 0 NUM american_scientific_journal-522 72 20 0 0 NUM american_scientific_journal-522 72 21 0 0 NUM american_scientific_journal-522 72 22 ν ν X american_scientific_journal-522 72 23 e e X american_scientific_journal-522 72 24 1−ν2 1−ν2 NUM american_scientific_journal-522 72 25 e e SYM american_scientific_journal-522 72 26 1−ν2 1−ν2 NUM american_scientific_journal-522 72 27 0 0 NUM american_scientific_journal-522 72 28 0 0 NUM american_scientific_journal-522 72 29 0 0 NUM american_scientific_journal-522 72 30 0 0 NUM american_scientific_journal-522 72 31 0 0 NUM american_scientific_journal-522 72 32 e e NOUN american_scientific_journal-522 72 33 2(1+ν 2(1+ν NUM american_scientific_journal-522 72 34 ) ) PUNCT american_scientific_journal-522 72 35 0 0 NUM american_scientific_journal-522 72 36 0 0 NUM american_scientific_journal-522 72 37 0 0 NUM american_scientific_journal-522 72 38 0 0 NUM american_scientific_journal-522 72 39 0 0 NUM american_scientific_journal-522 72 40 e e NOUN american_scientific_journal-522 72 41 2(1+ν 2(1+ν NUM american_scientific_journal-522 72 42 ) ) PUNCT american_scientific_journal-522 72 43 0 0 NUM american_scientific_journal-522 72 44 0 0 NUM american_scientific_journal-522 72 45 0 0 NUM american_scientific_journal-522 72 46 0 0 NUM american_scientific_journal-522 72 47 0 0 NUM american_scientific_journal-522 72 48 e e NOUN american_scientific_journal-522 72 49 2(1+ν 2(1+ν NUM american_scientific_journal-522 72 50 ) ) PUNCT american_scientific_journal-522 72 51 ⎦ ⎦ NOUN american_scientific_journal-522 72 52 ⎥ ⎥ PROPN american_scientific_journal-522 72 53 ⎥ ⎥ PROPN american_scientific_journal-522 72 54 ⎥ ⎥ PROPN american_scientific_journal-522 72 55 ⎥ ⎥ PROPN american_scientific_journal-522 72 56 ⎥ ⎥ PROPN american_scientific_journal-522 72 57 ⎥ ⎥ PROPN american_scientific_journal-522 72 58 ⎤ ⎤ PROPN american_scientific_journal-522 72 59 ( ( PUNCT american_scientific_journal-522 72 60 6 6 NUM american_scientific_journal-522 72 61 ) ) PUNCT american_scientific_journal-522 72 62 ( ( PUNCT american_scientific_journal-522 72 63 1 1 X american_scientific_journal-522 72 64 ) ) PUNCT american_scientific_journal-522 72 65 3 3 NUM american_scientific_journal-522 72 66 american american PROPN american_scientific_journal-522 72 67 scientific scientific ADJ american_scientific_journal-522 72 68 research research NOUN american_scientific_journal-522 72 69 journal journal NOUN american_scientific_journal-522 72 70 for for ADP american_scientific_journal-522 72 71 engineering engineering NOUN american_scientific_journal-522 72 72 , , PUNCT american_scientific_journal-522 72 73 technology technology NOUN american_scientific_journal-522 72 74 , , PUNCT american_scientific_journal-522 72 75 and and CCONJ american_scientific_journal-522 72 76 sciences science NOUN american_scientific_journal-522 72 77 ( ( PUNCT american_scientific_journal-522 72 78 asrjets asrjet NOUN american_scientific_journal-522 72 79 ) ) PUNCT american_scientific_journal-522 72 80 ( ( PUNCT american_scientific_journal-522 72 81 2014 2014 NUM american_scientific_journal-522 72 82 ) ) PUNCT american_scientific_journal-522 72 83 volume volume NOUN american_scientific_journal-522 72 84 9 9 NUM american_scientific_journal-522 72 85 , , PUNCT american_scientific_journal-522 72 86 no no DET american_scientific_journal-522 72 87 1 1 NUM american_scientific_journal-522 72 88 , , PUNCT american_scientific_journal-522 72 89 pp pp ADV american_scientific_journal-522 72 90 1 1 NUM american_scientific_journal-522 72 91 - - SYM american_scientific_journal-522 72 92 19 19 NUM american_scientific_journal-522 72 93 here here ADV american_scientific_journal-522 72 94 ci ci PROPN american_scientific_journal-522 72 95 , , PUNCT american_scientific_journal-522 72 96 j j PROPN american_scientific_journal-522 72 97 are be AUX american_scientific_journal-522 72 98 the the DET american_scientific_journal-522 72 99 material material ADJ american_scientific_journal-522 72 100 property property NOUN american_scientific_journal-522 72 101 coefficients coefficient NOUN american_scientific_journal-522 72 102 , , PUNCT american_scientific_journal-522 72 103 in in ADP american_scientific_journal-522 72 104 which which PRON american_scientific_journal-522 72 105 e e NOUN american_scientific_journal-522 72 106 , , PUNCT american_scientific_journal-522 72 107 and and CCONJ american_scientific_journal-522 72 108 v v X american_scientific_journal-522 72 109 are be AUX american_scientific_journal-522 72 110 the the DET american_scientific_journal-522 72 111 young young ADJ american_scientific_journal-522 72 112 ’s ’s PART american_scientific_journal-522 72 113 modulus modulus NOUN american_scientific_journal-522 72 114 and and CCONJ american_scientific_journal-522 72 115 , , PUNCT american_scientific_journal-522 72 116 poisson poisson PROPN american_scientific_journal-522 72 117 ’s ’s PART american_scientific_journal-522 72 118 ratio ratio NOUN american_scientific_journal-522 72 119 , , PUNCT american_scientific_journal-522 72 120 respectively respectively ADV american_scientific_journal-522 72 121 . . PUNCT american_scientific_journal-522 73 1 the the DET american_scientific_journal-522 73 2 kinetic kinetic ADJ american_scientific_journal-522 73 3 energy energy NOUN american_scientific_journal-522 73 4 of of ADP american_scientific_journal-522 73 5 a a DET american_scientific_journal-522 73 6 bending bending NOUN american_scientific_journal-522 73 7 vibrating vibrate VERB american_scientific_journal-522 73 8 thick thick ADJ american_scientific_journal-522 73 9 plate plate NOUN american_scientific_journal-522 73 10 is be AUX american_scientific_journal-522 73 11 given give VERB american_scientific_journal-522 73 12 by by ADP american_scientific_journal-522 73 13 21 21 NUM american_scientific_journal-522 73 14 1 1 NUM american_scientific_journal-522 73 15 20 20 NUM american_scientific_journal-522 73 16 0 0 NUM american_scientific_journal-522 73 17 2 2 NUM american_scientific_journal-522 73 18 0 0 NUM american_scientific_journal-522 73 19 0 0 NUM american_scientific_journal-522 73 20 2 2 NUM american_scientific_journal-522 73 21 2 2 NUM american_scientific_journal-522 73 22 20 20 NUM american_scientific_journal-522 73 23 0 0 NUM american_scientific_journal-522 73 24 02 02 NUM american_scientific_journal-522 73 25 1 1 NUM american_scientific_journal-522 73 26 1 1 NUM american_scientific_journal-522 73 27 2 2 NUM american_scientific_journal-522 73 28 2 2 NUM american_scientific_journal-522 73 29 1 1 NUM american_scientific_journal-522 73 30 2 2 NUM american_scientific_journal-522 73 31 d d NOUN american_scientific_journal-522 74 1 d d X american_scientific_journal-522 75 1 x x X american_scientific_journal-522 76 1 f f NOUN american_scientific_journal-522 76 2 x x SYM american_scientific_journal-522 77 1 d d PROPN american_scientific_journal-522 77 2 d d X american_scientific_journal-522 77 3 y y PROPN american_scientific_journal-522 77 4 f f PROPN american_scientific_journal-522 77 5 y y PROPN american_scientific_journal-522 77 6 a a PROPN american_scientific_journal-522 77 7 w w PROPN american_scientific_journal-522 77 8 wec wec PROPN american_scientific_journal-522 77 9 a a DET american_scientific_journal-522 77 10 b b PROPN american_scientific_journal-522 77 11 a a PRON american_scientific_journal-522 77 12 a a DET american_scientific_journal-522 77 13 w w NOUN american_scientific_journal-522 77 14 w w PROPN american_scientific_journal-522 77 15 w w PROPN american_scientific_journal-522 77 16 d d PROPN american_scientific_journal-522 77 17 d d PROPN american_scientific_journal-522 77 18 a a DET american_scientific_journal-522 77 19 a a DET american_scientific_journal-522 77 20 ρ ρ PROPN american_scientific_journal-522 77 21 ρ ρ NUM american_scientific_journal-522 77 22 θ θ PROPN american_scientific_journal-522 77 23 ρ ρ NOUN american_scientific_journal-522 77 24 θ θ X american_scientific_journal-522 77 25 ξ ξ X american_scientific_journal-522 77 26 ξ ξ X american_scientific_journal-522 77 27 ρ ρ PROPN american_scientific_journal-522 77 28 ρ ρ NUM american_scientific_journal-522 77 29 θ θ PROPN american_scientific_journal-522 77 30 ρ ρ NUM american_scientific_journal-522 77 31 θ θ PROPN american_scientific_journal-522 77 32 ρ ρ PROPN american_scientific_journal-522 77 33 ξ ξ PROPN american_scientific_journal-522 77 34 η η PROPN american_scientific_journal-522 77 35 η η PROPN american_scientific_journal-522 77 36 η η PROPN american_scientific_journal-522 77 37   PROPN american_scientific_journal-522 77 38   PROPN american_scientific_journal-522 77 39 ∂ ∂ NUM american_scientific_journal-522 77 40   NOUN american_scientific_journal-522 77 41 ∂ ∂ NOUN american_scientific_journal-522 78 1 = = PUNCT american_scientific_journal-522 79 1 + + PUNCT american_scientific_journal-522 79 2 + + ADJ american_scientific_journal-522 79 3   ADJ american_scientific_journal-522 79 4   NOUN american_scientific_journal-522 79 5 ∂ ∂ PUNCT american_scientific_journal-522 79 6 ∂ ∂ ADJ american_scientific_journal-522 79 7   ADP american_scientific_journal-522 79 8   PROPN american_scientific_journal-522 79 9 ∂ ∂ NUM american_scientific_journal-522 79 10   NOUN american_scientific_journal-522 79 11 ∂ ∂ NOUN american_scientific_journal-522 80 1 + + CCONJ american_scientific_journal-522 80 2 + + PUNCT american_scientific_journal-522 80 3 + + CCONJ american_scientific_journal-522 80 4 + + CCONJ american_scientific_journal-522 80 5   ADJ american_scientific_journal-522 80 6 ∂ ∂ PUNCT american_scientific_journal-522 80 7 ∂ ∂ VERB american_scientific_journal-522 80 8   PUNCT american_scientific_journal-522 81 1   PRON american_scientific_journal-522 81 2 ∫ ∫ PROPN american_scientific_journal-522 81 3 ∫ ∫ PROPN american_scientific_journal-522 81 4   NOUN american_scientific_journal-522 81 5   NOUN american_scientific_journal-522 81 6   NOUN american_scientific_journal-522 81 7   NOUN american_scientific_journal-522 81 8   NOUN american_scientific_journal-522 81 9   NOUN american_scientific_journal-522 81 10   NOUN american_scientific_journal-522 81 11   NOUN american_scientific_journal-522 81 12   NOUN american_scientific_journal-522 81 13 ( ( PUNCT american_scientific_journal-522 81 14 7 7 NUM american_scientific_journal-522 81 15 ) ) PUNCT american_scientific_journal-522 81 16 where where SCONJ american_scientific_journal-522 81 17 ρ ρ PROPN american_scientific_journal-522 81 18 is be AUX american_scientific_journal-522 81 19 the the DET american_scientific_journal-522 81 20 mass mass ADJ american_scientific_journal-522 81 21 density density NOUN american_scientific_journal-522 81 22 per per ADP american_scientific_journal-522 81 23 unit unit NOUN american_scientific_journal-522 81 24 volume volume NOUN american_scientific_journal-522 81 25 . . PUNCT american_scientific_journal-522 81 26 / / SYM american_scientific_journal-522 81 27 2 2 NUM american_scientific_journal-522 81 28 / / SYM american_scientific_journal-522 81 29 2 2 NUM american_scientific_journal-522 81 30 , , PUNCT american_scientific_journal-522 81 31 h h NOUN american_scientific_journal-522 81 32 a a DET american_scientific_journal-522 81 33 h h NOUN american_scientific_journal-522 81 34 dzρ dzρ NOUN american_scientific_journal-522 81 35 ρ ρ NOUN american_scientific_journal-522 81 36 − − PROPN american_scientific_journal-522 81 37 = = SYM american_scientific_journal-522 81 38 ∫ ∫ PROPN american_scientific_journal-522 81 39 ( ( PUNCT american_scientific_journal-522 81 40 ) ) PUNCT american_scientific_journal-522 81 41 / / SYM american_scientific_journal-522 81 42 2 2 NUM american_scientific_journal-522 81 43 2 2 NUM american_scientific_journal-522 81 44 / / SYM american_scientific_journal-522 81 45 2 2 NUM american_scientific_journal-522 81 46 , , PUNCT american_scientific_journal-522 81 47 h h NOUN american_scientific_journal-522 82 1 d d NOUN american_scientific_journal-522 82 2 h h NOUN american_scientific_journal-522 83 1 f f PROPN american_scientific_journal-522 83 2 z z PROPN american_scientific_journal-522 83 3 dzρ dzρ PROPN american_scientific_journal-522 83 4 ρ ρ NOUN american_scientific_journal-522 83 5 − − PROPN american_scientific_journal-522 84 1 = = SYM american_scientific_journal-522 84 2 ∫ ∫ PROPN american_scientific_journal-522 84 3 ( ( PUNCT american_scientific_journal-522 84 4 ) ) PUNCT american_scientific_journal-522 84 5 ( ( PUNCT american_scientific_journal-522 84 6 ) ) PUNCT american_scientific_journal-522 84 7 ( ( PUNCT american_scientific_journal-522 84 8 ) ) PUNCT american_scientific_journal-522 84 9 / / SYM american_scientific_journal-522 84 10 2 2 NUM american_scientific_journal-522 84 11 2 2 NUM american_scientific_journal-522 84 12 2 2 NUM american_scientific_journal-522 84 13 / / SYM american_scientific_journal-522 84 14 2 2 NUM american_scientific_journal-522 84 15 2 2 NUM american_scientific_journal-522 84 16 h h NOUN american_scientific_journal-522 84 17 f f NOUN american_scientific_journal-522 84 18 h h NOUN american_scientific_journal-522 85 1 f f PROPN american_scientific_journal-522 85 2 z z NOUN american_scientific_journal-522 85 3 z z PROPN american_scientific_journal-522 86 1 f f PROPN american_scientific_journal-522 86 2 z z PROPN american_scientific_journal-522 86 3 z z PROPN american_scientific_journal-522 86 4 dzρ dzρ NOUN american_scientific_journal-522 86 5 ρ ρ NOUN american_scientific_journal-522 87 1 − − PROPN american_scientific_journal-522 87 2 = = PUNCT american_scientific_journal-522 88 1 − − PROPN american_scientific_journal-522 88 2 + + NUM american_scientific_journal-522 88 3 ∫ ∫ PROPN american_scientific_journal-522 88 4 the the DET american_scientific_journal-522 88 5 strain strain ADJ american_scientific_journal-522 88 6 energy energy NOUN american_scientific_journal-522 88 7 of of ADP american_scientific_journal-522 88 8 a a DET american_scientific_journal-522 88 9 thick thick ADJ american_scientific_journal-522 88 10 plate plate NOUN american_scientific_journal-522 88 11 is be AUX american_scientific_journal-522 88 12 expressed express VERB american_scientific_journal-522 88 13 as as ADP american_scientific_journal-522 88 14 2 2 NUM american_scientific_journal-522 88 15 21 21 NUM american_scientific_journal-522 88 16 1 1 NUM american_scientific_journal-522 88 17 2 2 NUM american_scientific_journal-522 88 18 2 2 NUM american_scientific_journal-522 88 19 2 2 NUM american_scientific_journal-522 88 20 2 2 NUM american_scientific_journal-522 88 21 0 0 NUM american_scientific_journal-522 88 22 0 0 NUM american_scientific_journal-522 88 23 0 0 NUM american_scientific_journal-522 88 24 011 011 NUM american_scientific_journal-522 88 25 11 11 NUM american_scientific_journal-522 88 26 11 11 NUM american_scientific_journal-522 88 27 11 11 NUM american_scientific_journal-522 88 28 4 4 NUM american_scientific_journal-522 88 29 2 2 NUM american_scientific_journal-522 88 30 4 4 NUM american_scientific_journal-522 88 31 2 2 NUM american_scientific_journal-522 88 32 3 3 NUM american_scientific_journal-522 88 33 2 2 NUM american_scientific_journal-522 88 34 3 3 NUM american_scientific_journal-522 88 35 2 2 NUM american_scientific_journal-522 88 36 0 0 NUM american_scientific_journal-522 88 37 0 0 NUM american_scientific_journal-522 88 38 22 22 NUM american_scientific_journal-522 88 39 2 2 NUM american_scientific_journal-522 88 40 2 2 NUM american_scientific_journal-522 88 41 2 2 NUM american_scientific_journal-522 88 42 0 0 NUM american_scientific_journal-522 88 43 0 0 NUM american_scientific_journal-522 88 44 011 011 NUM american_scientific_journal-522 88 45 11 11 NUM american_scientific_journal-522 88 46 12 12 NUM american_scientific_journal-522 88 47 12 12 NUM american_scientific_journal-522 88 48 2 2 NUM american_scientific_journal-522 88 49 2 2 NUM american_scientific_journal-522 88 50 2 2 NUM american_scientific_journal-522 88 51 2 2 NUM american_scientific_journal-522 88 52 2 2 NUM american_scientific_journal-522 88 53 2 2 NUM american_scientific_journal-522 88 54 2 2 NUM american_scientific_journal-522 88 55 2 2 NUM american_scientific_journal-522 88 56 2 2 NUM american_scientific_journal-522 88 57 21 21 NUM american_scientific_journal-522 88 58 2 2 NUM american_scientific_journal-522 88 59 2 2 NUM american_scientific_journal-522 88 60 2 2 NUM american_scientific_journal-522 88 61 yx yx NOUN american_scientific_journal-522 88 62 yx yx NOUN american_scientific_journal-522 88 63 x x PROPN american_scientific_journal-522 89 1 w w PROPN american_scientific_journal-522 89 2 w w PROPN american_scientific_journal-522 89 3 w w PROPN american_scientific_journal-522 89 4 wd wd PROPN american_scientific_journal-522 89 5 d d X american_scientific_journal-522 89 6 e e PROPN american_scientific_journal-522 89 7 eed ee VERB american_scientific_journal-522 89 8 ab ab PROPN american_scientific_journal-522 89 9 a a DET american_scientific_journal-522 89 10 b b PROPN american_scientific_journal-522 89 11 a a PRON american_scientific_journal-522 89 12 a a DET american_scientific_journal-522 89 13 w w NOUN american_scientific_journal-522 89 14 w w PROPN american_scientific_journal-522 89 15 wf wf PROPN american_scientific_journal-522 89 16 f f PROPN american_scientific_journal-522 89 17 d d PROPN american_scientific_journal-522 89 18 e e PROPN american_scientific_journal-522 89 19 a a PRON american_scientific_journal-522 89 20 b b NOUN american_scientific_journal-522 89 21 a a PRON american_scientific_journal-522 89 22 b b X american_scientific_journal-522 89 23 ab ab PROPN american_scientific_journal-522 89 24 θθ θθ PROPN american_scientific_journal-522 89 25 ξ ξ PROPN american_scientific_journal-522 89 26 η η X american_scientific_journal-522 89 27 ξ ξ PROPN american_scientific_journal-522 89 28 ξ ξ PROPN american_scientific_journal-522 89 29 η η PROPN american_scientific_journal-522 89 30 η η PROPN american_scientific_journal-522 89 31 θθ θθ ADP american_scientific_journal-522 89 32 θ θ PROPN american_scientific_journal-522 89 33 ξ ξ PROPN american_scientific_journal-522 89 34 η η PROPN american_scientific_journal-522 89 35 ξ ξ PROPN american_scientific_journal-522 89 36 η η PROPN american_scientific_journal-522 89 37 η η PROPN american_scientific_journal-522 89 38 ξ ξ PROPN american_scientific_journal-522 89 39   PROPN american_scientific_journal-522 89 40 ∂ ∂ PROPN american_scientific_journal-522 89 41   PROPN american_scientific_journal-522 89 42   PROPN american_scientific_journal-522 89 43   PROPN american_scientific_journal-522 89 44   PROPN american_scientific_journal-522 89 45   PROPN american_scientific_journal-522 89 46   PROPN american_scientific_journal-522 89 47 ∂ ∂ PROPN american_scientific_journal-522 89 48 ∂ ∂ NUM american_scientific_journal-522 89 49 ∂ ∂ NUM american_scientific_journal-522 89 50 ∂ ∂ NUM american_scientific_journal-522 89 51 ∂ ∂ NOUN american_scientific_journal-522 89 52 = = NOUN american_scientific_journal-522 89 53 + + PUNCT american_scientific_journal-522 90 1 + + CCONJ american_scientific_journal-522 90 2 + + ADJ american_scientific_journal-522 90 3   ADJ american_scientific_journal-522 90 4   NOUN american_scientific_journal-522 90 5   NOUN american_scientific_journal-522 90 6   NOUN american_scientific_journal-522 90 7   NOUN american_scientific_journal-522 90 8   NOUN american_scientific_journal-522 90 9   NOUN american_scientific_journal-522 90 10 ∂ ∂ X american_scientific_journal-522 90 11 ∂ ∂ NUM american_scientific_journal-522 90 12 ∂ ∂ NUM american_scientific_journal-522 90 13 ∂ ∂ NUM american_scientific_journal-522 90 14 ∂ ∂ NUM american_scientific_journal-522 90 15 ∂ ∂ NOUN american_scientific_journal-522 90 16   NOUN american_scientific_journal-522 90 17   PUNCT american_scientific_journal-522 91 1   NOUN american_scientific_journal-522 91 2   PUNCT american_scientific_journal-522 91 3   NOUN american_scientific_journal-522 91 4   PUNCT american_scientific_journal-522 92 1   NOUN american_scientific_journal-522 92 2   NOUN american_scientific_journal-522 92 3 ∂ ∂ NUM american_scientific_journal-522 92 4   PROPN american_scientific_journal-522 92 5   PROPN american_scientific_journal-522 92 6   PROPN american_scientific_journal-522 92 7   PUNCT american_scientific_journal-522 93 1   PROPN american_scientific_journal-522 93 2   NOUN american_scientific_journal-522 93 3 ∂ ∂ PROPN american_scientific_journal-522 93 4   PROPN american_scientific_journal-522 93 5 ∂ ∂ NUM american_scientific_journal-522 93 6 ∂ ∂ NUM american_scientific_journal-522 93 7 ∂ ∂ NUM american_scientific_journal-522 93 8 ∂ ∂ NOUN american_scientific_journal-522 94 1 + + CCONJ american_scientific_journal-522 95 1 + + PUNCT american_scientific_journal-522 95 2 + + PUNCT american_scientific_journal-522 95 3 + + ADJ american_scientific_journal-522 95 4   ADJ american_scientific_journal-522 95 5   NOUN american_scientific_journal-522 95 6   NOUN american_scientific_journal-522 95 7   NOUN american_scientific_journal-522 96 1   INTJ american_scientific_journal-522 96 2   X american_scientific_journal-522 97 1 ∂ ∂ X american_scientific_journal-522 97 2 ∂ ∂ NOUN american_scientific_journal-522 97 3 ∂ ∂ NUM american_scientific_journal-522 97 4 ∂ ∂ NUM american_scientific_journal-522 97 5 ∂ ∂ NOUN american_scientific_journal-522 97 6 ∂ ∂ NOUN american_scientific_journal-522 97 7   ADP american_scientific_journal-522 97 8   NOUN american_scientific_journal-522 97 9   PUNCT american_scientific_journal-522 97 10   NOUN american_scientific_journal-522 97 11   PUNCT american_scientific_journal-522 97 12   NOUN american_scientific_journal-522 97 13   PUNCT american_scientific_journal-522 98 1   NOUN american_scientific_journal-522 98 2 ∫ ∫ PROPN american_scientific_journal-522 98 3 ∫ ∫ PROPN american_scientific_journal-522 98 4   PROPN american_scientific_journal-522 98 5   VERB american_scientific_journal-522 98 6   PUNCT american_scientific_journal-522 99 1 2 2 NUM american_scientific_journal-522 99 2 22 22 NUM american_scientific_journal-522 99 3 2 2 NUM american_scientific_journal-522 99 4 2 2 NUM american_scientific_journal-522 99 5 0 0 NUM american_scientific_journal-522 99 6 0 0 NUM american_scientific_journal-522 99 7 012 012 NUM american_scientific_journal-522 99 8 12 12 NUM american_scientific_journal-522 99 9 12 12 NUM american_scientific_journal-522 99 10 122 122 NUM american_scientific_journal-522 99 11 2 2 NUM american_scientific_journal-522 99 12 4 4 NUM american_scientific_journal-522 99 13 2 2 NUM american_scientific_journal-522 99 14 4 4 NUM american_scientific_journal-522 99 15 2 2 NUM american_scientific_journal-522 99 16 222 222 NUM american_scientific_journal-522 99 17 2 2 NUM american_scientific_journal-522 99 18 0 0 NUM american_scientific_journal-522 99 19 012 012 NUM american_scientific_journal-522 99 20 12 12 NUM american_scientific_journal-522 99 21 12 12 NUM american_scientific_journal-522 99 22 12 12 NUM american_scientific_journal-522 99 23 3 3 NUM american_scientific_journal-522 99 24 2 2 NUM american_scientific_journal-522 99 25 3 3 NUM american_scientific_journal-522 99 26 2 2 NUM american_scientific_journal-522 99 27 2 2 NUM american_scientific_journal-522 99 28 2 2 NUM american_scientific_journal-522 99 29 2 2 NUM american_scientific_journal-522 99 30 2 2 NUM american_scientific_journal-522 99 31 33 33 NUM american_scientific_journal-522 99 32 0 0 NUM american_scientific_journal-522 99 33 0 0 NUM american_scientific_journal-522 99 34 2 2 NUM american_scientific_journal-522 99 35 2 2 NUM american_scientific_journal-522 99 36 2 2 NUM american_scientific_journal-522 99 37 2 2 NUM american_scientific_journal-522 99 38 2 2 NUM american_scientific_journal-522 99 39 2 2 NUM american_scientific_journal-522 99 40 2 2 NUM american_scientific_journal-522 99 41 2 2 NUM american_scientific_journal-522 99 42 4 4 NUM american_scientific_journal-522 99 43 y y NOUN american_scientific_journal-522 99 44 yx yx X american_scientific_journal-522 99 45 y y PROPN american_scientific_journal-522 99 46 yx yx PROPN american_scientific_journal-522 99 47 x x PUNCT american_scientific_journal-522 100 1 w w NOUN american_scientific_journal-522 100 2 w w NOUN american_scientific_journal-522 100 3 we we PRON american_scientific_journal-522 100 4 d d NOUN american_scientific_journal-522 100 5 df df VERB american_scientific_journal-522 100 6 a a DET american_scientific_journal-522 100 7 b b NOUN american_scientific_journal-522 100 8 a a DET american_scientific_journal-522 100 9 b b NOUN american_scientific_journal-522 101 1 w w NOUN american_scientific_journal-522 101 2 we we PRON american_scientific_journal-522 101 3 e e NOUN american_scientific_journal-522 101 4 f f PROPN american_scientific_journal-522 101 5 f f PROPN american_scientific_journal-522 102 1 a a DET american_scientific_journal-522 102 2 b b PROPN american_scientific_journal-522 102 3 b b PROPN american_scientific_journal-522 102 4 b b PROPN american_scientific_journal-522 102 5 d d PROPN american_scientific_journal-522 102 6 w w PROPN american_scientific_journal-522 102 7 w w PROPN american_scientific_journal-522 102 8 a a PRON american_scientific_journal-522 102 9 b b NUM american_scientific_journal-522 102 10 θ θ PROPN american_scientific_journal-522 102 11 θθ θθ ADP american_scientific_journal-522 102 12 ξ ξ PROPN american_scientific_journal-522 102 13 η η PROPN american_scientific_journal-522 102 14 ξ ξ PROPN american_scientific_journal-522 102 15 η η PROPN american_scientific_journal-522 102 16 ξ ξ PROPN american_scientific_journal-522 102 17 η η PROPN american_scientific_journal-522 102 18 θ θ PROPN american_scientific_journal-522 102 19 θθ θθ NOUN american_scientific_journal-522 102 20 θ θ PROPN american_scientific_journal-522 102 21 ξ ξ PROPN american_scientific_journal-522 102 22 ξ ξ PROPN american_scientific_journal-522 102 23 η η PROPN american_scientific_journal-522 102 24 η η PROPN american_scientific_journal-522 102 25 ξ ξ PROPN american_scientific_journal-522 102 26 η η PROPN american_scientific_journal-522 102 27 ξ ξ PROPN american_scientific_journal-522 102 28 η η PROPN american_scientific_journal-522 102 29 ∂ ∂ PROPN american_scientific_journal-522 102 30 ∂ ∂ PROPN american_scientific_journal-522 102 31   PROPN american_scientific_journal-522 102 32   PROPN american_scientific_journal-522 102 33   PROPN american_scientific_journal-522 102 34   PROPN american_scientific_journal-522 102 35   X american_scientific_journal-522 102 36 ∂ ∂ PROPN american_scientific_journal-522 102 37 ∂ ∂ NUM american_scientific_journal-522 102 38 ∂ ∂ NUM american_scientific_journal-522 102 39 ∂ ∂ NOUN american_scientific_journal-522 103 1 + + CCONJ american_scientific_journal-522 103 2 + + PUNCT american_scientific_journal-522 103 3 + + PUNCT american_scientific_journal-522 103 4 + + ADJ american_scientific_journal-522 103 5   ADJ american_scientific_journal-522 103 6   NOUN american_scientific_journal-522 103 7   NOUN american_scientific_journal-522 103 8   NOUN american_scientific_journal-522 103 9   NOUN american_scientific_journal-522 103 10   X american_scientific_journal-522 104 1 ∂ ∂ X american_scientific_journal-522 104 2 ∂ ∂ NUM american_scientific_journal-522 104 3 ∂ ∂ NUM american_scientific_journal-522 104 4 ∂ ∂ NUM american_scientific_journal-522 104 5 ∂ ∂ NOUN american_scientific_journal-522 104 6 ∂ ∂ NOUN american_scientific_journal-522 104 7   NOUN american_scientific_journal-522 104 8   PUNCT american_scientific_journal-522 105 1   NOUN american_scientific_journal-522 105 2   PUNCT american_scientific_journal-522 106 1   NOUN american_scientific_journal-522 106 2   PUNCT american_scientific_journal-522 106 3 ∂ ∂ NUM american_scientific_journal-522 106 4 ∂ ∂ PROPN american_scientific_journal-522 106 5   PROPN american_scientific_journal-522 106 6   PROPN american_scientific_journal-522 106 7   PROPN american_scientific_journal-522 106 8   PROPN american_scientific_journal-522 106 9 ∂ ∂ PROPN american_scientific_journal-522 106 10 ∂ ∂ NUM american_scientific_journal-522 106 11 ∂ ∂ NUM american_scientific_journal-522 106 12   PROPN american_scientific_journal-522 106 13 ∂ ∂ NUM american_scientific_journal-522 106 14   NOUN american_scientific_journal-522 107 1 + + X american_scientific_journal-522 108 1 + + PUNCT american_scientific_journal-522 108 2 + + PUNCT american_scientific_journal-522 108 3 + + ADJ american_scientific_journal-522 108 4   ADJ american_scientific_journal-522 108 5   NOUN american_scientific_journal-522 108 6   NOUN american_scientific_journal-522 108 7   NOUN american_scientific_journal-522 108 8   NOUN american_scientific_journal-522 108 9   X american_scientific_journal-522 109 1 ∂ ∂ X american_scientific_journal-522 109 2 ∂ ∂ NUM american_scientific_journal-522 109 3 ∂ ∂ NUM american_scientific_journal-522 109 4 ∂ ∂ NUM american_scientific_journal-522 109 5 ∂ ∂ NOUN american_scientific_journal-522 109 6 ∂ ∂ NOUN american_scientific_journal-522 109 7   PRON american_scientific_journal-522 109 8   NOUN american_scientific_journal-522 109 9   NOUN american_scientific_journal-522 109 10   PUNCT american_scientific_journal-522 110 1   NOUN american_scientific_journal-522 110 2   NOUN american_scientific_journal-522 110 3   PROPN american_scientific_journal-522 110 4 ∂ ∂ PROPN american_scientific_journal-522 110 5 ∂ ∂ NOUN american_scientific_journal-522 110 6 + + CCONJ american_scientific_journal-522 110 7   NOUN american_scientific_journal-522 110 8 ∂ ∂ ADJ american_scientific_journal-522 110 9 ∂ ∂ NOUN american_scientific_journal-522 110 10 2 2 NUM american_scientific_journal-522 110 11 2 2 NUM american_scientific_journal-522 110 12 33 33 NUM american_scientific_journal-522 110 13 0 0 NUM american_scientific_journal-522 110 14 33 33 NUM american_scientific_journal-522 110 15 0 0 NUM american_scientific_journal-522 110 16 2 2 NUM american_scientific_journal-522 110 17 2 2 NUM american_scientific_journal-522 110 18 22 22 NUM american_scientific_journal-522 110 19 2 2 NUM american_scientific_journal-522 110 20 33 33 NUM american_scientific_journal-522 110 21 33 33 NUM american_scientific_journal-522 110 22 33 33 NUM american_scientific_journal-522 110 23 33 33 NUM american_scientific_journal-522 110 24 0 0 NUM american_scientific_journal-522 110 25 33 33 NUM american_scientific_journal-522 110 26 0 0 NUM american_scientific_journal-522 110 27 2 2 NUM american_scientific_journal-522 110 28 2 2 NUM american_scientific_journal-522 110 29 2 2 NUM american_scientific_journal-522 110 30 2 2 NUM american_scientific_journal-522 110 31 2 2 NUM american_scientific_journal-522 110 32 0 0 NUM american_scientific_journal-522 110 33 044 044 NUM american_scientific_journal-522 110 34 44 44 NUM american_scientific_journal-522 110 35 33 33 NUM american_scientific_journal-522 110 36 442 442 NUM american_scientific_journal-522 110 37 4 4 NUM american_scientific_journal-522 110 38 4 4 NUM american_scientific_journal-522 110 39 2 2 NUM american_scientific_journal-522 110 40 2 2 NUM american_scientific_journal-522 110 41 2 2 NUM american_scientific_journal-522 110 42 yx yx NOUN american_scientific_journal-522 110 43 y y PROPN american_scientific_journal-522 110 44 yx yx NOUN american_scientific_journal-522 110 45 x x PUNCT american_scientific_journal-522 110 46 x x PUNCT american_scientific_journal-522 110 47 x x PUNCT american_scientific_journal-522 110 48 y y NOUN american_scientific_journal-522 110 49 h h NOUN american_scientific_journal-522 110 50 w w PROPN american_scientific_journal-522 110 51 h h PROPN american_scientific_journal-522 110 52 w w PROPN american_scientific_journal-522 110 53 ab ab PROPN american_scientific_journal-522 110 54 a a DET american_scientific_journal-522 110 55 b b NOUN american_scientific_journal-522 110 56 g g NOUN american_scientific_journal-522 110 57 g g PROPN american_scientific_journal-522 110 58 g g PROPN american_scientific_journal-522 111 1 i i PRON american_scientific_journal-522 111 2 w w VERB american_scientific_journal-522 112 1 i i PRON american_scientific_journal-522 113 1 w w PROPN american_scientific_journal-522 113 2 b b PROPN american_scientific_journal-522 113 3 a a PROPN american_scientific_journal-522 113 4 ab ab PROPN american_scientific_journal-522 113 5 a a DET american_scientific_journal-522 113 6 a a DET american_scientific_journal-522 113 7 w w PROPN american_scientific_journal-522 113 8 wi wi PROPN american_scientific_journal-522 113 9 ii ii PROPN american_scientific_journal-522 114 1 i i PROPN american_scientific_journal-522 114 2 b b PROPN american_scientific_journal-522 114 3 b b PROPN american_scientific_journal-522 114 4 θθ θθ ADP american_scientific_journal-522 114 5 ξ ξ PROPN american_scientific_journal-522 114 6 η η PROPN american_scientific_journal-522 114 7 η η PROPN american_scientific_journal-522 114 8 ξ ξ PROPN american_scientific_journal-522 114 9 η η PROPN american_scientific_journal-522 114 10 ξ ξ X american_scientific_journal-522 114 11 θ θ PROPN american_scientific_journal-522 114 12 θθ θθ NOUN american_scientific_journal-522 114 13 θ θ PROPN american_scientific_journal-522 114 14 θ θ PROPN american_scientific_journal-522 114 15 η η PROPN american_scientific_journal-522 114 16 ξ ξ PROPN american_scientific_journal-522 114 17 η η X american_scientific_journal-522 114 18 ξ ξ X american_scientific_journal-522 114 19 ξ ξ PROPN american_scientific_journal-522 114 20 ξ ξ PROPN american_scientific_journal-522 114 21 θ θ PROPN american_scientific_journal-522 114 22 θ θ PROPN american_scientific_journal-522 114 23 η η PROPN american_scientific_journal-522 114 24 η η PROPN american_scientific_journal-522 114 25 ∂ ∂ PROPN american_scientific_journal-522 114 26   PROPN american_scientific_journal-522 114 27   PROPN american_scientific_journal-522 114 28 ∂ ∂ PROPN american_scientific_journal-522 114 29 ∂ ∂ NUM american_scientific_journal-522 114 30 ∂ ∂ NOUN american_scientific_journal-522 114 31 + + CCONJ american_scientific_journal-522 114 32 + + ADJ american_scientific_journal-522 114 33   NOUN american_scientific_journal-522 114 34   NOUN american_scientific_journal-522 114 35   NOUN american_scientific_journal-522 114 36   NOUN american_scientific_journal-522 114 37 ∂ ∂ X american_scientific_journal-522 114 38 ∂ ∂ NUM american_scientific_journal-522 114 39 ∂ ∂ NUM american_scientific_journal-522 114 40 ∂ ∂ NUM american_scientific_journal-522 114 41 ∂ ∂ NOUN american_scientific_journal-522 114 42 ∂ ∂ NOUN american_scientific_journal-522 114 43   NOUN american_scientific_journal-522 114 44   PUNCT american_scientific_journal-522 115 1   NOUN american_scientific_journal-522 115 2   PUNCT american_scientific_journal-522 115 3 ∂ ∂ NUM american_scientific_journal-522 115 4 ∂ ∂ PROPN american_scientific_journal-522 115 5   PROPN american_scientific_journal-522 115 6   PROPN american_scientific_journal-522 115 7   NOUN american_scientific_journal-522 115 8 ∂ ∂ PROPN american_scientific_journal-522 115 9   PROPN american_scientific_journal-522 115 10 ∂ ∂ NUM american_scientific_journal-522 115 11   PROPN american_scientific_journal-522 115 12 ∂ ∂ PROPN american_scientific_journal-522 115 13   PROPN american_scientific_journal-522 115 14   PROPN american_scientific_journal-522 115 15 ∂ ∂ PROPN american_scientific_journal-522 115 16   NOUN american_scientific_journal-522 116 1 + + X american_scientific_journal-522 117 1 + + PUNCT american_scientific_journal-522 117 2 + + PUNCT american_scientific_journal-522 117 3 + + PUNCT american_scientific_journal-522 117 4 + + ADJ american_scientific_journal-522 117 5   NOUN american_scientific_journal-522 117 6   NOUN american_scientific_journal-522 117 7   NOUN american_scientific_journal-522 117 8   NOUN american_scientific_journal-522 117 9   NOUN american_scientific_journal-522 117 10   NOUN american_scientific_journal-522 117 11   NOUN american_scientific_journal-522 117 12   NOUN american_scientific_journal-522 117 13 ∂ ∂ X american_scientific_journal-522 117 14 ∂ ∂ NUM american_scientific_journal-522 117 15 ∂ ∂ NUM american_scientific_journal-522 117 16 ∂ ∂ NUM american_scientific_journal-522 117 17 ∂ ∂ NOUN american_scientific_journal-522 117 18 ∂ ∂ NOUN american_scientific_journal-522 117 19   ADP american_scientific_journal-522 117 20   NOUN american_scientific_journal-522 117 21   PUNCT american_scientific_journal-522 118 1   NOUN american_scientific_journal-522 118 2   VERB american_scientific_journal-522 118 3   PUNCT american_scientific_journal-522 119 1   NOUN american_scientific_journal-522 119 2   PUNCT american_scientific_journal-522 119 3   PROPN american_scientific_journal-522 119 4 ∂ ∂ NUM american_scientific_journal-522 119 5   PROPN american_scientific_journal-522 119 6   PROPN american_scientific_journal-522 119 7 ∂ ∂ PROPN american_scientific_journal-522 119 8   NOUN american_scientific_journal-522 120 1 + + X american_scientific_journal-522 121 1 + + PUNCT american_scientific_journal-522 121 2 + + PUNCT american_scientific_journal-522 121 3 + + ADJ american_scientific_journal-522 121 4   NOUN american_scientific_journal-522 121 5   NOUN american_scientific_journal-522 121 6   VERB american_scientific_journal-522 121 7 ∂ ∂ PUNCT american_scientific_journal-522 121 8 ∂ ∂ ADJ american_scientific_journal-522 121 9   ADP american_scientific_journal-522 121 10   NOUN american_scientific_journal-522 121 11   PUNCT american_scientific_journal-522 122 1 2 2 NUM american_scientific_journal-522 122 2 y y NOUN american_scientific_journal-522 122 3 d d PROPN american_scientific_journal-522 122 4 dθ dθ PROPN american_scientific_journal-522 122 5 ξ ξ PROPN american_scientific_journal-522 122 6 η η PROPN american_scientific_journal-522 122 7   PROPN american_scientific_journal-522 122 8   PROPN american_scientific_journal-522 122 9   PUNCT american_scientific_journal-522 122 10 ( ( PUNCT american_scientific_journal-522 122 11 11 11 NUM american_scientific_journal-522 122 12 ) ) PUNCT american_scientific_journal-522 122 13 where where SCONJ american_scientific_journal-522 122 14 ( ( PUNCT american_scientific_journal-522 122 15 ) ) PUNCT american_scientific_journal-522 122 16 / / SYM american_scientific_journal-522 122 17 2 2 NUM american_scientific_journal-522 122 18 2 2 NUM american_scientific_journal-522 122 19 , , PUNCT american_scientific_journal-522 122 20 , , PUNCT american_scientific_journal-522 122 21 / / SYM american_scientific_journal-522 122 22 2 2 NUM american_scientific_journal-522 122 23 , , PUNCT american_scientific_journal-522 123 1 h h NOUN american_scientific_journal-522 124 1 i i PRON american_scientific_journal-522 124 2 j j VERB american_scientific_journal-522 125 1 i i PRON american_scientific_journal-522 125 2 j j PROPN american_scientific_journal-522 126 1 h h NOUN american_scientific_journal-522 127 1 d d NOUN american_scientific_journal-522 127 2 c c PROPN american_scientific_journal-522 127 3 f f PROPN american_scientific_journal-522 127 4 z z NOUN american_scientific_journal-522 127 5 dz dz X american_scientific_journal-522 127 6 − − PROPN american_scientific_journal-522 128 1 = = SYM american_scientific_journal-522 128 2 ∫ ∫ PROPN american_scientific_journal-522 128 3 ( ( PUNCT american_scientific_journal-522 128 4 ) ) PUNCT american_scientific_journal-522 128 5 ( ( PUNCT american_scientific_journal-522 128 6 ) ) PUNCT american_scientific_journal-522 128 7 ( ( PUNCT american_scientific_journal-522 128 8 ) ) PUNCT american_scientific_journal-522 128 9 /2 /2 NUM american_scientific_journal-522 128 10 2 2 NUM american_scientific_journal-522 128 11 , , PUNCT american_scientific_journal-522 128 12 , , PUNCT american_scientific_journal-522 128 13 /2 /2 PROPN american_scientific_journal-522 128 14 2 2 NUM american_scientific_journal-522 129 1 h h NOUN american_scientific_journal-522 130 1 i i PRON american_scientific_journal-522 130 2 j j VERB american_scientific_journal-522 131 1 i i PRON american_scientific_journal-522 131 2 j j NOUN american_scientific_journal-522 132 1 h h NOUN american_scientific_journal-522 133 1 e e NOUN american_scientific_journal-522 133 2 c c PROPN american_scientific_journal-522 133 3 f f PROPN american_scientific_journal-522 133 4 z z PROPN american_scientific_journal-522 133 5 z z PROPN american_scientific_journal-522 133 6 f f PROPN american_scientific_journal-522 133 7 z z NOUN american_scientific_journal-522 133 8 dz dz NOUN american_scientific_journal-522 133 9 − − NOUN american_scientific_journal-522 134 1 = = PUNCT american_scientific_journal-522 134 2 −∫ −∫ X american_scientific_journal-522 134 3 ( ( PUNCT american_scientific_journal-522 134 4 8 8 NUM american_scientific_journal-522 134 5 , , PUNCT american_scientific_journal-522 134 6 9 9 NUM american_scientific_journal-522 134 7 , , PUNCT american_scientific_journal-522 134 8 10 10 NUM american_scientific_journal-522 134 9 ) ) PUNCT american_scientific_journal-522 134 10 ( ( PUNCT american_scientific_journal-522 134 11 12 12 NUM american_scientific_journal-522 134 12 , , PUNCT american_scientific_journal-522 134 13 13 13 NUM american_scientific_journal-522 134 14 ) ) PUNCT american_scientific_journal-522 134 15 4 4 NUM american_scientific_journal-522 134 16 american american ADJ american_scientific_journal-522 134 17 scientific scientific ADJ american_scientific_journal-522 134 18 research research NOUN american_scientific_journal-522 134 19 journal journal NOUN american_scientific_journal-522 134 20 for for ADP american_scientific_journal-522 134 21 engineering engineering NOUN american_scientific_journal-522 134 22 , , PUNCT american_scientific_journal-522 134 23 technology technology NOUN american_scientific_journal-522 134 24 , , PUNCT american_scientific_journal-522 134 25 and and CCONJ american_scientific_journal-522 134 26 sciences science NOUN american_scientific_journal-522 134 27 ( ( PUNCT american_scientific_journal-522 134 28 asrjets asrjet NOUN american_scientific_journal-522 134 29 ) ) PUNCT american_scientific_journal-522 134 30 ( ( PUNCT american_scientific_journal-522 134 31 2014 2014 NUM american_scientific_journal-522 134 32 ) ) PUNCT american_scientific_journal-522 134 33 volume volume NOUN american_scientific_journal-522 134 34 9 9 NUM american_scientific_journal-522 134 35 , , PUNCT american_scientific_journal-522 134 36 no no DET american_scientific_journal-522 134 37 1 1 NUM american_scientific_journal-522 134 38 , , PUNCT american_scientific_journal-522 134 39 pp pp ADV american_scientific_journal-522 134 40 1 1 NUM american_scientific_journal-522 134 41 - - SYM american_scientific_journal-522 134 42 19 19 NUM american_scientific_journal-522 134 43 ( ( PUNCT american_scientific_journal-522 134 44 ) ) PUNCT american_scientific_journal-522 134 45 ( ( PUNCT american_scientific_journal-522 134 46 ) ) PUNCT american_scientific_journal-522 134 47 ( ( PUNCT american_scientific_journal-522 134 48 ) ) PUNCT american_scientific_journal-522 134 49 /2 /2 PUNCT american_scientific_journal-522 135 1 2 2 NUM american_scientific_journal-522 135 2 2 2 NUM american_scientific_journal-522 135 3 , , PUNCT american_scientific_journal-522 135 4 , , PUNCT american_scientific_journal-522 135 5 /2 /2 PROPN american_scientific_journal-522 136 1 2 2 NUM american_scientific_journal-522 136 2 h h NOUN american_scientific_journal-522 137 1 i i PRON american_scientific_journal-522 137 2 j j VERB american_scientific_journal-522 138 1 i i PRON american_scientific_journal-522 138 2 j j PROPN american_scientific_journal-522 139 1 h h NOUN american_scientific_journal-522 140 1 f f NOUN american_scientific_journal-522 140 2 c c PROPN american_scientific_journal-522 141 1 f f PROPN american_scientific_journal-522 141 2 z z NOUN american_scientific_journal-522 141 3 z z PROPN american_scientific_journal-522 142 1 f f PROPN american_scientific_journal-522 142 2 z z NOUN american_scientific_journal-522 142 3 z z NOUN american_scientific_journal-522 142 4 dz dz NOUN american_scientific_journal-522 142 5 − − PROPN american_scientific_journal-522 142 6 = = PUNCT american_scientific_journal-522 143 1 − − PROPN american_scientific_journal-522 143 2 + + NUM american_scientific_journal-522 143 3 ∫ ∫ PROPN american_scientific_journal-522 143 4 , , PUNCT american_scientific_journal-522 143 5 ( ( PUNCT american_scientific_journal-522 143 6 ) ) PUNCT american_scientific_journal-522 143 7 ( ( PUNCT american_scientific_journal-522 143 8 ) ) PUNCT american_scientific_journal-522 143 9 ( ( PUNCT american_scientific_journal-522 143 10 ) ) PUNCT american_scientific_journal-522 143 11 /2 /2 NUM american_scientific_journal-522 143 12 2 2 NUM american_scientific_journal-522 143 13 , , PUNCT american_scientific_journal-522 143 14 , , PUNCT american_scientific_journal-522 143 15 /2 /2 NOUN american_scientific_journal-522 143 16 2 2 NUM american_scientific_journal-522 143 17 1 1 NUM american_scientific_journal-522 143 18 h h NOUN american_scientific_journal-522 144 1 i i PRON american_scientific_journal-522 144 2 j j VERB american_scientific_journal-522 145 1 i i PRON american_scientific_journal-522 145 2 j j PROPN american_scientific_journal-522 145 3 h h NOUN american_scientific_journal-522 146 1 g g PROPN american_scientific_journal-522 146 2 c c PROPN american_scientific_journal-522 146 3 f f PROPN american_scientific_journal-522 146 4 z z PROPN american_scientific_journal-522 146 5 f f PROPN american_scientific_journal-522 146 6 z z NOUN american_scientific_journal-522 146 7 dz dz X american_scientific_journal-522 146 8 − − PROPN american_scientific_journal-522 147 1 = = PUNCT american_scientific_journal-522 148 1 − − PROPN american_scientific_journal-522 148 2 + + NUM american_scientific_journal-522 148 3 ∫ ∫ PROPN american_scientific_journal-522 148 4 ( ( PUNCT american_scientific_journal-522 148 5 ) ) PUNCT american_scientific_journal-522 148 6 ( ( PUNCT american_scientific_journal-522 148 7 ) ) PUNCT american_scientific_journal-522 148 8 ( ( PUNCT american_scientific_journal-522 148 9 ) ) PUNCT american_scientific_journal-522 148 10 /2 /2 NUM american_scientific_journal-522 148 11 2 2 NUM american_scientific_journal-522 148 12 , , PUNCT american_scientific_journal-522 148 13 , , PUNCT american_scientific_journal-522 148 14 /2 /2 PROPN american_scientific_journal-522 149 1 h h NOUN american_scientific_journal-522 150 1 i i PRON american_scientific_journal-522 150 2 j j VERB american_scientific_journal-522 151 1 i i PRON american_scientific_journal-522 151 2 j j PROPN american_scientific_journal-522 152 1 h h NOUN american_scientific_journal-522 152 2 h h NOUN american_scientific_journal-522 153 1 c c NOUN american_scientific_journal-522 153 2 f f PROPN american_scientific_journal-522 153 3 z z PROPN american_scientific_journal-522 153 4 f f PROPN american_scientific_journal-522 153 5 z z NOUN american_scientific_journal-522 153 6 dz dz NOUN american_scientific_journal-522 153 7 − − NOUN american_scientific_journal-522 154 1 = = PUNCT american_scientific_journal-522 154 2 −∫ −∫ NOUN american_scientific_journal-522 154 3 , , PUNCT american_scientific_journal-522 154 4 ( ( PUNCT american_scientific_journal-522 154 5 ) ) PUNCT american_scientific_journal-522 154 6 ( ( PUNCT american_scientific_journal-522 154 7 ) ) PUNCT american_scientific_journal-522 154 8 2/2 2/2 NUM american_scientific_journal-522 154 9 , , PUNCT american_scientific_journal-522 154 10 , , PUNCT american_scientific_journal-522 154 11 /2 /2 ADJ american_scientific_journal-522 154 12 2 2 NUM american_scientific_journal-522 154 13 1 1 NUM american_scientific_journal-522 154 14 h h NOUN american_scientific_journal-522 155 1 i i PRON american_scientific_journal-522 155 2 j j VERB american_scientific_journal-522 156 1 i i PRON american_scientific_journal-522 156 2 j j PROPN american_scientific_journal-522 157 1 h h NOUN american_scientific_journal-522 158 1 f f NOUN american_scientific_journal-522 158 2 z z NOUN american_scientific_journal-522 159 1 f f PROPN american_scientific_journal-522 159 2 z z NOUN american_scientific_journal-522 160 1 i i PRON american_scientific_journal-522 160 2 c c NOUN american_scientific_journal-522 160 3 dz dz PROPN american_scientific_journal-522 160 4 z z PROPN american_scientific_journal-522 160 5 z− z− PROPN american_scientific_journal-522 160 6   PROPN american_scientific_journal-522 160 7 ∂ ∂ VERB american_scientific_journal-522 160 8 ∂ ∂ PROPN american_scientific_journal-522 160 9   PROPN american_scientific_journal-522 160 10   PROPN american_scientific_journal-522 160 11 = = PROPN american_scientific_journal-522 160 12 − − PROPN american_scientific_journal-522 161 1 + + NOUN american_scientific_journal-522 161 2   NOUN american_scientific_journal-522 161 3   X american_scientific_journal-522 161 4 ∂ ∂ X american_scientific_journal-522 161 5 ∂ ∂ ADJ american_scientific_journal-522 161 6   PROPN american_scientific_journal-522 161 7   PUNCT american_scientific_journal-522 161 8 ∫ ∫ PROPN american_scientific_journal-522 161 9 where where SCONJ american_scientific_journal-522 161 10 ξ(= ξ(= PROPN american_scientific_journal-522 161 11 x x PROPN american_scientific_journal-522 161 12 / / SYM american_scientific_journal-522 161 13 a a NOUN american_scientific_journal-522 161 14 ) ) PUNCT american_scientific_journal-522 161 15 and and CCONJ american_scientific_journal-522 161 16 η(= η(= ADP american_scientific_journal-522 161 17 y y PROPN american_scientific_journal-522 161 18 / / SYM american_scientific_journal-522 161 19 b b NOUN american_scientific_journal-522 161 20 ) ) PUNCT american_scientific_journal-522 161 21 are be AUX american_scientific_journal-522 161 22 the the DET american_scientific_journal-522 161 23 non non ADJ american_scientific_journal-522 161 24 - - ADJ american_scientific_journal-522 161 25 dimensional dimensional ADJ american_scientific_journal-522 161 26 coordinates coordinate NOUN american_scientific_journal-522 161 27 . . PUNCT american_scientific_journal-522 162 1 2.1 2.1 NUM american_scientific_journal-522 162 2 . . PUNCT american_scientific_journal-522 163 1 hierarchical hierarchical ADJ american_scientific_journal-522 163 2 finite finite PROPN american_scientific_journal-522 163 3 element element NOUN american_scientific_journal-522 163 4 formulation formulation NOUN american_scientific_journal-522 163 5 a a DET american_scientific_journal-522 163 6 fournode fournode ADJ american_scientific_journal-522 163 7 rectangular rectangular ADJ american_scientific_journal-522 163 8 hierarchical hierarchical ADJ american_scientific_journal-522 163 9 finite finite NOUN american_scientific_journal-522 163 10 element element NOUN american_scientific_journal-522 163 11 with with ADP american_scientific_journal-522 163 12 six six NUM american_scientific_journal-522 163 13 degrees degree NOUN american_scientific_journal-522 163 14 of of ADP american_scientific_journal-522 163 15 freedom freedom NOUN american_scientific_journal-522 163 16 per per ADP american_scientific_journal-522 163 17 node node NOUN american_scientific_journal-522 163 18 ( ( PUNCT american_scientific_journal-522 163 19 𝑤𝑤0 𝑤𝑤0 PROPN american_scientific_journal-522 163 20 , , PUNCT american_scientific_journal-522 163 21 𝜕𝜕𝑤𝑤0/𝜕𝜕𝜕𝜕 𝜕𝜕𝑤𝑤0/𝜕𝜕𝜕𝜕 PROPN american_scientific_journal-522 163 22 , , PUNCT american_scientific_journal-522 163 23 𝜕𝜕𝑤𝑤0/𝜕𝜕𝜕𝜕 𝜕𝜕𝑤𝑤0/𝜕𝜕𝜕𝜕 PROPN american_scientific_journal-522 163 24 , , PUNCT american_scientific_journal-522 163 25 𝜕𝜕𝑤𝑤0/𝜕𝜕𝜕𝜕𝜕𝜕 𝜕𝜕𝑤𝑤0/𝜕𝜕𝜕𝜕𝜕𝜕 NOUN american_scientific_journal-522 163 26 , , PUNCT american_scientific_journal-522 163 27 𝜃𝜃𝜕𝜕 𝜃𝜃𝜕𝜕 NOUN american_scientific_journal-522 163 28 , , PUNCT american_scientific_journal-522 163 29 𝜃𝜃𝜕𝜕 𝜃𝜃𝜕𝜕 NOUN american_scientific_journal-522 163 30 ) ) PUNCT american_scientific_journal-522 163 31 is be AUX american_scientific_journal-522 163 32 developed develop VERB american_scientific_journal-522 163 33 on on ADP american_scientific_journal-522 163 34 the the DET american_scientific_journal-522 163 35 basis basis NOUN american_scientific_journal-522 163 36 of of ADP american_scientific_journal-522 163 37 a a DET american_scientific_journal-522 163 38 third third ADJ american_scientific_journal-522 163 39 - - PUNCT american_scientific_journal-522 163 40 order order NOUN american_scientific_journal-522 163 41 plate plate NOUN american_scientific_journal-522 163 42 theory theory NOUN american_scientific_journal-522 163 43 ( ( PUNCT american_scientific_journal-522 163 44 see see VERB american_scientific_journal-522 163 45 fig fig NOUN american_scientific_journal-522 163 46 . . PUNCT american_scientific_journal-522 164 1 2 2 NUM american_scientific_journal-522 164 2 ) ) PUNCT american_scientific_journal-522 164 3 . . PUNCT american_scientific_journal-522 165 1 trigonometric trigonometric ADJ american_scientific_journal-522 165 2 hierarchical hierarchical ADJ american_scientific_journal-522 165 3 functions function NOUN american_scientific_journal-522 165 4 are be AUX american_scientific_journal-522 165 5 used use VERB american_scientific_journal-522 165 6 as as ADP american_scientific_journal-522 165 7 shape shape NOUN american_scientific_journal-522 165 8 functions function NOUN american_scientific_journal-522 165 9 . . PUNCT american_scientific_journal-522 166 1 the the DET american_scientific_journal-522 166 2 model model NOUN american_scientific_journal-522 166 3 requires require VERB american_scientific_journal-522 166 4 c0 c0 NOUN american_scientific_journal-522 166 5 continuity continuity NOUN american_scientific_journal-522 166 6 for for ADP american_scientific_journal-522 166 7 𝜃𝜃𝜕𝜕 𝜃𝜃𝜕𝜕 NOUN american_scientific_journal-522 166 8 and and CCONJ american_scientific_journal-522 166 9 𝜃𝜃𝜕𝜕 𝜃𝜃𝜕𝜕 NOUN american_scientific_journal-522 166 10 and and CCONJ american_scientific_journal-522 166 11 c1continuity c1continuity NOUN american_scientific_journal-522 166 12 for for ADP american_scientific_journal-522 166 13 𝑤𝑤0 𝑤𝑤0 PROPN american_scientific_journal-522 166 14 . . PUNCT american_scientific_journal-522 167 1 the the DET american_scientific_journal-522 167 2 displacement displacement NOUN american_scientific_journal-522 167 3 and and CCONJ american_scientific_journal-522 167 4 rotations rotation NOUN american_scientific_journal-522 167 5 of of ADP american_scientific_journal-522 167 6 the the DET american_scientific_journal-522 167 7 rectangular rectangular ADJ american_scientific_journal-522 167 8 plate plate NOUN american_scientific_journal-522 167 9 p p NOUN american_scientific_journal-522 167 10 - - PUNCT american_scientific_journal-522 167 11 element element NOUN american_scientific_journal-522 167 12 are be AUX american_scientific_journal-522 167 13 expressed express VERB american_scientific_journal-522 167 14 as as ADP american_scientific_journal-522 167 15 𝑤𝑤0(𝜉𝜉 𝑤𝑤0(𝜉𝜉 NOUN american_scientific_journal-522 167 16 , , PUNCT american_scientific_journal-522 167 17 𝜂𝜂 𝜂𝜂 NOUN american_scientific_journal-522 167 18 , , PUNCT american_scientific_journal-522 167 19 𝑡𝑡 𝑡𝑡 ADJ american_scientific_journal-522 167 20 ) ) PUNCT american_scientific_journal-522 167 21 = = SYM american_scientific_journal-522 167 22 � � PROPN american_scientific_journal-522 167 23 � � PROPN american_scientific_journal-522 167 24 𝑊𝑊𝑚𝑚𝑚𝑚 𝑊𝑊𝑚𝑚𝑚𝑚 PROPN american_scientific_journal-522 167 25 ( ( PUNCT american_scientific_journal-522 167 26 𝑡𝑡)𝑔𝑔𝑚𝑚(𝜉𝜉)𝑔𝑔𝑚𝑚(𝜂𝜂 𝑡𝑡)𝑔𝑔𝑚𝑚(𝜉𝜉)𝑔𝑔𝑚𝑚(𝜂𝜂 NOUN american_scientific_journal-522 167 27 ) ) PUNCT american_scientific_journal-522 167 28 𝑃𝑃𝑤𝑤 𝑃𝑃𝑤𝑤 PROPN american_scientific_journal-522 167 29 𝑚𝑚=1 𝑚𝑚=1 PROPN american_scientific_journal-522 167 30 𝑃𝑃𝑤𝑤 𝑃𝑃𝑤𝑤 ADJ american_scientific_journal-522 167 31 𝑚𝑚=1 𝑚𝑚=1 NOUN american_scientific_journal-522 167 32 𝜃𝜃𝜕𝜕(𝜉𝜉 𝜃𝜃𝜕𝜕(𝜉𝜉 NOUN american_scientific_journal-522 167 33 , , PUNCT american_scientific_journal-522 167 34 𝜂𝜂 𝜂𝜂 NOUN american_scientific_journal-522 167 35 , , PUNCT american_scientific_journal-522 167 36 𝑡𝑡 𝑡𝑡 ADJ american_scientific_journal-522 167 37 ) ) PUNCT american_scientific_journal-522 167 38 = = SYM american_scientific_journal-522 167 39 � � PROPN american_scientific_journal-522 167 40 � � PROPN american_scientific_journal-522 167 41 𝜃𝜃𝜕𝜕𝑚𝑚𝑚𝑚 𝜃𝜃𝜕𝜕𝑚𝑚𝑚𝑚 X american_scientific_journal-522 167 42 ( ( PUNCT american_scientific_journal-522 167 43 𝑡𝑡)𝑓𝑓𝑚𝑚(𝜉𝜉)𝑓𝑓𝑚𝑚(𝜂𝜂 𝑡𝑡)𝑓𝑓𝑚𝑚(𝜉𝜉)𝑓𝑓𝑚𝑚(𝜂𝜂 NOUN american_scientific_journal-522 167 44 ) ) PUNCT american_scientific_journal-522 167 45 𝑃𝑃𝜃𝜃 𝑃𝑃𝜃𝜃 PROPN american_scientific_journal-522 167 46 𝑚𝑚=1 𝑚𝑚=1 PUNCT american_scientific_journal-522 167 47 𝑃𝑃𝜃𝜃 𝑃𝑃𝜃𝜃 PROPN american_scientific_journal-522 167 48 𝑚𝑚=1 𝑚𝑚=1 X american_scientific_journal-522 167 49 ( ( PUNCT american_scientific_journal-522 167 50 18 18 NUM american_scientific_journal-522 167 51 ) ) PUNCT american_scientific_journal-522 167 52 𝜃𝜃𝜕𝜕(𝜉𝜉 𝜃𝜃𝜕𝜕(𝜉𝜉 NOUN american_scientific_journal-522 167 53 , , PUNCT american_scientific_journal-522 167 54 𝜂𝜂 𝜂𝜂 NOUN american_scientific_journal-522 167 55 , , PUNCT american_scientific_journal-522 167 56 𝑡𝑡 𝑡𝑡 ADJ american_scientific_journal-522 167 57 ) ) PUNCT american_scientific_journal-522 167 58 = = SYM american_scientific_journal-522 167 59 � � PROPN american_scientific_journal-522 167 60 � � PROPN american_scientific_journal-522 167 61 𝜃𝜃𝜕𝜕𝑚𝑚𝑚𝑚 𝜃𝜃𝜕𝜕𝑚𝑚𝑚𝑚 X american_scientific_journal-522 167 62 ( ( PUNCT american_scientific_journal-522 167 63 𝑡𝑡)𝑓𝑓𝑚𝑚(𝜉𝜉)𝑓𝑓𝑚𝑚(𝜂𝜂 𝑡𝑡)𝑓𝑓𝑚𝑚(𝜉𝜉)𝑓𝑓𝑚𝑚(𝜂𝜂 NOUN american_scientific_journal-522 167 64 ) ) PUNCT american_scientific_journal-522 167 65 𝑃𝑃𝜃𝜃 𝑃𝑃𝜃𝜃 PROPN american_scientific_journal-522 167 66 𝑚𝑚=1 𝑚𝑚=1 PUNCT american_scientific_journal-522 167 67 𝑃𝑃𝜃𝜃 𝑃𝑃𝜃𝜃 PROPN american_scientific_journal-522 167 68 𝑚𝑚=1 𝑚𝑚=1 PROPN american_scientific_journal-522 167 69 where where SCONJ american_scientific_journal-522 167 70 𝑃𝑃𝑤𝑤 𝑃𝑃𝑤𝑤 PROPN american_scientific_journal-522 167 71 and and CCONJ american_scientific_journal-522 167 72 𝑃𝑃𝜃𝜃 𝑃𝑃𝜃𝜃 PROPN american_scientific_journal-522 167 73 are be AUX american_scientific_journal-522 167 74 the the DET american_scientific_journal-522 167 75 number number NOUN american_scientific_journal-522 167 76 of of ADP american_scientific_journal-522 167 77 shape shape NOUN american_scientific_journal-522 167 78 functions function NOUN american_scientific_journal-522 167 79 used use VERB american_scientific_journal-522 167 80 in in ADP american_scientific_journal-522 167 81 the the DET american_scientific_journal-522 167 82 model model NOUN american_scientific_journal-522 167 83 . . PUNCT american_scientific_journal-522 168 1 the the DET american_scientific_journal-522 168 2 firsts first NOUN american_scientific_journal-522 168 3 shape shape NOUN american_scientific_journal-522 168 4 functions function NOUN american_scientific_journal-522 168 5 ( ( PUNCT american_scientific_journal-522 168 6 𝑓𝑓1 𝑓𝑓1 PROPN american_scientific_journal-522 168 7 𝑓𝑓2 𝑓𝑓2 ADV american_scientific_journal-522 168 8 and and CCONJ american_scientific_journal-522 168 9 𝑔𝑔1to𝑔𝑔4 𝑔𝑔1to𝑔𝑔4 X american_scientific_journal-522 168 10 ) ) PUNCT american_scientific_journal-522 168 11 are be AUX american_scientific_journal-522 168 12 commonly commonly ADV american_scientific_journal-522 168 13 used use VERB american_scientific_journal-522 168 14 in in ADP american_scientific_journal-522 168 15 the the DET american_scientific_journal-522 168 16 finite finite ADJ american_scientific_journal-522 168 17 element element NOUN american_scientific_journal-522 168 18 method method NOUN american_scientific_journal-522 168 19 . . PUNCT american_scientific_journal-522 169 1 the the DET american_scientific_journal-522 169 2 functions function NOUN american_scientific_journal-522 169 3 ( ( PUNCT american_scientific_journal-522 169 4 𝑓𝑓𝑚𝑚+2 𝑓𝑓𝑚𝑚+2 PROPN american_scientific_journal-522 169 5 and and CCONJ american_scientific_journal-522 169 6 𝑔𝑔𝑚𝑚+4 𝑔𝑔𝑚𝑚+4 NOUN american_scientific_journal-522 169 7 ) ) PUNCT american_scientific_journal-522 169 8 are be AUX american_scientific_journal-522 169 9 the the DET american_scientific_journal-522 169 10 trigonometric trigonometric ADJ american_scientific_journal-522 169 11 shape shape NOUN american_scientific_journal-522 169 12 functions function NOUN american_scientific_journal-522 169 13 and and CCONJ american_scientific_journal-522 169 14 lead lead VERB american_scientific_journal-522 169 15 to to ADP american_scientific_journal-522 169 16 zero zero NUM american_scientific_journal-522 169 17 transverse transverse NOUN american_scientific_journal-522 169 18 displacement displacement NOUN american_scientific_journal-522 169 19 , , PUNCT american_scientific_journal-522 169 20 and and CCONJ american_scientific_journal-522 169 21 zero zero NUM american_scientific_journal-522 169 22 slope slope NOUN american_scientific_journal-522 169 23 at at ADP american_scientific_journal-522 169 24 each each DET american_scientific_journal-522 169 25 node node NOUN american_scientific_journal-522 169 26 . . PUNCT american_scientific_journal-522 170 1 this this DET american_scientific_journal-522 170 2 feature feature NOUN american_scientific_journal-522 170 3 is be AUX american_scientific_journal-522 170 4 highly highly ADV american_scientific_journal-522 170 5 significant significant ADJ american_scientific_journal-522 170 6 since since SCONJ american_scientific_journal-522 170 7 these these DET american_scientific_journal-522 170 8 functions function NOUN american_scientific_journal-522 170 9 only only ADV american_scientific_journal-522 170 10 give give VERB american_scientific_journal-522 170 11 additional additional ADJ american_scientific_journal-522 170 12 freedom freedom NOUN american_scientific_journal-522 170 13 to to ADP american_scientific_journal-522 170 14 the the DET american_scientific_journal-522 170 15 edges edge NOUN american_scientific_journal-522 170 16 and and CCONJ american_scientific_journal-522 170 17 the the DET american_scientific_journal-522 170 18 interior interior NOUN american_scientific_journal-522 170 19 of of ADP american_scientific_journal-522 170 20 the the DET american_scientific_journal-522 170 21 element element NOUN american_scientific_journal-522 170 22 . . PUNCT american_scientific_journal-522 171 1 the the DET american_scientific_journal-522 171 2 trigonometric trigonometric ADJ american_scientific_journal-522 171 3 hierarchical hierarchical ADJ american_scientific_journal-522 171 4 shape shape NOUN american_scientific_journal-522 171 5 functions function NOUN american_scientific_journal-522 171 6 𝑓𝑓𝑖𝑖(𝜉𝜉 𝑓𝑓𝑖𝑖(𝜉𝜉 NOUN american_scientific_journal-522 171 7 ) ) PUNCT american_scientific_journal-522 171 8 for for ADP american_scientific_journal-522 171 9 c0 c0 NOUN american_scientific_journal-522 171 10 continuity continuity NOUN american_scientific_journal-522 171 11 and and CCONJ american_scientific_journal-522 171 12 𝑔𝑔𝑖𝑖(𝜉𝜉)for 𝑔𝑔𝑖𝑖(𝜉𝜉)for ADP american_scientific_journal-522 171 13 c1 c1 NOUN american_scientific_journal-522 171 14 continuity continuity NOUN american_scientific_journal-522 171 15 are be AUX american_scientific_journal-522 171 16 given give VERB american_scientific_journal-522 171 17 by by ADP american_scientific_journal-522 171 18 [ [ PUNCT american_scientific_journal-522 171 19 24 24 NUM american_scientific_journal-522 171 20 ] ] PUNCT american_scientific_journal-522 171 21   ADJ american_scientific_journal-522 171 22   PROPN american_scientific_journal-522 171 23   PROPN american_scientific_journal-522 171 24   PROPN american_scientific_journal-522 171 25   PROPN american_scientific_journal-522 171 26   PROPN american_scientific_journal-522 171 27   X american_scientific_journal-522 171 28   NOUN american_scientific_journal-522 171 29 = = SYM american_scientific_journal-522 171 30 = = PUNCT american_scientific_journal-522 172 1 = = PUNCT american_scientific_journal-522 172 2 = = PUNCT american_scientific_journal-522 172 3 −= −= X american_scientific_journal-522 172 4 + + X american_scientific_journal-522 172 5 , , PUNCT american_scientific_journal-522 172 6 ... ... PUNCT american_scientific_journal-522 172 7 3,2,1 3,2,1 NUM american_scientific_journal-522 172 8 ) ) PUNCT american_scientific_journal-522 172 9 ( ( PUNCT american_scientific_journal-522 172 10 sin sin NOUN american_scientific_journal-522 172 11 1 1 NUM american_scientific_journal-522 172 12 2 2 NUM american_scientific_journal-522 172 13 2 2 NUM american_scientific_journal-522 172 14 1 1 NUM american_scientific_journal-522 172 15 r r NOUN american_scientific_journal-522 172 16 rr rr NOUN american_scientific_journal-522 172 17 rf rf PROPN american_scientific_journal-522 172 18 f f PROPN american_scientific_journal-522 172 19 f f PROPN american_scientific_journal-522 172 20 n n ADV american_scientific_journal-522 172 21 πδ πδ VERB american_scientific_journal-522 172 22 ξδ ξδ ADP american_scientific_journal-522 172 23 ξ ξ PROPN american_scientific_journal-522 172 24 ξ ξ PROPN american_scientific_journal-522 172 25 ( ( PUNCT american_scientific_journal-522 172 26 19 19 NUM american_scientific_journal-522 172 27 ) ) PUNCT american_scientific_journal-522 172 28 ( ( PUNCT american_scientific_journal-522 172 29 14 14 NUM american_scientific_journal-522 172 30 , , PUNCT american_scientific_journal-522 172 31 15 15 NUM american_scientific_journal-522 172 32 ) ) PUNCT american_scientific_journal-522 172 33 ( ( PUNCT american_scientific_journal-522 172 34 16 16 NUM american_scientific_journal-522 172 35 , , PUNCT american_scientific_journal-522 172 36 17 17 NUM american_scientific_journal-522 172 37 ) ) PUNCT american_scientific_journal-522 172 38 5 5 NUM american_scientific_journal-522 172 39 american american ADJ american_scientific_journal-522 172 40 scientific scientific ADJ american_scientific_journal-522 172 41 research research NOUN american_scientific_journal-522 172 42 journal journal NOUN american_scientific_journal-522 172 43 for for ADP american_scientific_journal-522 172 44 engineering engineering NOUN american_scientific_journal-522 172 45 , , PUNCT american_scientific_journal-522 172 46 technology technology NOUN american_scientific_journal-522 172 47 , , PUNCT american_scientific_journal-522 172 48 and and CCONJ american_scientific_journal-522 172 49 sciences science NOUN american_scientific_journal-522 172 50 ( ( PUNCT american_scientific_journal-522 172 51 asrjets asrjet NOUN american_scientific_journal-522 172 52 ) ) PUNCT american_scientific_journal-522 172 53 ( ( PUNCT american_scientific_journal-522 172 54 2014 2014 NUM american_scientific_journal-522 172 55 ) ) PUNCT american_scientific_journal-522 172 56 volume volume NOUN american_scientific_journal-522 172 57 9 9 NUM american_scientific_journal-522 172 58 , , PUNCT american_scientific_journal-522 172 59 no no DET american_scientific_journal-522 172 60 1 1 NUM american_scientific_journal-522 172 61 , , PUNCT american_scientific_journal-522 172 62 pp pp ADV american_scientific_journal-522 172 63 1 1 NUM american_scientific_journal-522 172 64 - - SYM american_scientific_journal-522 172 65 19 19 NUM american_scientific_journal-522 172 66 and and CCONJ american_scientific_journal-522 172 67 ( ( PUNCT american_scientific_journal-522 172 68 ) ) PUNCT american_scientific_journal-522 172 69 ( ( PUNCT american_scientific_journal-522 172 70 ) ) PUNCT american_scientific_journal-522 172 71 ( ( PUNCT american_scientific_journal-522 172 72 ) ) PUNCT american_scientific_journal-522 172 73 ( ( PUNCT american_scientific_journal-522 172 74 ) ) PUNCT american_scientific_journal-522 172 75 [ [ PUNCT american_scientific_journal-522 172 76 ] ] X american_scientific_journal-522 172 77 ( ( PUNCT american_scientific_journal-522 172 78 ) ) PUNCT american_scientific_journal-522 172 79   PROPN american_scientific_journal-522 172 80   PROPN american_scientific_journal-522 172 81   PROPN american_scientific_journal-522 172 82   PROPN american_scientific_journal-522 172 83   ADJ american_scientific_journal-522 172 84   PROPN american_scientific_journal-522 172 85   PROPN american_scientific_journal-522 172 86   PROPN american_scientific_journal-522 172 87   PROPN american_scientific_journal-522 172 88   X american_scientific_journal-522 172 89   NOUN american_scientific_journal-522 172 90 = = PUNCT american_scientific_journal-522 173 1 = = PUNCT american_scientific_journal-522 173 2 + + NUM american_scientific_journal-522 173 3 −+−−++−= −+−−++−= PROPN american_scientific_journal-522 173 4 + + NOUN american_scientific_journal-522 173 5 −= −= X american_scientific_journal-522 173 6 −= −= X american_scientific_journal-522 173 7 + + NOUN american_scientific_journal-522 173 8 −= −= NOUN american_scientific_journal-522 173 9 + + NOUN american_scientific_journal-522 173 10 −= −= NOUN american_scientific_journal-522 173 11 + + X american_scientific_journal-522 173 12 , , PUNCT american_scientific_journal-522 173 13 ... ... PUNCT american_scientific_journal-522 173 14 3,2,1 3,2,1 NUM american_scientific_journal-522 173 15 sin1112 sin1112 NOUN american_scientific_journal-522 173 16 23 23 NUM american_scientific_journal-522 173 17 2 2 NUM american_scientific_journal-522 173 18 231 231 NUM american_scientific_journal-522 173 19 32 32 NUM american_scientific_journal-522 173 20 4 4 NUM american_scientific_journal-522 173 21 32 32 NUM american_scientific_journal-522 173 22 4 4 NUM american_scientific_journal-522 173 23 32 32 NUM american_scientific_journal-522 173 24 3 3 NUM american_scientific_journal-522 173 25 32 32 NUM american_scientific_journal-522 173 26 2 2 NUM american_scientific_journal-522 173 27 32 32 NUM american_scientific_journal-522 173 28 1 1 NUM american_scientific_journal-522 173 29 r r NOUN american_scientific_journal-522 173 30 rr rr NOUN american_scientific_journal-522 173 31 rrg rrg PROPN american_scientific_journal-522 173 32 g g PROPN american_scientific_journal-522 173 33 g g PROPN american_scientific_journal-522 173 34 g g PROPN american_scientific_journal-522 173 35 g g PROPN american_scientific_journal-522 173 36 rr rr PROPN american_scientific_journal-522 173 37 n n ADV american_scientific_journal-522 173 38 πδ πδ ADV american_scientific_journal-522 173 39 ξδξξξδ ξδξξξδ VERB american_scientific_journal-522 173 40 ξξ ξξ ADV american_scientific_journal-522 173 41 ξξ ξξ VERB american_scientific_journal-522 173 42 ξξξ ξξξ NOUN american_scientific_journal-522 174 1 ξξ ξξ CCONJ american_scientific_journal-522 174 2 ( ( PUNCT american_scientific_journal-522 174 3 20 20 NUM american_scientific_journal-522 174 4 ) ) PUNCT american_scientific_journal-522 174 5 the the DET american_scientific_journal-522 174 6 displacement displacement NOUN american_scientific_journal-522 174 7 and and CCONJ american_scientific_journal-522 174 8 rotationscan rotationscan ADJ american_scientific_journal-522 174 9 be be AUX american_scientific_journal-522 174 10 expressed express VERB american_scientific_journal-522 174 11 in in ADP american_scientific_journal-522 174 12 matrix matrix NOUN american_scientific_journal-522 174 13 form form NOUN american_scientific_journal-522 174 14 � � PROPN american_scientific_journal-522 174 15 𝑤𝑤0 𝑤𝑤0 ADP american_scientific_journal-522 174 16 𝜃𝜃𝜕𝜕 𝜃𝜃𝜕𝜕 NOUN american_scientific_journal-522 174 17 𝜃𝜃𝜕𝜕 𝜃𝜃𝜕𝜕 NOUN american_scientific_journal-522 174 18 � � PROPN american_scientific_journal-522 175 1 = = PUNCT american_scientific_journal-522 176 1 [ [ X american_scientific_journal-522 176 2 𝑁𝑁]{𝑞𝑞 𝑁𝑁]{𝑞𝑞 X american_scientific_journal-522 176 3 } } PUNCT american_scientific_journal-522 176 4 ( ( PUNCT american_scientific_journal-522 176 5 21 21 NUM american_scientific_journal-522 176 6 ) ) PUNCT american_scientific_journal-522 177 1 [ [ X american_scientific_journal-522 177 2 n n X american_scientific_journal-522 177 3 ] ] X american_scientific_journal-522 177 4 is be AUX american_scientific_journal-522 177 5 the the DET american_scientific_journal-522 177 6 matrix matrix NOUN american_scientific_journal-522 177 7 of of ADP american_scientific_journal-522 177 8 the the DET american_scientific_journal-522 177 9 shape shape NOUN american_scientific_journal-522 177 10 functions function NOUN american_scientific_journal-522 177 11 , , PUNCT american_scientific_journal-522 177 12 given give VERB american_scientific_journal-522 177 13 by by ADP american_scientific_journal-522 177 14 [ [ X american_scientific_journal-522 177 15 𝑁𝑁 𝑁𝑁 PROPN american_scientific_journal-522 177 16 ] ] X american_scientific_journal-522 177 17 = = PUNCT american_scientific_journal-522 177 18 � � PROPN american_scientific_journal-522 178 1 [ [ X american_scientific_journal-522 178 2 𝑁𝑁𝑤𝑤 𝑁𝑁𝑤𝑤 X american_scientific_journal-522 178 3 ] ] PUNCT american_scientific_journal-522 178 4 0 0 NUM american_scientific_journal-522 178 5 0 0 NUM american_scientific_journal-522 178 6 0 0 NUM american_scientific_journal-522 179 1 [ [ X american_scientific_journal-522 179 2 𝑁𝑁𝜃𝜃 𝑁𝑁𝜃𝜃 X american_scientific_journal-522 179 3 ] ] PUNCT american_scientific_journal-522 179 4 0 0 NUM american_scientific_journal-522 179 5 0 0 NUM american_scientific_journal-522 179 6 0 0 NUM american_scientific_journal-522 180 1 [ [ X american_scientific_journal-522 180 2 𝑁𝑁𝜃𝜃 𝑁𝑁𝜃𝜃 PROPN american_scientific_journal-522 180 3 ] ] X american_scientific_journal-522 180 4 � � PROPN american_scientific_journal-522 180 5 ( ( PUNCT american_scientific_journal-522 180 6 22 22 NUM american_scientific_journal-522 180 7 ) ) PUNCT american_scientific_journal-522 180 8 where where SCONJ american_scientific_journal-522 180 9 { { PUNCT american_scientific_journal-522 180 10 𝑞𝑞 𝑞𝑞 PROPN american_scientific_journal-522 180 11 } } PUNCT american_scientific_journal-522 180 12 = = SYM american_scientific_journal-522 180 13 � � PROPN american_scientific_journal-522 180 14 𝑞𝑞𝑤𝑤 𝑞𝑞𝑤𝑤 PROPN american_scientific_journal-522 180 15 𝑞𝑞𝜃𝜃𝜕𝜕 𝑞𝑞𝜃𝜃𝜕𝜕 PROPN american_scientific_journal-522 180 16 𝑞𝑞𝜃𝜃𝜕𝜕 𝑞𝑞𝜃𝜃𝜕𝜕 PROPN american_scientific_journal-522 180 17 � � PROPN american_scientific_journal-522 180 18 ( ( PUNCT american_scientific_journal-522 180 19 23 23 NUM american_scientific_journal-522 180 20 ) ) PUNCT american_scientific_journal-522 180 21 in in ADP american_scientific_journal-522 180 22 which which PRON american_scientific_journal-522 180 23 𝑞𝑞𝑤𝑤 𝑞𝑞𝑤𝑤 ADJ american_scientific_journal-522 180 24 , , PUNCT american_scientific_journal-522 180 25 𝑞𝑞𝜃𝜃𝜕𝜕 𝑞𝑞𝜃𝜃𝜕𝜕 PROPN american_scientific_journal-522 180 26 and and CCONJ american_scientific_journal-522 180 27 𝑞𝑞𝜃𝜃𝜕𝜕 𝑞𝑞𝜃𝜃𝜕𝜕 PROPN american_scientific_journal-522 180 28 are be AUX american_scientific_journal-522 180 29 the the DET american_scientific_journal-522 180 30 generalized generalized ADJ american_scientific_journal-522 180 31 displacements displacement NOUN american_scientific_journal-522 180 32 . . PUNCT american_scientific_journal-522 181 1 the the DET american_scientific_journal-522 181 2 matrices matrix NOUN american_scientific_journal-522 181 3 of of ADP american_scientific_journal-522 181 4 theshape theshape NOUN american_scientific_journal-522 181 5 functions function NOUN american_scientific_journal-522 181 6 are be AUX american_scientific_journal-522 181 7 given give VERB american_scientific_journal-522 181 8 by by ADP american_scientific_journal-522 181 9 [ [ PUNCT american_scientific_journal-522 181 10 ] ] X american_scientific_journal-522 181 11 ( ( PUNCT american_scientific_journal-522 181 12 ) ) PUNCT american_scientific_journal-522 181 13 ( ( PUNCT american_scientific_journal-522 181 14 ) ) PUNCT american_scientific_journal-522 181 15 ( ( PUNCT american_scientific_journal-522 181 16 ) ) PUNCT american_scientific_journal-522 181 17 ( ( PUNCT american_scientific_journal-522 181 18 ) ) PUNCT american_scientific_journal-522 181 19 ( ( PUNCT american_scientific_journal-522 181 20 ) ) PUNCT american_scientific_journal-522 181 21 ( ( PUNCT american_scientific_journal-522 181 22 ) ) PUNCT american_scientific_journal-522 181 23 ( ( PUNCT american_scientific_journal-522 181 24 ) ) PUNCT american_scientific_journal-522 181 25 ( ( PUNCT american_scientific_journal-522 181 26 ) ) PUNCT american_scientific_journal-522 181 27 ( ( PUNCT american_scientific_journal-522 181 28 ) ) PUNCT american_scientific_journal-522 181 29 ( ( PUNCT american_scientific_journal-522 181 30 ) ) PUNCT american_scientific_journal-522 181 31 ( ( PUNCT american_scientific_journal-522 181 32 ) ) PUNCT american_scientific_journal-522 181 33 ( ( PUNCT american_scientific_journal-522 181 34 ) ) PUNCT american_scientific_journal-522 181 35 1 1 NUM american_scientific_journal-522 181 36 1 1 NUM american_scientific_journal-522 181 37 1 1 NUM american_scientific_journal-522 181 38 2 2 NUM american_scientific_journal-522 181 39 p p NOUN american_scientific_journal-522 181 40 p1 p1 NOUN american_scientific_journal-522 181 41 2 2 NUM american_scientific_journal-522 181 42 p p NOUN american_scientific_journal-522 181 43 p p NOUN american_scientific_journal-522 181 44 , , PUNCT american_scientific_journal-522 181 45 , , PUNCT american_scientific_journal-522 181 46 ... ... PUNCT american_scientific_journal-522 181 47 , , PUNCT american_scientific_journal-522 181 48 ... ... PUNCT american_scientific_journal-522 182 1 w w X american_scientific_journal-522 182 2 w w PROPN american_scientific_journal-522 182 3 w w PROPN american_scientific_journal-522 182 4 w w PROPN american_scientific_journal-522 182 5 w w PROPN american_scientific_journal-522 182 6 k k PROPN american_scientific_journal-522 182 7 l l NOUN american_scientific_journal-522 182 8 r r NOUN american_scientific_journal-522 182 9 n n NOUN american_scientific_journal-522 182 10 g g NOUN american_scientific_journal-522 182 11 g g NOUN american_scientific_journal-522 182 12 g g PROPN american_scientific_journal-522 182 13 g g PROPN american_scientific_journal-522 182 14 g g PROPN american_scientific_journal-522 182 15 g g PROPN american_scientific_journal-522 182 16 g g PROPN american_scientific_journal-522 182 17 gξ gξ PROPN american_scientific_journal-522 182 18 η η PROPN american_scientific_journal-522 182 19 ξ ξ PROPN american_scientific_journal-522 182 20 η η PROPN american_scientific_journal-522 182 21 ξ ξ PROPN american_scientific_journal-522 182 22 η η X american_scientific_journal-522 182 23 ξ ξ PROPN american_scientific_journal-522 182 24 η η NOUN american_scientific_journal-522 182 25 = = NUM american_scientific_journal-522 182 26   ADJ american_scientific_journal-522 182 27   ADJ american_scientific_journal-522 182 28   NOUN american_scientific_journal-522 182 29 ( ( PUNCT american_scientific_journal-522 182 30 24 24 NUM american_scientific_journal-522 182 31 ) ) PUNCT american_scientific_journal-522 182 32 where where SCONJ american_scientific_journal-522 182 33 1 1 NUM american_scientific_journal-522 182 34 wk wk INTJ american_scientific_journal-522 182 35 , , PUNCT american_scientific_journal-522 182 36 ... ... PUNCT american_scientific_journal-522 182 37 , , PUNCT american_scientific_journal-522 182 38 p= p= NOUN american_scientific_journal-522 182 39 , , PUNCT american_scientific_journal-522 182 40 1 1 NUM american_scientific_journal-522 182 41 wl wl NOUN american_scientific_journal-522 182 42 , , PUNCT american_scientific_journal-522 182 43 ... ... PUNCT american_scientific_journal-522 182 44 , , PUNCT american_scientific_journal-522 182 45 p= p= ADJ american_scientific_journal-522 182 46 , , PUNCT american_scientific_journal-522 182 47 and and CCONJ american_scientific_journal-522 182 48 ( ( PUNCT american_scientific_journal-522 182 49 ) ) SYM american_scientific_journal-522 182 50 1 1 NUM american_scientific_journal-522 182 51 wr wr PROPN american_scientific_journal-522 182 52 j j PROPN american_scientific_journal-522 183 1 i i PRON american_scientific_journal-522 183 2 p= p= VERB american_scientific_journal-522 184 1 + + CCONJ american_scientific_journal-522 184 2 − − PROPN american_scientific_journal-522 184 3 and and CCONJ american_scientific_journal-522 184 4 6 6 NUM american_scientific_journal-522 184 5 american american ADJ american_scientific_journal-522 184 6 scientific scientific ADJ american_scientific_journal-522 184 7 research research NOUN american_scientific_journal-522 184 8 journal journal NOUN american_scientific_journal-522 184 9 for for ADP american_scientific_journal-522 184 10 engineering engineering NOUN american_scientific_journal-522 184 11 , , PUNCT american_scientific_journal-522 184 12 technology technology NOUN american_scientific_journal-522 184 13 , , PUNCT american_scientific_journal-522 184 14 and and CCONJ american_scientific_journal-522 184 15 sciences science NOUN american_scientific_journal-522 184 16 ( ( PUNCT american_scientific_journal-522 184 17 asrjets asrjet NOUN american_scientific_journal-522 184 18 ) ) PUNCT american_scientific_journal-522 184 19 ( ( PUNCT american_scientific_journal-522 184 20 2014 2014 NUM american_scientific_journal-522 184 21 ) ) PUNCT american_scientific_journal-522 184 22 volume volume NOUN american_scientific_journal-522 184 23 9 9 NUM american_scientific_journal-522 184 24 , , PUNCT american_scientific_journal-522 184 25 no no DET american_scientific_journal-522 184 26 1 1 NUM american_scientific_journal-522 184 27 , , PUNCT american_scientific_journal-522 184 28 pp pp ADV american_scientific_journal-522 184 29 1 1 NUM american_scientific_journal-522 184 30 - - SYM american_scientific_journal-522 184 31 19 19 NUM american_scientific_journal-522 184 32 [ [ PUNCT american_scientific_journal-522 184 33 ] ] X american_scientific_journal-522 184 34 ( ( PUNCT american_scientific_journal-522 184 35 ) ) PUNCT american_scientific_journal-522 184 36 ( ( PUNCT american_scientific_journal-522 184 37 ) ) PUNCT american_scientific_journal-522 184 38 ( ( PUNCT american_scientific_journal-522 184 39 ) ) PUNCT american_scientific_journal-522 184 40 ( ( PUNCT american_scientific_journal-522 184 41 ) ) PUNCT american_scientific_journal-522 184 42 ( ( PUNCT american_scientific_journal-522 184 43 ) ) PUNCT american_scientific_journal-522 184 44 ( ( PUNCT american_scientific_journal-522 184 45 ) ) PUNCT american_scientific_journal-522 184 46 ( ( PUNCT american_scientific_journal-522 184 47 ) ) PUNCT american_scientific_journal-522 184 48 ( ( PUNCT american_scientific_journal-522 184 49 ) ) PUNCT american_scientific_journal-522 184 50 ( ( PUNCT american_scientific_journal-522 184 51 ) ) PUNCT american_scientific_journal-522 184 52 ( ( PUNCT american_scientific_journal-522 184 53 ) ) PUNCT american_scientific_journal-522 184 54 ( ( PUNCT american_scientific_journal-522 184 55 ) ) PUNCT american_scientific_journal-522 184 56 ( ( PUNCT american_scientific_journal-522 184 57 ) ) PUNCT american_scientific_journal-522 184 58 1 1 NUM american_scientific_journal-522 184 59 1 1 NUM american_scientific_journal-522 184 60 1 1 NUM american_scientific_journal-522 184 61 2 2 NUM american_scientific_journal-522 184 62 p p NOUN american_scientific_journal-522 184 63 p1 p1 NOUN american_scientific_journal-522 184 64 2 2 NUM american_scientific_journal-522 184 65 p p NOUN american_scientific_journal-522 184 66 p p NOUN american_scientific_journal-522 184 67 , , PUNCT american_scientific_journal-522 184 68 , , PUNCT american_scientific_journal-522 184 69 ... ... PUNCT american_scientific_journal-522 184 70 , , PUNCT american_scientific_journal-522 184 71 ... ... PUNCT american_scientific_journal-522 185 1 i i PRON american_scientific_journal-522 185 2 j j PROPN american_scientific_journal-522 185 3 m m VERB american_scientific_journal-522 185 4 n n VERB american_scientific_journal-522 186 1 f f NOUN american_scientific_journal-522 186 2 f f PROPN american_scientific_journal-522 187 1 f f PROPN american_scientific_journal-522 187 2 f f X american_scientific_journal-522 188 1 f f X american_scientific_journal-522 188 2 f f X american_scientific_journal-522 188 3 f f PROPN american_scientific_journal-522 188 4 f f PROPN american_scientific_journal-522 188 5 θ θ NOUN american_scientific_journal-522 188 6 θ θ NOUN american_scientific_journal-522 188 7 θ θ X american_scientific_journal-522 188 8 θ θ X american_scientific_journal-522 188 9 θ θ X american_scientific_journal-522 188 10 ξ ξ X american_scientific_journal-522 188 11 η η X american_scientific_journal-522 188 12 ξ ξ PROPN american_scientific_journal-522 188 13 η η PROPN american_scientific_journal-522 188 14 ξ ξ PROPN american_scientific_journal-522 188 15 η η X american_scientific_journal-522 188 16 ξ ξ PROPN american_scientific_journal-522 188 17 η η NOUN american_scientific_journal-522 188 18 = = NUM american_scientific_journal-522 188 19   ADJ american_scientific_journal-522 188 20   ADJ american_scientific_journal-522 188 21   NOUN american_scientific_journal-522 188 22 ( ( PUNCT american_scientific_journal-522 188 23 25 25 NUM american_scientific_journal-522 188 24 ) ) PUNCT american_scientific_journal-522 188 25 where where SCONJ american_scientific_journal-522 188 26 1i 1i NOUN american_scientific_journal-522 188 27 , , PUNCT american_scientific_journal-522 188 28 ... ... PUNCT american_scientific_journal-522 188 29 , , PUNCT american_scientific_journal-522 188 30 pθ= pθ= NOUN american_scientific_journal-522 188 31 , , PUNCT american_scientific_journal-522 188 32 1j 1j NUM american_scientific_journal-522 188 33 , , PUNCT american_scientific_journal-522 188 34 ... ... PUNCT american_scientific_journal-522 188 35 , , PUNCT american_scientific_journal-522 188 36 pθ= pθ= NOUN american_scientific_journal-522 188 37 , , PUNCT american_scientific_journal-522 188 38 and and CCONJ american_scientific_journal-522 188 39 ( ( PUNCT american_scientific_journal-522 188 40 ) ) PUNCT american_scientific_journal-522 188 41 1 1 NUM american_scientific_journal-522 188 42 m m NOUN american_scientific_journal-522 188 43 j j NOUN american_scientific_journal-522 188 44 i i PROPN american_scientific_journal-522 188 45 pθ= pθ= PROPN american_scientific_journal-522 188 46 + + CCONJ american_scientific_journal-522 188 47 − − PROPN american_scientific_journal-522 188 48 . . PUNCT american_scientific_journal-522 189 1 the the DET american_scientific_journal-522 189 2 discretized discretized ADJ american_scientific_journal-522 189 3 system system NOUN american_scientific_journal-522 189 4 of of ADP american_scientific_journal-522 189 5 equations equation NOUN american_scientific_journal-522 189 6 of of ADP american_scientific_journal-522 189 7 bending bend VERB american_scientific_journal-522 189 8 of of ADP american_scientific_journal-522 189 9 free free ADJ american_scientific_journal-522 189 10 vibration vibration NOUN american_scientific_journal-522 189 11 of of ADP american_scientific_journal-522 189 12 isotropic isotropic ADJ american_scientific_journal-522 189 13 plate plate NOUN american_scientific_journal-522 189 14 can can AUX american_scientific_journal-522 189 15 be be AUX american_scientific_journal-522 189 16 expressed express VERB american_scientific_journal-522 189 17 as as ADP american_scientific_journal-522 189 18 [ [ PUNCT american_scientific_journal-522 189 19 ] ] X american_scientific_journal-522 189 20 { { PUNCT american_scientific_journal-522 189 21 } } PUNCT american_scientific_journal-522 189 22 [ [ PUNCT american_scientific_journal-522 189 23 ] ] X american_scientific_journal-522 189 24 { { PUNCT american_scientific_journal-522 189 25 } } PUNCT american_scientific_journal-522 189 26 0=+ 0=+ PROPN american_scientific_journal-522 189 27 qkqm qkqm NOUN american_scientific_journal-522 189 28   NOUN american_scientific_journal-522 189 29 ( ( PUNCT american_scientific_journal-522 189 30 26 26 NUM american_scientific_journal-522 189 31 ) ) PUNCT american_scientific_journal-522 189 32 here here ADV american_scientific_journal-522 190 1 [ [ X american_scientific_journal-522 190 2 k k X american_scientific_journal-522 190 3 ] ] X american_scientific_journal-522 190 4 is be AUX american_scientific_journal-522 190 5 the the DET american_scientific_journal-522 190 6 stiffness stiffness ADJ american_scientific_journal-522 190 7 matrix matrix NOUN american_scientific_journal-522 190 8 of of ADP american_scientific_journal-522 190 9 the the DET american_scientific_journal-522 190 10 p p NOUN american_scientific_journal-522 190 11 - - PUNCT american_scientific_journal-522 190 12 element element NOUN american_scientific_journal-522 190 13 , , PUNCT american_scientific_journal-522 190 14 determined determine VERB american_scientific_journal-522 190 15 from from ADP american_scientific_journal-522 190 16 the the DET american_scientific_journal-522 190 17 strain strain NOUN american_scientific_journal-522 190 18 energy energy NOUN american_scientific_journal-522 190 19 [ [ X american_scientific_journal-522 190 20 𝐾𝐾 𝐾𝐾 NOUN american_scientific_journal-522 190 21 ] ] X american_scientific_journal-522 190 22 = = PUNCT american_scientific_journal-522 190 23 � � PROPN american_scientific_journal-522 191 1 [ [ X american_scientific_journal-522 191 2 𝐾𝐾𝑤𝑤𝑤𝑤 𝐾𝐾𝑤𝑤𝑤𝑤 X american_scientific_journal-522 191 3 ] ] X american_scientific_journal-522 192 1 [ [ X american_scientific_journal-522 192 2 𝐾𝐾wθx 𝐾𝐾wθx PROPN american_scientific_journal-522 192 3 ] ] PUNCT american_scientific_journal-522 192 4 � � PROPN american_scientific_journal-522 192 5 𝐾𝐾wθy 𝐾𝐾wθy PROPN american_scientific_journal-522 192 6 � � PROPN american_scientific_journal-522 193 1 [ [ X american_scientific_journal-522 193 2 𝐾𝐾wθx]𝑇𝑇 𝐾𝐾wθx]𝑇𝑇 X american_scientific_journal-522 193 3 [ [ X american_scientific_journal-522 193 4 𝐾𝐾θxθx 𝐾𝐾θxθx X american_scientific_journal-522 193 5 ] ] X american_scientific_journal-522 193 6 � � PROPN american_scientific_journal-522 193 7 𝐾𝐾θxθy 𝐾𝐾θxθy PROPN american_scientific_journal-522 193 8 � � PROPN american_scientific_journal-522 193 9 � � PROPN american_scientific_journal-522 193 10 𝐾𝐾wθy 𝐾𝐾wθy PROPN american_scientific_journal-522 193 11 � � PROPN american_scientific_journal-522 193 12 𝑇𝑇 𝑇𝑇 PROPN american_scientific_journal-522 193 13 � � PROPN american_scientific_journal-522 193 14 𝐾𝐾θxθy 𝐾𝐾θxθy PROPN american_scientific_journal-522 193 15 � � PROPN american_scientific_journal-522 193 16 𝑇𝑇 𝑇𝑇 PROPN american_scientific_journal-522 193 17 � � PROPN american_scientific_journal-522 193 18 𝐾𝐾θyθy 𝐾𝐾θyθy PROPN american_scientific_journal-522 193 19 � � PROPN american_scientific_journal-522 193 20 � � PROPN american_scientific_journal-522 193 21 ( ( PUNCT american_scientific_journal-522 193 22 27 27 NUM american_scientific_journal-522 193 23 ) ) PUNCT american_scientific_journal-522 194 1 where where SCONJ american_scientific_journal-522 194 2 [ [ PUNCT american_scientific_journal-522 194 3 ] ] X american_scientific_journal-522 194 4 [ [ PUNCT american_scientific_journal-522 194 5 ] ] X american_scientific_journal-522 194 6 [ [ PUNCT american_scientific_journal-522 194 7 ] ] X american_scientific_journal-522 194 8 [ [ PUNCT american_scientific_journal-522 194 9 ] ] X american_scientific_journal-522 194 10 [ [ PUNCT american_scientific_journal-522 194 11 ] ] X american_scientific_journal-522 194 12 [ [ PUNCT american_scientific_journal-522 194 13 ] ] X american_scientific_journal-522 194 14 [ [ PUNCT american_scientific_journal-522 194 15 ] ] X american_scientific_journal-522 194 16 [ [ PUNCT american_scientific_journal-522 194 17 ] ] X american_scientific_journal-522 194 18 [ [ PUNCT american_scientific_journal-522 194 19 ] ] X american_scientific_journal-522 194 20 [ [ PUNCT american_scientific_journal-522 194 21 ] ] X american_scientific_journal-522 194 22 [ [ PUNCT american_scientific_journal-522 194 23 ] ] X american_scientific_journal-522 194 24 [ [ PUNCT american_scientific_journal-522 194 25 ] ] X american_scientific_journal-522 194 26 [ [ PUNCT american_scientific_journal-522 194 27 ] ] SYM american_scientific_journal-522 194 28 1 1 NUM american_scientific_journal-522 194 29 1 1 NUM american_scientific_journal-522 194 30 2 2 NUM american_scientific_journal-522 194 31 2 2 NUM american_scientific_journal-522 194 32 2 2 NUM american_scientific_journal-522 194 33 2 2 NUM american_scientific_journal-522 194 34 2 2 NUM american_scientific_journal-522 194 35 2 2 NUM american_scientific_journal-522 194 36 11 11 NUM american_scientific_journal-522 194 37 12 12 NUM american_scientific_journal-522 194 38 22 22 NUM american_scientific_journal-522 194 39 4 4 NUM american_scientific_journal-522 194 40 2 2 NUM american_scientific_journal-522 194 41 2 2 NUM american_scientific_journal-522 194 42 2 2 NUM american_scientific_journal-522 194 43 2 2 NUM american_scientific_journal-522 194 44 2 2 NUM american_scientific_journal-522 194 45 2 2 NUM american_scientific_journal-522 194 46 4 4 NUM american_scientific_journal-522 194 47 2 2 NUM american_scientific_journal-522 194 48 2 2 NUM american_scientific_journal-522 194 49 0 0 NUM american_scientific_journal-522 194 50 0 0 NUM american_scientific_journal-522 194 51 33 33 NUM american_scientific_journal-522 194 52 44 44 NUM american_scientific_journal-522 194 53 44 44 NUM american_scientific_journal-522 194 54 2 2 NUM american_scientific_journal-522 194 55 2 2 NUM american_scientific_journal-522 194 56 2 2 NUM american_scientific_journal-522 194 57 2 2 NUM american_scientific_journal-522 194 58 2 2 NUM american_scientific_journal-522 194 59 2 2 NUM american_scientific_journal-522 194 60 2 2 NUM american_scientific_journal-522 194 61 4 4 NUM american_scientific_journal-522 194 62 t t NOUN american_scientific_journal-522 194 63 t t NOUN american_scientific_journal-522 194 64 t t PROPN american_scientific_journal-522 194 65 w w PROPN american_scientific_journal-522 194 66 w w PROPN american_scientific_journal-522 194 67 w w PROPN american_scientific_journal-522 194 68 w w PROPN american_scientific_journal-522 194 69 w w PROPN american_scientific_journal-522 194 70 w w PROPN american_scientific_journal-522 194 71 ww ww PROPN american_scientific_journal-522 194 72 t t PROPN american_scientific_journal-522 194 73 t t PROPN american_scientific_journal-522 194 74 t t PROPN american_scientific_journal-522 194 75 w w PROPN american_scientific_journal-522 194 76 w w PROPN american_scientific_journal-522 194 77 w w PROPN american_scientific_journal-522 194 78 w w PROPN american_scientific_journal-522 194 79 w w PROPN american_scientific_journal-522 194 80 w w PROPN american_scientific_journal-522 194 81 n n CCONJ american_scientific_journal-522 194 82 n n CCONJ american_scientific_journal-522 194 83 n n CCONJ american_scientific_journal-522 194 84 n n CCONJ american_scientific_journal-522 194 85 n n NOUN american_scientific_journal-522 194 86 nd nd NOUN american_scientific_journal-522 194 87 d d PROPN american_scientific_journal-522 194 88 d d X american_scientific_journal-522 194 89 k k PROPN american_scientific_journal-522 194 90 ab ab PROPN american_scientific_journal-522 194 91 a a PRON american_scientific_journal-522 194 92 a a DET american_scientific_journal-522 194 93 b b PROPN american_scientific_journal-522 194 94 b b PROPN american_scientific_journal-522 194 95 n n CCONJ american_scientific_journal-522 194 96 n n CCONJ american_scientific_journal-522 194 97 n n CCONJ american_scientific_journal-522 194 98 n n PROPN american_scientific_journal-522 194 99 n n INTJ american_scientific_journal-522 194 100 nd nd NOUN american_scientific_journal-522 195 1 f f PROPN american_scientific_journal-522 195 2 f f PROPN american_scientific_journal-522 196 1 d d PROPN american_scientific_journal-522 196 2 d d PROPN american_scientific_journal-522 196 3 a a DET american_scientific_journal-522 196 4 b b NOUN american_scientific_journal-522 196 5 a a DET american_scientific_journal-522 196 6 b b NOUN american_scientific_journal-522 196 7 a a DET american_scientific_journal-522 196 8 b b X american_scientific_journal-522 196 9 ξ ξ X american_scientific_journal-522 196 10 ξ ξ PROPN american_scientific_journal-522 196 11 ξ ξ PROPN american_scientific_journal-522 196 12 η η PROPN american_scientific_journal-522 196 13 η η PROPN american_scientific_journal-522 196 14 η η PROPN american_scientific_journal-522 196 15 ξ ξ PROPN american_scientific_journal-522 196 16 η η PROPN american_scientific_journal-522 196 17 ξ ξ PROPN american_scientific_journal-522 196 18 η η PROPN american_scientific_journal-522 196 19 ξ ξ PROPN american_scientific_journal-522 196 20 η η PROPN american_scientific_journal-522 196 21 ξ ξ PROPN american_scientific_journal-522 196 22 ξ ξ PROPN american_scientific_journal-522 196 23 η η PROPN american_scientific_journal-522 196 24 η η PROPN american_scientific_journal-522 196 25   PROPN american_scientific_journal-522 196 26 ∂ ∂ NUM american_scientific_journal-522 196 27 ∂ ∂ NUM american_scientific_journal-522 196 28 ∂ ∂ NUM american_scientific_journal-522 196 29 ∂ ∂ NUM american_scientific_journal-522 196 30 ∂ ∂ NUM american_scientific_journal-522 196 31 ∂ ∂ NOUN american_scientific_journal-522 196 32 = = NOUN american_scientific_journal-522 197 1 + + PUNCT american_scientific_journal-522 197 2 + + ADJ american_scientific_journal-522 197 3   ADJ american_scientific_journal-522 197 4 ∂ ∂ NUM american_scientific_journal-522 197 5 ∂ ∂ NUM american_scientific_journal-522 197 6 ∂ ∂ NUM american_scientific_journal-522 197 7 ∂ ∂ NUM american_scientific_journal-522 197 8 ∂ ∂ NOUN american_scientific_journal-522 197 9 ∂ ∂ PROPN american_scientific_journal-522 197 10 ∂ ∂ PROPN american_scientific_journal-522 197 11 ∂ ∂ NUM american_scientific_journal-522 197 12 ∂ ∂ NUM american_scientific_journal-522 197 13 ∂ ∂ NUM american_scientific_journal-522 197 14 ∂ ∂ NUM american_scientific_journal-522 197 15 ∂ ∂ NOUN american_scientific_journal-522 198 1 + + CCONJ american_scientific_journal-522 198 2 + + PUNCT american_scientific_journal-522 198 3 + + CCONJ american_scientific_journal-522 198 4   PROPN american_scientific_journal-522 198 5 ∂ ∂ NUM american_scientific_journal-522 198 6 ∂ ∂ NUM american_scientific_journal-522 198 7 ∂ ∂ NUM american_scientific_journal-522 198 8 ∂ ∂ NUM american_scientific_journal-522 198 9 ∂ ∂ NUM american_scientific_journal-522 198 10 ∂ ∂ NUM american_scientific_journal-522 198 11 ∂ ∂ NUM american_scientific_journal-522 198 12 ∂ ∂ NOUN american_scientific_journal-522 198 13   NUM american_scientific_journal-522 199 1 ∫ ∫ PROPN american_scientific_journal-522 199 2 ∫ ∫ PROPN american_scientific_journal-522 199 3 ( ( PUNCT american_scientific_journal-522 199 4 28 28 NUM american_scientific_journal-522 199 5 ) ) PUNCT american_scientific_journal-522 199 6 [ [ PUNCT american_scientific_journal-522 199 7 ] ] X american_scientific_journal-522 199 8 [ [ PUNCT american_scientific_journal-522 199 9 ] ] X american_scientific_journal-522 199 10 [ [ PUNCT american_scientific_journal-522 199 11 ] ] X american_scientific_journal-522 199 12 [ [ PUNCT american_scientific_journal-522 199 13 ] ] X american_scientific_journal-522 199 14 [ [ PUNCT american_scientific_journal-522 199 15 ] ] X american_scientific_journal-522 199 16 [ [ PUNCT american_scientific_journal-522 199 17 ] ] X american_scientific_journal-522 199 18 [ [ PUNCT american_scientific_journal-522 199 19 ] ] X american_scientific_journal-522 199 20 [ [ PUNCT american_scientific_journal-522 199 21 ] ] X american_scientific_journal-522 199 22 [ [ PUNCT american_scientific_journal-522 199 23 ] ] SYM american_scientific_journal-522 199 24 1 1 NUM american_scientific_journal-522 199 25 1 1 NUM american_scientific_journal-522 199 26 2 2 NUM american_scientific_journal-522 199 27 2 2 NUM american_scientific_journal-522 199 28 2 2 NUM american_scientific_journal-522 199 29 3311 3311 NUM american_scientific_journal-522 199 30 12 12 NUM american_scientific_journal-522 199 31 2 2 NUM american_scientific_journal-522 199 32 2 2 NUM american_scientific_journal-522 199 33 2 2 NUM american_scientific_journal-522 199 34 2 2 NUM american_scientific_journal-522 199 35 2 2 NUM american_scientific_journal-522 199 36 0 0 NUM american_scientific_journal-522 199 37 0 0 NUM american_scientific_journal-522 199 38 44 44 NUM american_scientific_journal-522 199 39 wθx wθx NOUN american_scientific_journal-522 199 40 22 22 NUM american_scientific_journal-522 199 41 2 2 NUM american_scientific_journal-522 199 42 2 2 NUM american_scientific_journal-522 199 43 t t NOUN american_scientific_journal-522 199 44 t t NOUN american_scientific_journal-522 199 45 t t PROPN american_scientific_journal-522 199 46 w w PROPN american_scientific_journal-522 199 47 w w PROPN american_scientific_journal-522 199 48 w w PROPN american_scientific_journal-522 199 49 t t PROPN american_scientific_journal-522 199 50 w w PROPN american_scientific_journal-522 199 51 n n PROPN american_scientific_journal-522 199 52 n n CCONJ american_scientific_journal-522 199 53 n n CCONJ american_scientific_journal-522 199 54 n n CCONJ american_scientific_journal-522 199 55 n n CCONJ american_scientific_journal-522 199 56 nee nee NOUN american_scientific_journal-522 199 57 e e PROPN american_scientific_journal-522 199 58 ab ab PROPN american_scientific_journal-522 199 59 a a DET american_scientific_journal-522 199 60 a a PRON american_scientific_journal-522 199 61 b b X american_scientific_journal-522 199 62 ab ab PROPN american_scientific_journal-522 199 63 nf nf PROPN american_scientific_journal-522 199 64 n n PROPN american_scientific_journal-522 199 65 d d PROPN american_scientific_journal-522 199 66 d d PROPN american_scientific_journal-522 199 67 a a DET american_scientific_journal-522 199 68 k k NOUN american_scientific_journal-522 199 69 θ θ NOUN american_scientific_journal-522 199 70 θ θ NOUN american_scientific_journal-522 199 71 θ θ X american_scientific_journal-522 199 72 θ θ PUNCT american_scientific_journal-522 199 73 ξ ξ X american_scientific_journal-522 199 74 ξ ξ X american_scientific_journal-522 199 75 ξ ξ PROPN american_scientific_journal-522 199 76 η η PROPN american_scientific_journal-522 199 77 ηξ ηξ PROPN american_scientific_journal-522 199 78 η η PROPN american_scientific_journal-522 199 79 ξ ξ PROPN american_scientific_journal-522 199 80 η η PROPN american_scientific_journal-522 199 81 ξ ξ PROPN american_scientific_journal-522 199 82   PROPN american_scientific_journal-522 199 83 ∂ ∂ NUM american_scientific_journal-522 199 84 ∂ ∂ NUM american_scientific_journal-522 199 85 ∂ ∂ NUM american_scientific_journal-522 199 86 ∂ ∂ NUM american_scientific_journal-522 199 87 ∂ ∂ NUM american_scientific_journal-522 199 88 ∂ ∂ NOUN american_scientific_journal-522 199 89 = = NOUN american_scientific_journal-522 200 1 + + PUNCT american_scientific_journal-522 200 2 + + ADJ american_scientific_journal-522 200 3   ADJ american_scientific_journal-522 200 4 ∂ ∂ NUM american_scientific_journal-522 200 5 ∂ ∂ NUM american_scientific_journal-522 200 6 ∂ ∂ NUM american_scientific_journal-522 200 7 ∂ ∂ NOUN american_scientific_journal-522 200 8 ∂∂ ∂∂ NOUN american_scientific_journal-522 200 9 ∂ ∂ NOUN american_scientific_journal-522 200 10 ∂ ∂ NOUN american_scientific_journal-522 200 11 + + CCONJ american_scientific_journal-522 200 12   PROPN american_scientific_journal-522 200 13 ∂ ∂ NOUN american_scientific_journal-522 200 14   NUM american_scientific_journal-522 201 1 ∫ ∫ PROPN american_scientific_journal-522 201 2 ∫ ∫ PROPN american_scientific_journal-522 201 3 ( ( PUNCT american_scientific_journal-522 201 4 29 29 NUM american_scientific_journal-522 201 5 ) ) PUNCT american_scientific_journal-522 201 6 [ [ PUNCT american_scientific_journal-522 201 7 ] ] X american_scientific_journal-522 201 8 [ [ PUNCT american_scientific_journal-522 201 9 ] ] X american_scientific_journal-522 201 10 [ [ PUNCT american_scientific_journal-522 201 11 ] ] X american_scientific_journal-522 201 12 [ [ PUNCT american_scientific_journal-522 201 13 ] ] X american_scientific_journal-522 201 14 [ [ PUNCT american_scientific_journal-522 201 15 ] ] X american_scientific_journal-522 201 16 [ [ PUNCT american_scientific_journal-522 201 17 ] ] X american_scientific_journal-522 201 18 [ [ PUNCT american_scientific_journal-522 201 19 ] ] X american_scientific_journal-522 201 20 [ [ PUNCT american_scientific_journal-522 201 21 ] ] SYM american_scientific_journal-522 201 22 1 1 NUM american_scientific_journal-522 201 23 1 1 NUM american_scientific_journal-522 201 24 2 2 NUM american_scientific_journal-522 201 25 2 2 NUM american_scientific_journal-522 201 26 2 2 NUM american_scientific_journal-522 201 27 3312 3312 NUM american_scientific_journal-522 201 28 22 22 NUM american_scientific_journal-522 201 29 2 2 NUM american_scientific_journal-522 201 30 2 2 NUM american_scientific_journal-522 201 31 3 3 NUM american_scientific_journal-522 201 32 2 2 NUM american_scientific_journal-522 201 33 2 2 NUM american_scientific_journal-522 201 34 0 0 NUM american_scientific_journal-522 201 35 0 0 NUM american_scientific_journal-522 201 36 55 55 NUM american_scientific_journal-522 201 37 wθy wθy NOUN american_scientific_journal-522 201 38 42 42 NUM american_scientific_journal-522 201 39 2 2 NUM american_scientific_journal-522 201 40 2 2 NUM american_scientific_journal-522 201 41 t t NOUN american_scientific_journal-522 201 42 t t NOUN american_scientific_journal-522 201 43 t t PROPN american_scientific_journal-522 201 44 w w PROPN american_scientific_journal-522 201 45 w w PROPN american_scientific_journal-522 201 46 w w PROPN american_scientific_journal-522 201 47 t t PROPN american_scientific_journal-522 201 48 w w PROPN american_scientific_journal-522 201 49 n n PROPN american_scientific_journal-522 201 50 n n CCONJ american_scientific_journal-522 201 51 n n CCONJ american_scientific_journal-522 201 52 n n CCONJ american_scientific_journal-522 201 53 n n CCONJ american_scientific_journal-522 201 54 nee nee NOUN american_scientific_journal-522 201 55 e e PROPN american_scientific_journal-522 201 56 a a PRON american_scientific_journal-522 201 57 b b NOUN american_scientific_journal-522 201 58 a a DET american_scientific_journal-522 201 59 b b PROPN american_scientific_journal-522 201 60 b b PROPN american_scientific_journal-522 201 61 a a DET american_scientific_journal-522 201 62 b b PROPN american_scientific_journal-522 201 63 nf nf NOUN american_scientific_journal-522 201 64 n n PROPN american_scientific_journal-522 202 1 d d NOUN american_scientific_journal-522 202 2 k k PROPN american_scientific_journal-522 202 3 d d X american_scientific_journal-522 202 4 a a DET american_scientific_journal-522 202 5 θ θ NOUN american_scientific_journal-522 202 6 θ θ NOUN american_scientific_journal-522 202 7 θ θ X american_scientific_journal-522 202 8 θ θ PROPN american_scientific_journal-522 202 9 η η PROPN american_scientific_journal-522 202 10 η η PROPN american_scientific_journal-522 202 11 ξ ξ PROPN american_scientific_journal-522 202 12 η η PROPN american_scientific_journal-522 202 13 ξξ ξξ ADP american_scientific_journal-522 202 14 η η PROPN american_scientific_journal-522 202 15 ξ ξ PROPN american_scientific_journal-522 202 16 η η PROPN american_scientific_journal-522 202 17 η η PROPN american_scientific_journal-522 202 18   PROPN american_scientific_journal-522 202 19 ∂ ∂ NUM american_scientific_journal-522 202 20 ∂ ∂ NUM american_scientific_journal-522 202 21 ∂ ∂ NUM american_scientific_journal-522 202 22 ∂ ∂ NUM american_scientific_journal-522 202 23 ∂ ∂ NUM american_scientific_journal-522 202 24 ∂ ∂ NOUN american_scientific_journal-522 202 25   NOUN american_scientific_journal-522 202 26   NUM american_scientific_journal-522 202 27 = = SYM american_scientific_journal-522 202 28 + + PUNCT american_scientific_journal-522 202 29 + + ADJ american_scientific_journal-522 202 30   ADJ american_scientific_journal-522 202 31   NOUN american_scientific_journal-522 202 32 ∂ ∂ NUM american_scientific_journal-522 202 33 ∂ ∂ NUM american_scientific_journal-522 202 34 ∂ ∂ NUM american_scientific_journal-522 202 35 ∂ ∂ NOUN american_scientific_journal-522 202 36 ∂∂ ∂∂ NOUN american_scientific_journal-522 202 37 ∂ ∂ NOUN american_scientific_journal-522 202 38 ∂ ∂ NOUN american_scientific_journal-522 202 39 + + CCONJ american_scientific_journal-522 202 40   PROPN american_scientific_journal-522 202 41 ∂ ∂ NOUN american_scientific_journal-522 202 42   NUM american_scientific_journal-522 202 43 ∫ ∫ PROPN american_scientific_journal-522 202 44 ∫ ∫ PROPN american_scientific_journal-522 202 45 ( ( PUNCT american_scientific_journal-522 202 46 30 30 NUM american_scientific_journal-522 202 47 ) ) PUNCT american_scientific_journal-522 202 48 7 7 NUM american_scientific_journal-522 202 49 american american ADJ american_scientific_journal-522 202 50 scientific scientific ADJ american_scientific_journal-522 202 51 research research NOUN american_scientific_journal-522 202 52 journal journal NOUN american_scientific_journal-522 202 53 for for ADP american_scientific_journal-522 202 54 engineering engineering NOUN american_scientific_journal-522 202 55 , , PUNCT american_scientific_journal-522 202 56 technology technology NOUN american_scientific_journal-522 202 57 , , PUNCT american_scientific_journal-522 202 58 and and CCONJ american_scientific_journal-522 202 59 sciences science NOUN american_scientific_journal-522 202 60 ( ( PUNCT american_scientific_journal-522 202 61 asrjets asrjet NOUN american_scientific_journal-522 202 62 ) ) PUNCT american_scientific_journal-522 202 63 ( ( PUNCT american_scientific_journal-522 202 64 2014 2014 NUM american_scientific_journal-522 202 65 ) ) PUNCT american_scientific_journal-522 202 66 volume volume NOUN american_scientific_journal-522 202 67 9 9 NUM american_scientific_journal-522 202 68 , , PUNCT american_scientific_journal-522 202 69 no no DET american_scientific_journal-522 202 70 1 1 NUM american_scientific_journal-522 202 71 , , PUNCT american_scientific_journal-522 202 72 pp pp ADV american_scientific_journal-522 202 73 1 1 NUM american_scientific_journal-522 202 74 - - SYM american_scientific_journal-522 202 75 19 19 NUM american_scientific_journal-522 202 76 [ [ PUNCT american_scientific_journal-522 202 77 ] ] X american_scientific_journal-522 202 78 [ [ PUNCT american_scientific_journal-522 202 79 ] ] X american_scientific_journal-522 202 80 [ [ PUNCT american_scientific_journal-522 202 81 ] ] X american_scientific_journal-522 202 82 [ [ PUNCT american_scientific_journal-522 202 83 ] ] X american_scientific_journal-522 202 84 [ [ PUNCT american_scientific_journal-522 202 85 ] ] X american_scientific_journal-522 202 86 [ [ PUNCT american_scientific_journal-522 202 87 ] ] X american_scientific_journal-522 202 88 [ [ PUNCT american_scientific_journal-522 202 89 ] ] SYM american_scientific_journal-522 202 90 1 1 NUM american_scientific_journal-522 202 91 1 1 NUM american_scientific_journal-522 202 92 3311 3311 NUM american_scientific_journal-522 202 93 442 442 NUM american_scientific_journal-522 202 94 0 0 NUM american_scientific_journal-522 202 95 θxθ θxθ ADJ american_scientific_journal-522 202 96 2 2 NUM american_scientific_journal-522 202 97 0 0 NUM american_scientific_journal-522 202 98 x x SYM american_scientific_journal-522 202 99 t t PROPN american_scientific_journal-522 202 100 t t PROPN american_scientific_journal-522 202 101 tn tn PROPN american_scientific_journal-522 202 102 n n PROPN american_scientific_journal-522 202 103 n n PROPN american_scientific_journal-522 202 104 ngg ngg PROPN american_scientific_journal-522 202 105 ab ab PROPN american_scientific_journal-522 202 106 f f PROPN american_scientific_journal-522 202 107 n n CCONJ american_scientific_journal-522 202 108 n n PROPN american_scientific_journal-522 202 109 d d PROPN american_scientific_journal-522 202 110 d d PROPN american_scientific_journal-522 202 111 a a DET american_scientific_journal-522 202 112 b b NOUN american_scientific_journal-522 202 113 k k NOUN american_scientific_journal-522 202 114 θ θ NOUN american_scientific_journal-522 202 115 θ θ NOUN american_scientific_journal-522 202 116 θ θ X american_scientific_journal-522 202 117 θ θ NOUN american_scientific_journal-522 202 118 θ θ X american_scientific_journal-522 202 119 θ θ X american_scientific_journal-522 202 120 ξ ξ X american_scientific_journal-522 202 121 η η X american_scientific_journal-522 202 122 ξ ξ PROPN american_scientific_journal-522 202 123 ξ ξ PROPN american_scientific_journal-522 202 124 η η PROPN american_scientific_journal-522 202 125 η η PROPN american_scientific_journal-522 202 126   PROPN american_scientific_journal-522 202 127 ∂ ∂ PROPN american_scientific_journal-522 202 128 ∂ ∂ NUM american_scientific_journal-522 202 129 ∂ ∂ NUM american_scientific_journal-522 202 130 ∂ ∂ NOUN american_scientific_journal-522 202 131 = = NOUN american_scientific_journal-522 203 1 + + PUNCT american_scientific_journal-522 203 2 + + ADJ american_scientific_journal-522 203 3   ADJ american_scientific_journal-522 203 4   PROPN american_scientific_journal-522 203 5 ∂ ∂ NOUN american_scientific_journal-522 203 6 ∂ ∂ NUM american_scientific_journal-522 203 7 ∂ ∂ NUM american_scientific_journal-522 203 8 ∂ ∂ NOUN american_scientific_journal-522 203 9   NOUN american_scientific_journal-522 203 10 ∫ ∫ VERB american_scientific_journal-522 203 11 ∫ ∫ PROPN american_scientific_journal-522 203 12 ( ( PUNCT american_scientific_journal-522 203 13 31 31 NUM american_scientific_journal-522 203 14 ) ) PUNCT american_scientific_journal-522 204 1 [ [ PUNCT american_scientific_journal-522 204 2 ] ] X american_scientific_journal-522 204 3 [ [ PUNCT american_scientific_journal-522 204 4 ] ] X american_scientific_journal-522 204 5 [ [ PUNCT american_scientific_journal-522 204 6 ] ] X american_scientific_journal-522 204 7 [ [ PUNCT american_scientific_journal-522 204 8 ] ] X american_scientific_journal-522 204 9 [ [ PUNCT american_scientific_journal-522 204 10 ] ] X american_scientific_journal-522 204 11 [ [ PUNCT american_scientific_journal-522 204 12 ] ] SYM american_scientific_journal-522 204 13 1 1 NUM american_scientific_journal-522 204 14 1 1 NUM american_scientific_journal-522 204 15 33 33 NUM american_scientific_journal-522 204 16 22 22 NUM american_scientific_journal-522 204 17 44θyθy 44θyθy NUM american_scientific_journal-522 204 18 2 2 NUM american_scientific_journal-522 204 19 2 2 NUM american_scientific_journal-522 204 20 0 0 NUM american_scientific_journal-522 204 21 0 0 NUM american_scientific_journal-522 204 22 t t PROPN american_scientific_journal-522 204 23 t t PROPN american_scientific_journal-522 204 24 tn tn PROPN american_scientific_journal-522 204 25 n n PROPN american_scientific_journal-522 204 26 n n PRON american_scientific_journal-522 204 27 ng ng PROPN american_scientific_journal-522 204 28 g g PROPN american_scientific_journal-522 204 29 ab ab PROPN american_scientific_journal-522 204 30 f f PROPN american_scientific_journal-522 204 31 n n CCONJ american_scientific_journal-522 204 32 n n PROPN american_scientific_journal-522 204 33 d d PROPN american_scientific_journal-522 204 34 d d PROPN american_scientific_journal-522 204 35 a a DET american_scientific_journal-522 204 36 b b NOUN american_scientific_journal-522 204 37 k k NOUN american_scientific_journal-522 204 38 θ θ NOUN american_scientific_journal-522 204 39 θ θ NOUN american_scientific_journal-522 204 40 θ θ X american_scientific_journal-522 204 41 θ θ NOUN american_scientific_journal-522 204 42 θ θ X american_scientific_journal-522 204 43 θ θ X american_scientific_journal-522 204 44 ξ ξ X american_scientific_journal-522 204 45 η η X american_scientific_journal-522 204 46 ξ ξ PROPN american_scientific_journal-522 204 47 ξ ξ PROPN american_scientific_journal-522 204 48 η η PROPN american_scientific_journal-522 204 49 η η PROPN american_scientific_journal-522 204 50   PROPN american_scientific_journal-522 204 51 ∂ ∂ PROPN american_scientific_journal-522 204 52 ∂ ∂ NUM american_scientific_journal-522 204 53 ∂ ∂ NUM american_scientific_journal-522 204 54 ∂ ∂ NOUN american_scientific_journal-522 204 55   NOUN american_scientific_journal-522 204 56   NUM american_scientific_journal-522 204 57 = = SYM american_scientific_journal-522 204 58 + + PUNCT american_scientific_journal-522 204 59 + + ADJ american_scientific_journal-522 204 60   ADJ american_scientific_journal-522 204 61   ADJ american_scientific_journal-522 204 62   NOUN american_scientific_journal-522 204 63 ∂ ∂ NUM american_scientific_journal-522 204 64 ∂ ∂ NUM american_scientific_journal-522 204 65 ∂ ∂ NUM american_scientific_journal-522 204 66 ∂ ∂ NOUN american_scientific_journal-522 204 67   NOUN american_scientific_journal-522 204 68 ∫ ∫ VERB american_scientific_journal-522 204 69 ∫ ∫ PROPN american_scientific_journal-522 204 70 ( ( PUNCT american_scientific_journal-522 204 71 32 32 NUM american_scientific_journal-522 204 72 ) ) PUNCT american_scientific_journal-522 204 73 [ [ PUNCT american_scientific_journal-522 204 74 ] ] X american_scientific_journal-522 204 75 [ [ PUNCT american_scientific_journal-522 204 76 ] ] X american_scientific_journal-522 204 77 [ [ PUNCT american_scientific_journal-522 204 78 ] ] X american_scientific_journal-522 204 79 [ [ PUNCT american_scientific_journal-522 204 80 ] ] SYM american_scientific_journal-522 204 81 1 1 NUM american_scientific_journal-522 204 82 1 1 NUM american_scientific_journal-522 204 83 3312 3312 NUM american_scientific_journal-522 204 84 0 0 NUM american_scientific_journal-522 204 85 θ θ NOUN american_scientific_journal-522 204 86 0 0 NUM american_scientific_journal-522 204 87 xθy xθy PROPN american_scientific_journal-522 205 1 22 22 NUM american_scientific_journal-522 205 2 t t PROPN american_scientific_journal-522 205 3 tn tn PROPN american_scientific_journal-522 205 4 n n PROPN american_scientific_journal-522 205 5 n n PROPN american_scientific_journal-522 205 6 ngg ngg PROPN american_scientific_journal-522 206 1 ab ab PROPN american_scientific_journal-522 206 2 d d PROPN american_scientific_journal-522 206 3 d d PROPN american_scientific_journal-522 206 4 ab ab PROPN american_scientific_journal-522 206 5 ab ab PROPN american_scientific_journal-522 206 6 k k PROPN american_scientific_journal-522 206 7 θ θ X american_scientific_journal-522 206 8 θ θ PUNCT american_scientific_journal-522 206 9 θ θ X american_scientific_journal-522 206 10 θ θ X american_scientific_journal-522 206 11 ξ ξ X american_scientific_journal-522 206 12 η η X american_scientific_journal-522 206 13 ξ ξ PROPN american_scientific_journal-522 206 14 η η PROPN american_scientific_journal-522 206 15 η η PROPN american_scientific_journal-522 206 16 ξ ξ PROPN american_scientific_journal-522 206 17   PROPN american_scientific_journal-522 206 18 ∂ ∂ NOUN american_scientific_journal-522 206 19 ∂ ∂ NUM american_scientific_journal-522 206 20 ∂ ∂ NUM american_scientific_journal-522 206 21 ∂ ∂ NOUN american_scientific_journal-522 206 22   NOUN american_scientific_journal-522 206 23   PROPN american_scientific_journal-522 206 24 = = SYM american_scientific_journal-522 207 1 + + ADJ american_scientific_journal-522 207 2   ADJ american_scientific_journal-522 207 3   ADJ american_scientific_journal-522 207 4   NOUN american_scientific_journal-522 207 5 ∂ ∂ NUM american_scientific_journal-522 207 6 ∂ ∂ NUM american_scientific_journal-522 207 7 ∂ ∂ NUM american_scientific_journal-522 207 8 ∂ ∂ NOUN american_scientific_journal-522 207 9   NOUN american_scientific_journal-522 207 10 ∫ ∫ VERB american_scientific_journal-522 207 11 ∫ ∫ PROPN american_scientific_journal-522 207 12 ( ( PUNCT american_scientific_journal-522 207 13 33 33 NUM american_scientific_journal-522 207 14 ) ) PUNCT american_scientific_journal-522 208 1 [ [ X american_scientific_journal-522 208 2 m]is m]is X american_scientific_journal-522 208 3 themass themass NOUN american_scientific_journal-522 208 4 matrix matrix NOUN american_scientific_journal-522 208 5 of of ADP american_scientific_journal-522 208 6 the the DET american_scientific_journal-522 208 7 p p NOUN american_scientific_journal-522 208 8 - - PUNCT american_scientific_journal-522 208 9 element element NOUN american_scientific_journal-522 208 10 , , PUNCT american_scientific_journal-522 208 11 given give VERB american_scientific_journal-522 208 12 by by ADP american_scientific_journal-522 208 13 the the DET american_scientific_journal-522 208 14 following follow VERB american_scientific_journal-522 208 15 relation relation NOUN american_scientific_journal-522 208 16 [ [ X american_scientific_journal-522 208 17 𝑀𝑀 𝑀𝑀 X american_scientific_journal-522 208 18 ] ] X american_scientific_journal-522 208 19 = = PUNCT american_scientific_journal-522 208 20 � � PROPN american_scientific_journal-522 208 21 [ [ X american_scientific_journal-522 208 22 𝑀𝑀𝑤𝑤𝑤𝑤 𝑀𝑀𝑤𝑤𝑤𝑤 PROPN american_scientific_journal-522 208 23 ] ] PUNCT american_scientific_journal-522 209 1 [ [ X american_scientific_journal-522 209 2 𝑀𝑀wθx 𝑀𝑀wθx X american_scientific_journal-522 209 3 ] ] X american_scientific_journal-522 210 1 [ [ X american_scientific_journal-522 210 2 𝑀𝑀wθy 𝑀𝑀wθy X american_scientific_journal-522 210 3 ] ] X american_scientific_journal-522 211 1 [ [ X american_scientific_journal-522 211 2 𝑀𝑀wθx]𝑇𝑇 𝑀𝑀wθx]𝑇𝑇 ADP american_scientific_journal-522 211 3 [ [ X american_scientific_journal-522 211 4 𝑀𝑀θxθx 𝑀𝑀θxθx X american_scientific_journal-522 211 5 ] ] X american_scientific_journal-522 211 6 [ [ X american_scientific_journal-522 211 7 𝑀𝑀θxθy 𝑀𝑀θxθy X american_scientific_journal-522 211 8 ] ] X american_scientific_journal-522 211 9 [ [ X american_scientific_journal-522 211 10 𝑀𝑀wθy]𝑇𝑇 𝑀𝑀wθy]𝑇𝑇 X american_scientific_journal-522 211 11 [ [ X american_scientific_journal-522 211 12 𝑀𝑀θxθy]𝑇𝑇 𝑀𝑀θxθy]𝑇𝑇 X american_scientific_journal-522 211 13 [ [ X american_scientific_journal-522 211 14 𝑀𝑀θyθy 𝑀𝑀θyθy X american_scientific_journal-522 211 15 ] ] X american_scientific_journal-522 211 16 � � PROPN american_scientific_journal-522 211 17 ( ( PUNCT american_scientific_journal-522 211 18 34 34 NUM american_scientific_journal-522 211 19 ) ) PUNCT american_scientific_journal-522 211 20 where where SCONJ american_scientific_journal-522 211 21 [ [ PUNCT american_scientific_journal-522 211 22 ] ] X american_scientific_journal-522 211 23 [ [ PUNCT american_scientific_journal-522 211 24 ] ] X american_scientific_journal-522 211 25 [ [ PUNCT american_scientific_journal-522 211 26 ] ] X american_scientific_journal-522 211 27 [ [ PUNCT american_scientific_journal-522 211 28 ] ] X american_scientific_journal-522 211 29 [ [ PUNCT american_scientific_journal-522 211 30 ] ] X american_scientific_journal-522 211 31 [ [ PUNCT american_scientific_journal-522 211 32 ] ] X american_scientific_journal-522 211 33 [ [ PUNCT american_scientific_journal-522 211 34 ] ] SYM american_scientific_journal-522 211 35 1 1 NUM american_scientific_journal-522 211 36 1 1 NUM american_scientific_journal-522 211 37 2 2 NUM american_scientific_journal-522 211 38 2 2 NUM american_scientific_journal-522 211 39 0 0 NUM american_scientific_journal-522 211 40 0 0 NUM american_scientific_journal-522 212 1 t t NOUN american_scientific_journal-522 213 1 t t PROPN american_scientific_journal-522 214 1 t t PROPN american_scientific_journal-522 215 1 w w PROPN american_scientific_journal-522 216 1 w w PROPN american_scientific_journal-522 217 1 w w NOUN american_scientific_journal-522 218 1 we we PRON american_scientific_journal-522 219 1 e e PROPN american_scientific_journal-522 219 2 ww ww PROPN american_scientific_journal-522 219 3 a a DET american_scientific_journal-522 219 4 w w PROPN american_scientific_journal-522 219 5 w w PROPN american_scientific_journal-522 219 6 n n CCONJ american_scientific_journal-522 219 7 n n CCONJ american_scientific_journal-522 219 8 n n CCONJ american_scientific_journal-522 219 9 n n NOUN american_scientific_journal-522 219 10 m m VERB american_scientific_journal-522 219 11 a a DET american_scientific_journal-522 219 12 b b PROPN american_scientific_journal-522 219 13 n n CCONJ american_scientific_journal-522 219 14 n n NOUN american_scientific_journal-522 219 15 d d PROPN american_scientific_journal-522 219 16 d d PROPN american_scientific_journal-522 219 17 a a DET american_scientific_journal-522 219 18 b b PROPN american_scientific_journal-522 219 19 ρ ρ PROPN american_scientific_journal-522 219 20 ρρ ρρ PROPN american_scientific_journal-522 219 21 ξ ξ PROPN american_scientific_journal-522 219 22 η η X american_scientific_journal-522 219 23 ξ ξ PROPN american_scientific_journal-522 219 24 ξ ξ PROPN american_scientific_journal-522 219 25 η η PROPN american_scientific_journal-522 219 26 η η PROPN american_scientific_journal-522 219 27   PROPN american_scientific_journal-522 219 28 ∂ ∂ PROPN american_scientific_journal-522 219 29 ∂ ∂ NUM american_scientific_journal-522 219 30 ∂ ∂ NUM american_scientific_journal-522 219 31 ∂ ∂ NOUN american_scientific_journal-522 219 32 = = NOUN american_scientific_journal-522 220 1 + + PUNCT american_scientific_journal-522 220 2 + + ADJ american_scientific_journal-522 220 3   ADJ american_scientific_journal-522 220 4   PROPN american_scientific_journal-522 220 5 ∂ ∂ NOUN american_scientific_journal-522 220 6 ∂ ∂ NUM american_scientific_journal-522 220 7 ∂ ∂ NUM american_scientific_journal-522 220 8 ∂ ∂ NOUN american_scientific_journal-522 220 9   NOUN american_scientific_journal-522 220 10 ∫ ∫ VERB american_scientific_journal-522 220 11 ∫ ∫ PROPN american_scientific_journal-522 220 12 ( ( PUNCT american_scientific_journal-522 220 13 35 35 NUM american_scientific_journal-522 220 14 ) ) PUNCT american_scientific_journal-522 220 15 [ [ PUNCT american_scientific_journal-522 220 16 ] ] X american_scientific_journal-522 220 17 [ [ PUNCT american_scientific_journal-522 220 18 ] ] X american_scientific_journal-522 220 19 [ [ PUNCT american_scientific_journal-522 220 20 ] ] X american_scientific_journal-522 220 21 1 1 NUM american_scientific_journal-522 220 22 1 1 NUM american_scientific_journal-522 220 23 0 0 NUM american_scientific_journal-522 220 24 0 0 NUM american_scientific_journal-522 221 1 t t PROPN american_scientific_journal-522 221 2 w w PROPN american_scientific_journal-522 221 3 w w PROPN american_scientific_journal-522 221 4 x x SYM american_scientific_journal-522 221 5 g g PROPN american_scientific_journal-522 221 6 n n INTJ american_scientific_journal-522 221 7 m m VERB american_scientific_journal-522 221 8 a a DET american_scientific_journal-522 221 9 b b NOUN american_scientific_journal-522 221 10 n n NOUN american_scientific_journal-522 222 1 d d NOUN american_scientific_journal-522 222 2 dθ dθ PROPN american_scientific_journal-522 222 3 θρ θρ PROPN american_scientific_journal-522 222 4 ξ ξ PROPN american_scientific_journal-522 222 5 η η X american_scientific_journal-522 222 6 ξ ξ PROPN american_scientific_journal-522 222 7 ∂ ∂ NUM american_scientific_journal-522 222 8 = = SYM american_scientific_journal-522 222 9 ∂∫ ∂∫ PROPN american_scientific_journal-522 222 10 ∫ ∫ PROPN american_scientific_journal-522 222 11 ( ( PUNCT american_scientific_journal-522 222 12 36 36 NUM american_scientific_journal-522 222 13 ) ) PUNCT american_scientific_journal-522 223 1 [ [ PUNCT american_scientific_journal-522 223 2 ] ] X american_scientific_journal-522 223 3 [ [ PUNCT american_scientific_journal-522 223 4 ] ] X american_scientific_journal-522 223 5 1 1 NUM american_scientific_journal-522 223 6 1 1 NUM american_scientific_journal-522 223 7 0 0 NUM american_scientific_journal-522 223 8 0 0 NUM american_scientific_journal-522 224 1 t t PROPN american_scientific_journal-522 225 1 w w PROPN american_scientific_journal-522 226 1 w w PROPN american_scientific_journal-522 227 1 y y PROPN american_scientific_journal-522 228 1 g g PROPN american_scientific_journal-522 229 1 n n PROPN american_scientific_journal-522 230 1 m m PROPN american_scientific_journal-522 230 2 ab ab PROPN american_scientific_journal-522 231 1 n n PROPN american_scientific_journal-522 231 2 d d PROPN american_scientific_journal-522 231 3 dθ dθ PROPN american_scientific_journal-522 231 4 θρ θρ PROPN american_scientific_journal-522 231 5 ξ ξ PROPN american_scientific_journal-522 231 6 η η PROPN american_scientific_journal-522 231 7 η η PROPN american_scientific_journal-522 231 8 ∂ ∂ PROPN american_scientific_journal-522 231 9   PROPN american_scientific_journal-522 231 10   PROPN american_scientific_journal-522 231 11 = = NUM american_scientific_journal-522 231 12   NOUN american_scientific_journal-522 231 13   NOUN american_scientific_journal-522 231 14 ∂∫ ∂∫ NOUN american_scientific_journal-522 231 15 ∫ ∫ NOUN american_scientific_journal-522 231 16 ( ( PUNCT american_scientific_journal-522 231 17 37 37 NUM american_scientific_journal-522 231 18 ) ) PUNCT american_scientific_journal-522 231 19 [ [ PUNCT american_scientific_journal-522 231 20 ] ] X american_scientific_journal-522 231 21 [ [ PUNCT american_scientific_journal-522 231 22 ] ] X american_scientific_journal-522 231 23 [ [ PUNCT american_scientific_journal-522 231 24 ] ] X american_scientific_journal-522 231 25 θxθx θxθx ADP american_scientific_journal-522 231 26 θy θy PRON american_scientific_journal-522 231 27 1 1 NUM american_scientific_journal-522 231 28 1 1 NUM american_scientific_journal-522 231 29 0 0 NUM american_scientific_journal-522 231 30 θy θy NOUN american_scientific_journal-522 231 31 0 0 NUM american_scientific_journal-522 232 1 t t INTJ american_scientific_journal-522 232 2 hm hm INTJ american_scientific_journal-522 232 3 m m VERB american_scientific_journal-522 232 4 ab ab PROPN american_scientific_journal-522 232 5 n n CCONJ american_scientific_journal-522 232 6 n n PROPN american_scientific_journal-522 233 1 d d NOUN american_scientific_journal-522 233 2 dθ dθ PROPN american_scientific_journal-522 233 3 θρ θρ PROPN american_scientific_journal-522 233 4 ξ ξ PROPN american_scientific_journal-522 233 5 η η NOUN american_scientific_journal-522 233 6 = = PUNCT american_scientific_journal-522 234 1 = = NOUN american_scientific_journal-522 234 2   X american_scientific_journal-522 234 3   PROPN american_scientific_journal-522 234 4 ∫ ∫ PROPN american_scientific_journal-522 234 5 ∫ ∫ PROPN american_scientific_journal-522 234 6 ( ( PUNCT american_scientific_journal-522 234 7 38 38 NUM american_scientific_journal-522 234 8 ) ) PUNCT american_scientific_journal-522 234 9 3 3 NUM american_scientific_journal-522 234 10 . . PUNCT american_scientific_journal-522 234 11 numerical numerical ADJ american_scientific_journal-522 234 12 results result NOUN american_scientific_journal-522 234 13 and and CCONJ american_scientific_journal-522 234 14 discussion discussion NOUN american_scientific_journal-522 234 15 3.1 3.1 NUM american_scientific_journal-522 234 16 . . PUNCT american_scientific_journal-522 234 17 convergence convergence NOUN american_scientific_journal-522 234 18 study study NOUN american_scientific_journal-522 234 19 tables table NOUN american_scientific_journal-522 234 20 1 1 NUM american_scientific_journal-522 234 21 to to PART american_scientific_journal-522 234 22 5 5 NUM american_scientific_journal-522 234 23 show show VERB american_scientific_journal-522 234 24 that that SCONJ american_scientific_journal-522 234 25 good good ADJ american_scientific_journal-522 234 26 convergence convergence NOUN american_scientific_journal-522 234 27 and and CCONJ american_scientific_journal-522 234 28 accuracy accuracy NOUN american_scientific_journal-522 234 29 of of ADP american_scientific_journal-522 234 30 the the DET american_scientific_journal-522 234 31 solutions solution NOUN american_scientific_journal-522 234 32 are be AUX american_scientific_journal-522 234 33 obtained obtain VERB american_scientific_journal-522 234 34 by by ADP american_scientific_journal-522 234 35 increasing increase VERB american_scientific_journal-522 234 36 the the DET american_scientific_journal-522 234 37 number number NOUN american_scientific_journal-522 234 38 of of ADP american_scientific_journal-522 234 39 trigonometric trigonometric ADJ american_scientific_journal-522 234 40 shape shape NOUN american_scientific_journal-522 234 41 functions function NOUN american_scientific_journal-522 234 42 , , PUNCT american_scientific_journal-522 234 43 for for ADP american_scientific_journal-522 234 44 all all DET american_scientific_journal-522 234 45 cases case NOUN american_scientific_journal-522 234 46 . . PUNCT american_scientific_journal-522 235 1 it it PRON american_scientific_journal-522 235 2 is be AUX american_scientific_journal-522 235 3 seen see VERB american_scientific_journal-522 235 4 that that SCONJ american_scientific_journal-522 235 5 good good ADJ american_scientific_journal-522 235 6 results result NOUN american_scientific_journal-522 235 7 from from ADP american_scientific_journal-522 235 8 thick thick ADJ american_scientific_journal-522 235 9 plates plate NOUN american_scientific_journal-522 235 10 are be AUX american_scientific_journal-522 235 11 obtained obtain VERB american_scientific_journal-522 235 12 by by ADP american_scientific_journal-522 235 13 8 8 NUM american_scientific_journal-522 235 14 american american ADJ american_scientific_journal-522 235 15 scientific scientific ADJ american_scientific_journal-522 235 16 research research NOUN american_scientific_journal-522 235 17 journal journal NOUN american_scientific_journal-522 235 18 for for ADP american_scientific_journal-522 235 19 engineering engineering NOUN american_scientific_journal-522 235 20 , , PUNCT american_scientific_journal-522 235 21 technology technology NOUN american_scientific_journal-522 235 22 , , PUNCT american_scientific_journal-522 235 23 and and CCONJ american_scientific_journal-522 235 24 sciences science NOUN american_scientific_journal-522 235 25 ( ( PUNCT american_scientific_journal-522 235 26 asrjets asrjet NOUN american_scientific_journal-522 235 27 ) ) PUNCT american_scientific_journal-522 235 28 ( ( PUNCT american_scientific_journal-522 235 29 2014 2014 NUM american_scientific_journal-522 235 30 ) ) PUNCT american_scientific_journal-522 235 31 volume volume NOUN american_scientific_journal-522 235 32 9 9 NUM american_scientific_journal-522 235 33 , , PUNCT american_scientific_journal-522 235 34 no no DET american_scientific_journal-522 235 35 1 1 NUM american_scientific_journal-522 235 36 , , PUNCT american_scientific_journal-522 235 37 pp pp ADV american_scientific_journal-522 235 38 1 1 NUM american_scientific_journal-522 235 39 - - SYM american_scientific_journal-522 235 40 19 19 NUM american_scientific_journal-522 235 41 using using NOUN american_scientific_journal-522 235 42 , , PUNCT american_scientific_journal-522 235 43 only only ADV american_scientific_journal-522 235 44 six six NUM american_scientific_journal-522 235 45 shape shape NOUN american_scientific_journal-522 235 46 function function NOUN american_scientific_journal-522 235 47 in in ADP american_scientific_journal-522 235 48 the the DET american_scientific_journal-522 235 49 case case NOUN american_scientific_journal-522 235 50 of of ADP american_scientific_journal-522 235 51 ssss ssss NOUN american_scientific_journal-522 235 52 plates plate NOUN american_scientific_journal-522 235 53 , , PUNCT american_scientific_journal-522 235 54 14 14 NUM american_scientific_journal-522 235 55 shape shape NOUN american_scientific_journal-522 235 56 functions function NOUN american_scientific_journal-522 235 57 in in ADP american_scientific_journal-522 235 58 the the DET american_scientific_journal-522 235 59 case case NOUN american_scientific_journal-522 235 60 cccc cccc NOUN american_scientific_journal-522 235 61 plates,12 plates,12 NOUN american_scientific_journal-522 235 62 shape shape NOUN american_scientific_journal-522 235 63 functions function NOUN american_scientific_journal-522 235 64 in in ADP american_scientific_journal-522 235 65 the the DET american_scientific_journal-522 235 66 case case NOUN american_scientific_journal-522 235 67 of of ADP american_scientific_journal-522 235 68 ffff ffff ADJ american_scientific_journal-522 235 69 plates plate NOUN american_scientific_journal-522 235 70 , , PUNCT american_scientific_journal-522 235 71 and and CCONJ american_scientific_journal-522 235 72 17 17 NUM american_scientific_journal-522 235 73 shape shape NOUN american_scientific_journal-522 235 74 functions function NOUN american_scientific_journal-522 235 75 in in ADP american_scientific_journal-522 235 76 others other NOUN american_scientific_journal-522 235 77 cases case NOUN american_scientific_journal-522 235 78 . . PUNCT american_scientific_journal-522 236 1 table table NOUN american_scientific_journal-522 236 2 1.convergence 1.convergence NUM american_scientific_journal-522 236 3 of of ADP american_scientific_journal-522 236 4 frequency frequency NOUN american_scientific_journal-522 236 5 parameters parameter NOUN american_scientific_journal-522 236 6 ω ω NOUN american_scientific_journal-522 236 7 = = SYM american_scientific_journal-522 236 8 ω ω PROPN american_scientific_journal-522 236 9 b2 b2 PROPN american_scientific_journal-522 236 10 π2 π2 PROPN american_scientific_journal-522 236 11 � � PROPN american_scientific_journal-522 236 12 ρ ρ PROPN american_scientific_journal-522 236 13 h h PROPN american_scientific_journal-522 237 1 d d NOUN american_scientific_journal-522 237 2 for for ADP american_scientific_journal-522 237 3 a a DET american_scientific_journal-522 237 4 thick thick ADJ american_scientific_journal-522 237 5 plates plate NOUN american_scientific_journal-522 237 6 ( ( PUNCT american_scientific_journal-522 237 7 ν ν X american_scientific_journal-522 237 8 = = SYM american_scientific_journal-522 237 9 0.3 0.3 NUM american_scientific_journal-522 237 10 , , PUNCT american_scientific_journal-522 237 11 a a PRON american_scientific_journal-522 237 12 / / SYM american_scientific_journal-522 237 13 b b NOUN american_scientific_journal-522 237 14 = = SYM american_scientific_journal-522 237 15 1 1 NUM american_scientific_journal-522 237 16 , , PUNCT american_scientific_journal-522 237 17 h h NOUN american_scientific_journal-522 237 18 / / SYM american_scientific_journal-522 237 19 a a DET american_scientific_journal-522 237 20 = = NOUN american_scientific_journal-522 237 21 0.5 0.5 NUM american_scientific_journal-522 237 22 ) ) PUNCT american_scientific_journal-522 237 23 with with ADP american_scientific_journal-522 237 24 ssss ssss NOUN american_scientific_journal-522 237 25 boundary boundary ADJ american_scientific_journal-522 237 26 condition condition NOUN american_scientific_journal-522 237 27 . . PUNCT american_scientific_journal-522 238 1 pθ pθ VERB american_scientific_journal-522 238 2 = = SYM american_scientific_journal-522 239 1 pw pw PROPN american_scientific_journal-522 239 2 1 1 NUM american_scientific_journal-522 239 3 2 2 NUM american_scientific_journal-522 239 4 3 3 NUM american_scientific_journal-522 239 5 4 4 NUM american_scientific_journal-522 239 6 5 5 NUM american_scientific_journal-522 239 7 4 4 NUM american_scientific_journal-522 239 8 1.263 1.263 NUM american_scientific_journal-522 239 9 2.47 2.47 NUM american_scientific_journal-522 239 10 2.47 2.47 NUM american_scientific_journal-522 239 11 2.919 2.919 NUM american_scientific_journal-522 239 12 2.919 2.919 NUM american_scientific_journal-522 239 13 5 5 NUM american_scientific_journal-522 239 14 1.246 1.246 NUM american_scientific_journal-522 239 15 2.414 2.414 NUM american_scientific_journal-522 239 16 2.414 2.414 NUM american_scientific_journal-522 239 17 2.919 2.919 NUM american_scientific_journal-522 239 18 2.919 2.919 NUM american_scientific_journal-522 239 19 6 6 NUM american_scientific_journal-522 239 20 1.245 1.245 NUM american_scientific_journal-522 239 21 2.308 2.308 NUM american_scientific_journal-522 239 22 2.308 2.308 NUM american_scientific_journal-522 239 23 2.919 2.919 NUM american_scientific_journal-522 239 24 2.919 2.919 NUM american_scientific_journal-522 239 25 converged converged ADJ american_scientific_journal-522 239 26 solution solution NOUN american_scientific_journal-522 239 27 1.245 1.245 NUM american_scientific_journal-522 239 28 2.308 2.308 NUM american_scientific_journal-522 239 29 2.308 2.308 NUM american_scientific_journal-522 239 30 2.919 2.919 NUM american_scientific_journal-522 239 31 2.919 2.919 NUM american_scientific_journal-522 239 32 table table NOUN american_scientific_journal-522 239 33 2.convergence 2.convergence NUM american_scientific_journal-522 239 34 of of ADP american_scientific_journal-522 239 35 frequency frequency NOUN american_scientific_journal-522 239 36 parameters parameter NOUN american_scientific_journal-522 239 37 ω ω NOUN american_scientific_journal-522 239 38 = = SYM american_scientific_journal-522 239 39 ω ω PROPN american_scientific_journal-522 239 40 b2 b2 PROPN american_scientific_journal-522 239 41 π2 π2 PROPN american_scientific_journal-522 239 42 � � PROPN american_scientific_journal-522 239 43 ρ ρ PROPN american_scientific_journal-522 239 44 h h PROPN american_scientific_journal-522 239 45 d d NOUN american_scientific_journal-522 239 46 for for ADP american_scientific_journal-522 239 47 a a DET american_scientific_journal-522 239 48 thick thick ADJ american_scientific_journal-522 239 49 plates plate NOUN american_scientific_journal-522 239 50 ( ( PUNCT american_scientific_journal-522 239 51 ν ν X american_scientific_journal-522 239 52 = = SYM american_scientific_journal-522 239 53 0.3 0.3 NUM american_scientific_journal-522 239 54 , , PUNCT american_scientific_journal-522 239 55 a a PRON american_scientific_journal-522 239 56 / / SYM american_scientific_journal-522 239 57 b b NOUN american_scientific_journal-522 239 58 = = SYM american_scientific_journal-522 239 59 1 1 NUM american_scientific_journal-522 239 60 , , PUNCT american_scientific_journal-522 239 61 h h NOUN american_scientific_journal-522 239 62 / / SYM american_scientific_journal-522 240 1 a a DET american_scientific_journal-522 240 2 = = NOUN american_scientific_journal-522 240 3 0.5 0.5 NUM american_scientific_journal-522 240 4 ) ) PUNCT american_scientific_journal-522 240 5 with with ADP american_scientific_journal-522 240 6 cccc cccc PROPN american_scientific_journal-522 240 7 boundary boundary ADJ american_scientific_journal-522 240 8 condition condition NOUN american_scientific_journal-522 240 9 . . PUNCT american_scientific_journal-522 241 1 pθ pθ VERB american_scientific_journal-522 241 2 = = SYM american_scientific_journal-522 242 1 pw pw PROPN american_scientific_journal-522 242 2 1 1 NUM american_scientific_journal-522 242 3 2 2 NUM american_scientific_journal-522 242 4 3 3 NUM american_scientific_journal-522 242 5 4 4 NUM american_scientific_journal-522 242 6 5 5 NUM american_scientific_journal-522 242 7 4 4 NUM american_scientific_journal-522 242 8 3.623 3.623 NUM american_scientific_journal-522 242 9 3.623 3.623 NUM american_scientific_journal-522 242 10 4.026 4.026 NUM american_scientific_journal-522 242 11 4.557 4.557 NUM american_scientific_journal-522 243 1 5.069 5.069 NUM american_scientific_journal-522 243 2 5 5 NUM american_scientific_journal-522 243 3 1.662 1.662 NUM american_scientific_journal-522 243 4 3.617 3.617 NUM american_scientific_journal-522 243 5 3.617 3.617 NUM american_scientific_journal-522 243 6 3.965 3.965 NUM american_scientific_journal-522 243 7 4.515 4.515 NUM american_scientific_journal-522 243 8 6 6 NUM american_scientific_journal-522 243 9 1.659 1.659 NUM american_scientific_journal-522 243 10 2.639 2.639 NUM american_scientific_journal-522 243 11 2.639 2.639 NUM american_scientific_journal-522 243 12 3.466 3.466 NUM american_scientific_journal-522 243 13 3.695 3.695 NUM american_scientific_journal-522 243 14 7 7 NUM american_scientific_journal-522 243 15 1.618 1.618 NUM american_scientific_journal-522 243 16 2.613 2.613 NUM american_scientific_journal-522 243 17 2.613 2.613 NUM american_scientific_journal-522 243 18 3.448 3.448 NUM american_scientific_journal-522 243 19 3.691 3.691 NUM american_scientific_journal-522 243 20 8 8 NUM american_scientific_journal-522 243 21 1.615 1.615 NUM american_scientific_journal-522 243 22 2.586 2.586 NUM american_scientific_journal-522 243 23 2.586 2.586 NUM american_scientific_journal-522 243 24 3.405 3.405 NUM american_scientific_journal-522 243 25 3.687 3.687 NUM american_scientific_journal-522 243 26 9 9 NUM american_scientific_journal-522 243 27 1.604 1.604 NUM american_scientific_journal-522 243 28 2.575 2.575 NUM american_scientific_journal-522 243 29 2.575 2.575 NUM american_scientific_journal-522 243 30 3.392 3.392 NUM american_scientific_journal-522 243 31 3.686 3.686 NUM american_scientific_journal-522 243 32 10 10 NUM american_scientific_journal-522 243 33 1.601 1.601 NUM american_scientific_journal-522 243 34 2.566 2.566 NUM american_scientific_journal-522 243 35 2.566 2.566 NUM american_scientific_journal-522 243 36 3.379 3.379 NUM american_scientific_journal-522 243 37 3.686 3.686 NUM american_scientific_journal-522 243 38 11 11 NUM american_scientific_journal-522 243 39 1.598 1.598 NUM american_scientific_journal-522 243 40 2.559 2.559 NUM american_scientific_journal-522 243 41 2.559 2.559 NUM american_scientific_journal-522 243 42 3.369 3.369 NUM american_scientific_journal-522 243 43 3.685 3.685 NUM american_scientific_journal-522 243 44 12 12 NUM american_scientific_journal-522 243 45 1.595 1.595 NUM american_scientific_journal-522 243 46 2.556 2.556 NUM american_scientific_journal-522 243 47 2.556 2.556 NUM american_scientific_journal-522 243 48 3.366 3.366 NUM american_scientific_journal-522 243 49 3.685 3.685 NUM american_scientific_journal-522 243 50 13 13 NUM american_scientific_journal-522 243 51 1.595 1.595 NUM american_scientific_journal-522 243 52 2.552 2.552 NUM american_scientific_journal-522 243 53 2.552 2.552 NUM american_scientific_journal-522 243 54 3.358 3.358 NUM american_scientific_journal-522 243 55 3.685 3.685 NUM american_scientific_journal-522 243 56 14 14 NUM american_scientific_journal-522 243 57 1.593 1.593 NUM american_scientific_journal-522 243 58 2.55 2.55 NUM american_scientific_journal-522 243 59 2.55 2.55 NUM american_scientific_journal-522 243 60 3.358 3.358 NUM american_scientific_journal-522 243 61 3.685 3.685 NUM american_scientific_journal-522 243 62 converged converge VERB american_scientific_journal-522 243 63 solution solution NOUN american_scientific_journal-522 243 64 1.593 1.593 NUM american_scientific_journal-522 243 65 2.55 2.55 NUM american_scientific_journal-522 243 66 2.55 2.55 NUM american_scientific_journal-522 243 67 3.358 3.358 NUM american_scientific_journal-522 243 68 3.685 3.685 NUM american_scientific_journal-522 243 69 table table NOUN american_scientific_journal-522 243 70 3.convergence 3.convergence NUM american_scientific_journal-522 243 71 of of ADP american_scientific_journal-522 243 72 frequency frequency NOUN american_scientific_journal-522 243 73 parameters parameter NOUN american_scientific_journal-522 243 74 ω ω NOUN american_scientific_journal-522 243 75 = = SYM american_scientific_journal-522 243 76 ω ω PROPN american_scientific_journal-522 243 77 b2 b2 PROPN american_scientific_journal-522 243 78 π2 π2 PROPN american_scientific_journal-522 243 79 � � PROPN american_scientific_journal-522 243 80 ρ ρ PROPN american_scientific_journal-522 243 81 h h PROPN american_scientific_journal-522 243 82 d d NOUN american_scientific_journal-522 243 83 for for ADP american_scientific_journal-522 243 84 a a DET american_scientific_journal-522 243 85 thick thick ADJ american_scientific_journal-522 243 86 plates plate NOUN american_scientific_journal-522 243 87 ( ( PUNCT american_scientific_journal-522 243 88 ν ν X american_scientific_journal-522 243 89 = = SYM american_scientific_journal-522 243 90 0.3 0.3 NUM american_scientific_journal-522 243 91 , , PUNCT american_scientific_journal-522 243 92 a a PRON american_scientific_journal-522 243 93 / / SYM american_scientific_journal-522 243 94 b b NOUN american_scientific_journal-522 243 95 = = SYM american_scientific_journal-522 243 96 1 1 NUM american_scientific_journal-522 243 97 , , PUNCT american_scientific_journal-522 243 98 h h NOUN american_scientific_journal-522 243 99 / / SYM american_scientific_journal-522 243 100 a a DET american_scientific_journal-522 243 101 = = NOUN american_scientific_journal-522 243 102 0.5 0.5 NUM american_scientific_journal-522 243 103 ) ) PUNCT american_scientific_journal-522 243 104 with with ADP american_scientific_journal-522 243 105 ffff ffff ADJ american_scientific_journal-522 243 106 boundary boundary ADJ american_scientific_journal-522 243 107 condition condition NOUN american_scientific_journal-522 243 108 . . PUNCT american_scientific_journal-522 244 1 pθ pθ VERB american_scientific_journal-522 244 2 = = SYM american_scientific_journal-522 245 1 pw pw PROPN american_scientific_journal-522 245 2 1 1 NUM american_scientific_journal-522 245 3 2 2 NUM american_scientific_journal-522 245 4 3 3 NUM american_scientific_journal-522 245 5 4 4 NUM american_scientific_journal-522 245 6 5 5 NUM american_scientific_journal-522 245 7 4 4 NUM american_scientific_journal-522 245 8 0.905 0.905 NUM american_scientific_journal-522 245 9 1.354 1.354 NUM american_scientific_journal-522 245 10 1.693 1.693 NUM american_scientific_journal-522 245 11 1.939 1.939 NUM american_scientific_journal-522 245 12 1.939 1.939 NUM american_scientific_journal-522 245 13 5 5 NUM american_scientific_journal-522 245 14 0.905 0.905 NUM american_scientific_journal-522 245 15 1.266 1.266 NUM american_scientific_journal-522 245 16 1.514 1.514 NUM american_scientific_journal-522 245 17 1.805 1.805 NUM american_scientific_journal-522 245 18 1.805 1.805 NUM american_scientific_journal-522 245 19 9 9 NUM american_scientific_journal-522 245 20 american american ADJ american_scientific_journal-522 245 21 scientific scientific ADJ american_scientific_journal-522 245 22 research research NOUN american_scientific_journal-522 245 23 journal journal NOUN american_scientific_journal-522 245 24 for for ADP american_scientific_journal-522 245 25 engineering engineering NOUN american_scientific_journal-522 245 26 , , PUNCT american_scientific_journal-522 245 27 technology technology NOUN american_scientific_journal-522 245 28 , , PUNCT american_scientific_journal-522 245 29 and and CCONJ american_scientific_journal-522 245 30 sciences science NOUN american_scientific_journal-522 245 31 ( ( PUNCT american_scientific_journal-522 245 32 asrjets asrjet NOUN american_scientific_journal-522 245 33 ) ) PUNCT american_scientific_journal-522 245 34 ( ( PUNCT american_scientific_journal-522 245 35 2014 2014 NUM american_scientific_journal-522 245 36 ) ) PUNCT american_scientific_journal-522 245 37 volume volume NOUN american_scientific_journal-522 245 38 9 9 NUM american_scientific_journal-522 245 39 , , PUNCT american_scientific_journal-522 245 40 no no DET american_scientific_journal-522 245 41 1 1 NUM american_scientific_journal-522 245 42 , , PUNCT american_scientific_journal-522 245 43 pp pp ADV american_scientific_journal-522 245 44 1 1 NUM american_scientific_journal-522 245 45 - - SYM american_scientific_journal-522 245 46 19 19 NUM american_scientific_journal-522 245 47 6 6 NUM american_scientific_journal-522 245 48 0.895 0.895 NUM american_scientific_journal-522 245 49 1.266 1.266 NUM american_scientific_journal-522 245 50 1.514 1.514 NUM american_scientific_journal-522 245 51 1.798 1.798 NUM american_scientific_journal-522 245 52 1.798 1.798 NUM american_scientific_journal-522 245 53 7 7 NUM american_scientific_journal-522 245 54 0.895 0.895 NUM american_scientific_journal-522 245 55 1.265 1.265 NUM american_scientific_journal-522 245 56 1.511 1.511 NUM american_scientific_journal-522 245 57 1.793 1.793 NUM american_scientific_journal-522 245 58 1.793 1.793 NUM american_scientific_journal-522 245 59 8 8 NUM american_scientific_journal-522 245 60 0.893 0.893 NUM american_scientific_journal-522 245 61 1.265 1.265 NUM american_scientific_journal-522 245 62 1.511 1.511 NUM american_scientific_journal-522 245 63 1.792 1.792 NUM american_scientific_journal-522 245 64 1.792 1.792 NUM american_scientific_journal-522 245 65 9 9 NUM american_scientific_journal-522 245 66 0.893 0.893 NUM american_scientific_journal-522 245 67 1.265 1.265 NUM american_scientific_journal-522 245 68 1.511 1.511 NUM american_scientific_journal-522 245 69 1.79 1.79 NUM american_scientific_journal-522 245 70 1.790 1.790 NUM american_scientific_journal-522 245 71 10 10 NUM american_scientific_journal-522 245 72 0.892 0.892 NUM american_scientific_journal-522 245 73 1.265 1.265 NUM american_scientific_journal-522 245 74 1.511 1.511 NUM american_scientific_journal-522 245 75 1.79 1.79 NUM american_scientific_journal-522 245 76 1.790 1.790 NUM american_scientific_journal-522 245 77 11 11 NUM american_scientific_journal-522 245 78 0.892 0.892 NUM american_scientific_journal-522 245 79 1.265 1.265 NUM american_scientific_journal-522 245 80 1.511 1.511 NUM american_scientific_journal-522 245 81 1.789 1.789 NUM american_scientific_journal-522 245 82 1.789 1.789 NUM american_scientific_journal-522 245 83 12 12 NUM american_scientific_journal-522 245 84 0.892 0.892 NUM american_scientific_journal-522 245 85 1.264 1.264 NUM american_scientific_journal-522 245 86 1.511 1.511 NUM american_scientific_journal-522 245 87 1.789 1.789 NUM american_scientific_journal-522 245 88 1.789 1.789 NUM american_scientific_journal-522 245 89 converged converge VERB american_scientific_journal-522 245 90 solution solution NOUN american_scientific_journal-522 245 91 0.892 0.892 NUM american_scientific_journal-522 245 92 1.264 1.264 NUM american_scientific_journal-522 245 93 1.511 1.511 NUM american_scientific_journal-522 245 94 1.789 1.789 NUM american_scientific_journal-522 245 95 1.789 1.789 NUM american_scientific_journal-522 245 96 table table NOUN american_scientific_journal-522 245 97 4 4 NUM american_scientific_journal-522 245 98 . . PUNCT american_scientific_journal-522 246 1 convergence convergence NOUN american_scientific_journal-522 246 2 of of ADP american_scientific_journal-522 246 3 frequency frequency NOUN american_scientific_journal-522 246 4 parameters parameter NOUN american_scientific_journal-522 246 5 ω ω NOUN american_scientific_journal-522 246 6 = = SYM american_scientific_journal-522 246 7 ω ω PROPN american_scientific_journal-522 246 8 b2 b2 PROPN american_scientific_journal-522 246 9 π2 π2 PROPN american_scientific_journal-522 246 10 � � PROPN american_scientific_journal-522 246 11 ρ ρ PROPN american_scientific_journal-522 246 12 h h PROPN american_scientific_journal-522 246 13 d d NOUN american_scientific_journal-522 246 14 for for ADP american_scientific_journal-522 246 15 a a DET american_scientific_journal-522 246 16 thick thick ADJ american_scientific_journal-522 246 17 plates(ν plates(ν NOUN american_scientific_journal-522 246 18 = = PUNCT american_scientific_journal-522 246 19 0.3 0.3 NUM american_scientific_journal-522 246 20 , , PUNCT american_scientific_journal-522 246 21 a a PRON american_scientific_journal-522 246 22 / / SYM american_scientific_journal-522 246 23 b b NOUN american_scientific_journal-522 246 24 = = SYM american_scientific_journal-522 246 25 1 1 NUM american_scientific_journal-522 246 26 , , PUNCT american_scientific_journal-522 246 27 h h NOUN american_scientific_journal-522 246 28 / / SYM american_scientific_journal-522 246 29 a a DET american_scientific_journal-522 246 30 = = NOUN american_scientific_journal-522 246 31 0.5 0.5 NUM american_scientific_journal-522 246 32 ) ) PUNCT american_scientific_journal-522 246 33 with with ADP american_scientific_journal-522 246 34 cfcf cfcf ADJ american_scientific_journal-522 246 35 boundary boundary ADJ american_scientific_journal-522 246 36 condition condition NOUN american_scientific_journal-522 246 37 . . PUNCT american_scientific_journal-522 247 1 pθ pθ VERB american_scientific_journal-522 247 2 = = SYM american_scientific_journal-522 248 1 pw pw PROPN american_scientific_journal-522 248 2 1 1 NUM american_scientific_journal-522 248 3 2 2 NUM american_scientific_journal-522 248 4 3 3 NUM american_scientific_journal-522 248 5 4 4 NUM american_scientific_journal-522 248 6 5 5 NUM american_scientific_journal-522 248 7 4 4 NUM american_scientific_journal-522 248 8 2.883 2.883 NUM american_scientific_journal-522 248 9 3.378 3.378 NUM american_scientific_journal-522 248 10 3.45 3.45 NUM american_scientific_journal-522 248 11 3.56 3.56 NUM american_scientific_journal-522 248 12 3.792 3.792 NUM american_scientific_journal-522 248 13 5 5 NUM american_scientific_journal-522 248 14 1.139 1.139 NUM american_scientific_journal-522 248 15 1.248 1.248 NUM american_scientific_journal-522 248 16 1.947 1.947 NUM american_scientific_journal-522 248 17 2.721 2.721 NUM american_scientific_journal-522 248 18 3.369 3.369 NUM american_scientific_journal-522 248 19 6 6 NUM american_scientific_journal-522 248 20 1.137 1.137 NUM american_scientific_journal-522 248 21 1.241 1.241 NUM american_scientific_journal-522 248 22 1.944 1.944 NUM american_scientific_journal-522 248 23 2.261 2.261 NUM american_scientific_journal-522 248 24 2.450 2.450 NUM american_scientific_journal-522 248 25 7 7 NUM american_scientific_journal-522 248 26 1.114 1.114 NUM american_scientific_journal-522 248 27 1.213 1.213 NUM american_scientific_journal-522 248 28 1.913 1.913 NUM american_scientific_journal-522 248 29 2.252 2.252 NUM american_scientific_journal-522 248 30 2.439 2.439 NUM american_scientific_journal-522 248 31 8 8 NUM american_scientific_journal-522 248 32 1.112 1.112 NUM american_scientific_journal-522 248 33 1.209 1.209 NUM american_scientific_journal-522 248 34 1.91 1.91 NUM american_scientific_journal-522 248 35 2.226 2.226 NUM american_scientific_journal-522 248 36 2.411 2.411 NUM american_scientific_journal-522 248 37 9 9 NUM american_scientific_journal-522 248 38 1.106 1.106 NUM american_scientific_journal-522 248 39 1.202 1.202 NUM american_scientific_journal-522 248 40 1.903 1.903 NUM american_scientific_journal-522 248 41 2.218 2.218 NUM american_scientific_journal-522 248 42 2.403 2.403 NUM american_scientific_journal-522 248 43 10 10 NUM american_scientific_journal-522 248 44 1.103 1.103 NUM american_scientific_journal-522 248 45 1.199 1.199 NUM american_scientific_journal-522 248 46 1.900 1.900 NUM american_scientific_journal-522 248 47 2.210 2.210 NUM american_scientific_journal-522 248 48 2.395 2.395 NUM american_scientific_journal-522 248 49 11 11 NUM american_scientific_journal-522 248 50 1.102 1.102 NUM american_scientific_journal-522 248 51 1.197 1.197 NUM american_scientific_journal-522 248 52 1.898 1.898 NUM american_scientific_journal-522 248 53 2.204 2.204 NUM american_scientific_journal-522 248 54 2.389 2.389 NUM american_scientific_journal-522 248 55 12 12 NUM american_scientific_journal-522 248 56 1.100 1.100 NUM american_scientific_journal-522 248 57 1.195 1.195 NUM american_scientific_journal-522 248 58 1.897 1.897 NUM american_scientific_journal-522 248 59 2.202 2.202 NUM american_scientific_journal-522 248 60 2.387 2.387 NUM american_scientific_journal-522 248 61 13 13 NUM american_scientific_journal-522 248 62 1.100 1.100 NUM american_scientific_journal-522 248 63 1.195 1.195 NUM american_scientific_journal-522 248 64 1.896 1.896 NUM american_scientific_journal-522 248 65 2.198 2.198 NUM american_scientific_journal-522 248 66 2.382 2.382 NUM american_scientific_journal-522 248 67 14 14 NUM american_scientific_journal-522 248 68 1.099 1.099 NUM american_scientific_journal-522 248 69 1.193 1.193 NUM american_scientific_journal-522 248 70 1.895 1.895 NUM american_scientific_journal-522 248 71 2.198 2.198 NUM american_scientific_journal-522 248 72 2.382 2.382 NUM american_scientific_journal-522 248 73 15 15 NUM american_scientific_journal-522 248 74 1.099 1.099 NUM american_scientific_journal-522 248 75 1.193 1.193 NUM american_scientific_journal-522 248 76 1.895 1.895 NUM american_scientific_journal-522 248 77 2.194 2.194 NUM american_scientific_journal-522 248 78 2.379 2.379 NUM american_scientific_journal-522 248 79 16 16 NUM american_scientific_journal-522 248 80 1.098 1.098 NUM american_scientific_journal-522 248 81 1.192 1.192 NUM american_scientific_journal-522 248 82 1.894 1.894 NUM american_scientific_journal-522 248 83 2.194 2.194 NUM american_scientific_journal-522 248 84 2.378 2.378 NUM american_scientific_journal-522 248 85 17 17 NUM american_scientific_journal-522 248 86 1.098 1.098 NUM american_scientific_journal-522 248 87 1.192 1.192 NUM american_scientific_journal-522 248 88 1.894 1.894 NUM american_scientific_journal-522 248 89 2.192 2.192 NUM american_scientific_journal-522 248 90 2.376 2.376 NUM american_scientific_journal-522 248 91 converged converge VERB american_scientific_journal-522 248 92 solution solution NOUN american_scientific_journal-522 248 93 1.098 1.098 NUM american_scientific_journal-522 248 94 1.192 1.192 NUM american_scientific_journal-522 248 95 1.894 1.894 NUM american_scientific_journal-522 248 96 2.192 2.192 NUM american_scientific_journal-522 248 97 2.376 2.376 NUM american_scientific_journal-522 248 98 table table NOUN american_scientific_journal-522 248 99 5.convergence 5.convergence NUM american_scientific_journal-522 248 100 of of ADP american_scientific_journal-522 248 101 frequency frequency NOUN american_scientific_journal-522 248 102 parameters parameter NOUN american_scientific_journal-522 248 103 ω ω NOUN american_scientific_journal-522 248 104 = = SYM american_scientific_journal-522 248 105 ω ω PROPN american_scientific_journal-522 248 106 b2 b2 PROPN american_scientific_journal-522 248 107 π2 π2 PROPN american_scientific_journal-522 248 108 � � PROPN american_scientific_journal-522 248 109 ρ ρ PROPN american_scientific_journal-522 248 110 h h PROPN american_scientific_journal-522 248 111 d d NOUN american_scientific_journal-522 248 112 for for ADP american_scientific_journal-522 248 113 a a DET american_scientific_journal-522 248 114 thick thick ADJ american_scientific_journal-522 248 115 plates plate NOUN american_scientific_journal-522 248 116 ( ( PUNCT american_scientific_journal-522 248 117 ν ν X american_scientific_journal-522 248 118 = = SYM american_scientific_journal-522 248 119 0.3 0.3 NUM american_scientific_journal-522 248 120 , , PUNCT american_scientific_journal-522 248 121 a a PRON american_scientific_journal-522 248 122 / / SYM american_scientific_journal-522 248 123 b b NOUN american_scientific_journal-522 248 124 = = SYM american_scientific_journal-522 248 125 1 1 NUM american_scientific_journal-522 248 126 , , PUNCT american_scientific_journal-522 248 127 h h NOUN american_scientific_journal-522 248 128 / / SYM american_scientific_journal-522 249 1 a a DET american_scientific_journal-522 249 2 = = NOUN american_scientific_journal-522 249 3 0.5 0.5 NUM american_scientific_journal-522 249 4 ) ) PUNCT american_scientific_journal-522 249 5 with with ADP american_scientific_journal-522 249 6 cscs cscs PROPN american_scientific_journal-522 249 7 boundary boundary ADJ american_scientific_journal-522 249 8 condition condition NOUN american_scientific_journal-522 249 9 . . PUNCT american_scientific_journal-522 250 1 pθ pθ VERB american_scientific_journal-522 250 2 = = SYM american_scientific_journal-522 251 1 pw pw PROPN american_scientific_journal-522 251 2 1 1 NUM american_scientific_journal-522 251 3 2 2 NUM american_scientific_journal-522 251 4 3 3 NUM american_scientific_journal-522 251 5 4 4 NUM american_scientific_journal-522 251 6 5 5 NUM american_scientific_journal-522 251 7 4 4 NUM american_scientific_journal-522 251 8 3.418 3.418 NUM american_scientific_journal-522 252 1 3.499 3.499 NUM american_scientific_journal-522 252 2 3.592 3.592 NUM american_scientific_journal-522 252 3 4.331 4.331 NUM american_scientific_journal-522 252 4 4.432 4.432 NUM american_scientific_journal-522 252 5 5 5 NUM american_scientific_journal-522 252 6 1.656 1.656 NUM american_scientific_journal-522 252 7 3.418 3.418 NUM american_scientific_journal-522 252 8 3.485 3.485 NUM american_scientific_journal-522 252 9 3.585 3.585 NUM american_scientific_journal-522 252 10 4.073 4.073 NUM american_scientific_journal-522 252 11 6 6 NUM american_scientific_journal-522 252 12 1.654 1.654 NUM american_scientific_journal-522 252 13 2.611 2.611 NUM american_scientific_journal-522 252 14 2.635 2.635 NUM american_scientific_journal-522 252 15 3.351 3.351 NUM american_scientific_journal-522 252 16 3.521 3.521 NUM american_scientific_journal-522 252 17 10 10 NUM american_scientific_journal-522 252 18 american american ADJ american_scientific_journal-522 252 19 scientific scientific ADJ american_scientific_journal-522 252 20 research research NOUN american_scientific_journal-522 252 21 journal journal NOUN american_scientific_journal-522 252 22 for for ADP american_scientific_journal-522 252 23 engineering engineering NOUN american_scientific_journal-522 252 24 , , PUNCT american_scientific_journal-522 252 25 technology technology NOUN american_scientific_journal-522 252 26 , , PUNCT american_scientific_journal-522 252 27 and and CCONJ american_scientific_journal-522 252 28 sciences science NOUN american_scientific_journal-522 252 29 ( ( PUNCT american_scientific_journal-522 252 30 asrjets asrjet NOUN american_scientific_journal-522 252 31 ) ) PUNCT american_scientific_journal-522 252 32 ( ( PUNCT american_scientific_journal-522 252 33 2014 2014 NUM american_scientific_journal-522 252 34 ) ) PUNCT american_scientific_journal-522 252 35 volume volume NOUN american_scientific_journal-522 252 36 9 9 NUM american_scientific_journal-522 252 37 , , PUNCT american_scientific_journal-522 252 38 no no DET american_scientific_journal-522 252 39 1 1 NUM american_scientific_journal-522 252 40 , , PUNCT american_scientific_journal-522 252 41 pp pp ADV american_scientific_journal-522 252 42 1 1 NUM american_scientific_journal-522 252 43 - - SYM american_scientific_journal-522 252 44 19 19 NUM american_scientific_journal-522 252 45 7 7 NUM american_scientific_journal-522 252 46 1.612 1.612 NUM american_scientific_journal-522 252 47 2.580 2.580 NUM american_scientific_journal-522 252 48 2.610 2.610 NUM american_scientific_journal-522 252 49 3.343 3.343 NUM american_scientific_journal-522 252 50 3.517 3.517 NUM american_scientific_journal-522 252 51 8 8 NUM american_scientific_journal-522 252 52 1.609 1.609 NUM american_scientific_journal-522 252 53 2.554 2.554 NUM american_scientific_journal-522 252 54 2.583 2.583 NUM american_scientific_journal-522 252 55 3.304 3.304 NUM american_scientific_journal-522 252 56 3.514 3.514 NUM american_scientific_journal-522 252 57 9 9 NUM american_scientific_journal-522 252 58 1.599 1.599 NUM american_scientific_journal-522 252 59 2.542 2.542 NUM american_scientific_journal-522 252 60 2.572 2.572 NUM american_scientific_journal-522 252 61 3.295 3.295 NUM american_scientific_journal-522 252 62 3.513 3.513 NUM american_scientific_journal-522 252 63 10 10 NUM american_scientific_journal-522 252 64 1.595 1.595 NUM american_scientific_journal-522 252 65 2.533 2.533 NUM american_scientific_journal-522 252 66 2.563 2.563 NUM american_scientific_journal-522 252 67 3.284 3.284 NUM american_scientific_journal-522 252 68 3.513 3.513 NUM american_scientific_journal-522 252 69 11 11 NUM american_scientific_journal-522 252 70 1.593 1.593 NUM american_scientific_journal-522 252 71 2.526 2.526 NUM american_scientific_journal-522 252 72 2.556 2.556 NUM american_scientific_journal-522 252 73 3.276 3.276 NUM american_scientific_journal-522 252 74 3.512 3.512 NUM american_scientific_journal-522 252 75 12 12 NUM american_scientific_journal-522 252 76 1.590 1.590 NUM american_scientific_journal-522 252 77 2.523 2.523 NUM american_scientific_journal-522 252 78 2.553 2.553 NUM american_scientific_journal-522 252 79 3.273 3.273 NUM american_scientific_journal-522 252 80 3.512 3.512 NUM american_scientific_journal-522 252 81 13 13 NUM american_scientific_journal-522 252 82 1.590 1.590 NUM american_scientific_journal-522 252 83 2.519 2.519 NUM american_scientific_journal-522 252 84 2.549 2.549 NUM american_scientific_journal-522 252 85 3.267 3.267 NUM american_scientific_journal-522 252 86 3.512 3.512 NUM american_scientific_journal-522 252 87 14 14 NUM american_scientific_journal-522 252 88 1.587 1.587 NUM american_scientific_journal-522 252 89 2.517 2.517 NUM american_scientific_journal-522 252 90 2.548 2.548 NUM american_scientific_journal-522 252 91 3.267 3.267 NUM american_scientific_journal-522 252 92 3.512 3.512 NUM american_scientific_journal-522 252 93 15 15 NUM american_scientific_journal-522 252 94 1.587 1.587 NUM american_scientific_journal-522 252 95 2.514 2.514 NUM american_scientific_journal-522 252 96 2.545 2.545 NUM american_scientific_journal-522 252 97 3.263 3.263 NUM american_scientific_journal-522 252 98 3.512 3.512 NUM american_scientific_journal-522 252 99 16 16 NUM american_scientific_journal-522 252 100 1.586 1.586 NUM american_scientific_journal-522 252 101 2.514 2.514 NUM american_scientific_journal-522 252 102 2.544 2.544 NUM american_scientific_journal-522 252 103 3.263 3.263 NUM american_scientific_journal-522 252 104 3.512 3.512 NUM american_scientific_journal-522 252 105 17 17 NUM american_scientific_journal-522 252 106 1.586 1.586 NUM american_scientific_journal-522 252 107 2.512 2.512 NUM american_scientific_journal-522 252 108 2.542 2.542 NUM american_scientific_journal-522 252 109 3.260 3.260 NUM american_scientific_journal-522 252 110 3.512 3.512 NUM american_scientific_journal-522 252 111 converged converge VERB american_scientific_journal-522 252 112 solution solution NOUN american_scientific_journal-522 252 113 1.586 1.586 NUM american_scientific_journal-522 252 114 2.512 2.512 NUM american_scientific_journal-522 252 115 2.542 2.542 NUM american_scientific_journal-522 252 116 3.260 3.260 NUM american_scientific_journal-522 252 117 3.512 3.512 NUM american_scientific_journal-522 252 118 3.2 3.2 NUM american_scientific_journal-522 252 119 . . PUNCT american_scientific_journal-522 253 1 discussion discussion NOUN american_scientific_journal-522 253 2 the the DET american_scientific_journal-522 253 3 results result NOUN american_scientific_journal-522 253 4 obtained obtain VERB american_scientific_journal-522 253 5 for for ADP american_scientific_journal-522 253 6 an an DET american_scientific_journal-522 253 7 isotropic isotropic ADJ american_scientific_journal-522 253 8 plate plate NOUN american_scientific_journal-522 253 9 by by ADP american_scientific_journal-522 253 10 applying apply VERB american_scientific_journal-522 253 11 higher high ADJ american_scientific_journal-522 253 12 - - PUNCT american_scientific_journal-522 253 13 order order NOUN american_scientific_journal-522 253 14 using use VERB american_scientific_journal-522 253 15 rectangular rectangular ADJ american_scientific_journal-522 253 16 p p NOUN american_scientific_journal-522 253 17 - - PUNCT american_scientific_journal-522 253 18 element element NOUN american_scientific_journal-522 253 19 , , PUNCT american_scientific_journal-522 253 20 are be AUX american_scientific_journal-522 253 21 compared compare VERB american_scientific_journal-522 253 22 with with ADP american_scientific_journal-522 253 23 those those PRON american_scientific_journal-522 253 24 available available ADJ american_scientific_journal-522 253 25 in in ADP american_scientific_journal-522 253 26 the the DET american_scientific_journal-522 253 27 literature literature NOUN american_scientific_journal-522 253 28 . . PUNCT american_scientific_journal-522 254 1 the the DET american_scientific_journal-522 254 2 linear linear ADJ american_scientific_journal-522 254 3 natural natural ADJ american_scientific_journal-522 254 4 frequencies frequency NOUN american_scientific_journal-522 254 5 of of ADP american_scientific_journal-522 254 6 plates plate NOUN american_scientific_journal-522 254 7 with with ADP american_scientific_journal-522 254 8 free free ADJ american_scientific_journal-522 254 9 edges edge NOUN american_scientific_journal-522 254 10 ( ( PUNCT american_scientific_journal-522 254 11 ffff ffff NOUN american_scientific_journal-522 254 12 ) ) PUNCT american_scientific_journal-522 254 13 , , PUNCT american_scientific_journal-522 254 14 simply simply ADV american_scientific_journal-522 254 15 supported support VERB american_scientific_journal-522 254 16 ( ( PUNCT american_scientific_journal-522 254 17 ssss ssss NOUN american_scientific_journal-522 254 18 ) ) PUNCT american_scientific_journal-522 254 19 , , PUNCT american_scientific_journal-522 254 20 fully fully ADV american_scientific_journal-522 254 21 clamped clamp VERB american_scientific_journal-522 254 22 plates plate NOUN american_scientific_journal-522 254 23 ( ( PUNCT american_scientific_journal-522 254 24 cccc cccc NOUN american_scientific_journal-522 254 25 ) ) PUNCT american_scientific_journal-522 254 26 , , PUNCT american_scientific_journal-522 254 27 and and CCONJ american_scientific_journal-522 254 28 combined combine VERB american_scientific_journal-522 254 29 boundary boundary ADJ american_scientific_journal-522 254 30 condition condition NOUN american_scientific_journal-522 254 31 ( ( PUNCT american_scientific_journal-522 254 32 cfcf cfcf NOUN american_scientific_journal-522 254 33 ) ) PUNCT american_scientific_journal-522 254 34 , , PUNCT american_scientific_journal-522 254 35 ( ( PUNCT american_scientific_journal-522 254 36 sfsf sfsf NOUN american_scientific_journal-522 254 37 ) ) PUNCT american_scientific_journal-522 254 38 are be AUX american_scientific_journal-522 254 39 considered consider VERB american_scientific_journal-522 254 40 . . PUNCT american_scientific_journal-522 255 1 the the DET american_scientific_journal-522 255 2 frequency frequency NOUN american_scientific_journal-522 255 3 parameter parameter NOUN american_scientific_journal-522 255 4 of of ADP american_scientific_journal-522 255 5 the the DET american_scientific_journal-522 255 6 plate plate NOUN american_scientific_journal-522 255 7 is be AUX american_scientific_journal-522 255 8 expressed express VERB american_scientific_journal-522 255 9 as as ADP american_scientific_journal-522 255 10 ω ω NOUN american_scientific_journal-522 255 11 = = PUNCT american_scientific_journal-522 255 12 𝜔𝜔 𝜔𝜔 ADP american_scientific_journal-522 255 13 𝑏𝑏2 𝑏𝑏2 PROPN american_scientific_journal-522 255 14 𝜋𝜋2 𝜋𝜋2 PRON american_scientific_journal-522 255 15 � � PROPN american_scientific_journal-522 255 16 𝜌𝜌 𝜌𝜌 ADP american_scientific_journal-522 255 17 ℎ ℎ PROPN american_scientific_journal-522 255 18 𝐷𝐷 𝐷𝐷 PROPN american_scientific_journal-522 255 19 , , PUNCT american_scientific_journal-522 255 20 ( ( PUNCT american_scientific_journal-522 255 21 36 36 NUM american_scientific_journal-522 255 22 ) ) PUNCT american_scientific_journal-522 255 23 where where SCONJ american_scientific_journal-522 255 24 d d NOUN american_scientific_journal-522 255 25 = = SYM american_scientific_journal-522 255 26 e e NOUN american_scientific_journal-522 255 27 h3 h3 NOUN american_scientific_journal-522 255 28 12 12 NUM american_scientific_journal-522 255 29 ( ( PUNCT american_scientific_journal-522 255 30 1−ν2 1−ν2 NUM american_scientific_journal-522 255 31 ) ) PUNCT american_scientific_journal-522 255 32 is be AUX american_scientific_journal-522 255 33 the the DET american_scientific_journal-522 255 34 flexural flexural ADJ american_scientific_journal-522 255 35 rigidity rigidity NOUN american_scientific_journal-522 255 36 of of ADP american_scientific_journal-522 255 37 the the DET american_scientific_journal-522 255 38 plate plate NOUN american_scientific_journal-522 255 39 . . PUNCT american_scientific_journal-522 256 1 the the DET american_scientific_journal-522 256 2 first first ADJ american_scientific_journal-522 256 3 five five NUM american_scientific_journal-522 256 4 frequency frequency NOUN american_scientific_journal-522 256 5 parameters parameter NOUN american_scientific_journal-522 256 6 ω ω VERB american_scientific_journal-522 256 7 for for ADP american_scientific_journal-522 256 8 simply simply ADV american_scientific_journal-522 256 9 - - PUNCT american_scientific_journal-522 256 10 supported support VERB american_scientific_journal-522 256 11 ( ( PUNCT american_scientific_journal-522 256 12 ssss ssss NOUN american_scientific_journal-522 256 13 ) ) PUNCT american_scientific_journal-522 256 14 square square ADJ american_scientific_journal-522 256 15 plates plate NOUN american_scientific_journal-522 256 16 with with ADP american_scientific_journal-522 256 17 different different ADJ american_scientific_journal-522 256 18 thickness thickness NOUN american_scientific_journal-522 256 19 - - PUNCT american_scientific_journal-522 256 20 side side NOUN american_scientific_journal-522 256 21 ratio ratio NOUN american_scientific_journal-522 256 22 h h PROPN american_scientific_journal-522 256 23 / / SYM american_scientific_journal-522 256 24 b b PROPN american_scientific_journal-522 256 25 = = SYM american_scientific_journal-522 256 26 0.001 0.001 NUM american_scientific_journal-522 256 27 , , PUNCT american_scientific_journal-522 256 28 0.1 0.1 NUM american_scientific_journal-522 256 29 , , PUNCT american_scientific_journal-522 256 30 0.2 0.2 NUM american_scientific_journal-522 256 31 , , PUNCT american_scientific_journal-522 256 32 0.5 0.5 NUM american_scientific_journal-522 256 33 computed compute VERB american_scientific_journal-522 256 34 using use VERB american_scientific_journal-522 256 35 the the DET american_scientific_journal-522 256 36 present present ADJ american_scientific_journal-522 256 37 method method NOUN american_scientific_journal-522 256 38 are be AUX american_scientific_journal-522 256 39 given give VERB american_scientific_journal-522 256 40 in in ADP american_scientific_journal-522 256 41 table table NOUN american_scientific_journal-522 256 42 6 6 NUM american_scientific_journal-522 256 43 and and CCONJ american_scientific_journal-522 256 44 compared compare VERB american_scientific_journal-522 256 45 with with ADP american_scientific_journal-522 256 46 other other ADJ american_scientific_journal-522 256 47 published publish VERB american_scientific_journal-522 256 48 solutions solution NOUN american_scientific_journal-522 256 49 , , PUNCT american_scientific_journal-522 256 50 leissa leissa ADJ american_scientific_journal-522 256 51 [ [ X american_scientific_journal-522 256 52 17 17 NUM american_scientific_journal-522 256 53 ] ] PUNCT american_scientific_journal-522 256 54 , , PUNCT american_scientific_journal-522 256 55 houmat houmat PROPN american_scientific_journal-522 257 1 [ [ X american_scientific_journal-522 257 2 24 24 NUM american_scientific_journal-522 257 3 ] ] PUNCT american_scientific_journal-522 257 4 , , PUNCT american_scientific_journal-522 257 5 3 3 NUM american_scientific_journal-522 257 6 - - SYM american_scientific_journal-522 257 7 d d NOUN american_scientific_journal-522 257 8 exact exact ADJ american_scientific_journal-522 257 9 solution solution NOUN american_scientific_journal-522 257 10 [ [ X american_scientific_journal-522 257 11 18 18 NUM american_scientific_journal-522 257 12 ] ] PUNCT american_scientific_journal-522 257 13 , , PUNCT american_scientific_journal-522 257 14 nayak nayak PROPN american_scientific_journal-522 258 1 [ [ X american_scientific_journal-522 258 2 9 9 NUM american_scientific_journal-522 258 3 ] ] PUNCT american_scientific_journal-522 258 4 , , PUNCT american_scientific_journal-522 258 5 the the DET american_scientific_journal-522 258 6 authors author NOUN american_scientific_journal-522 258 7 in in ADP american_scientific_journal-522 258 8 1956 1956 NUM american_scientific_journal-522 258 9 [ [ X american_scientific_journal-522 258 10 2 2 NUM american_scientific_journal-522 258 11 ] ] PUNCT american_scientific_journal-522 258 12 , , PUNCT american_scientific_journal-522 258 13 lim lim PROPN american_scientific_journal-522 258 14 and and CCONJ american_scientific_journal-522 258 15 his his PRON american_scientific_journal-522 258 16 colleagues colleague NOUN american_scientific_journal-522 259 1 [ [ X american_scientific_journal-522 259 2 18 18 NUM american_scientific_journal-522 259 3 ] ] PUNCT american_scientific_journal-522 259 4 , , PUNCT american_scientific_journal-522 259 5 srinivas srinivas PROPN american_scientific_journal-522 259 6 and and CCONJ american_scientific_journal-522 259 7 his his PRON american_scientific_journal-522 259 8 colleagues colleague NOUN american_scientific_journal-522 260 1 [ [ X american_scientific_journal-522 260 2 19 19 NUM american_scientific_journal-522 260 3 ] ] PUNCT american_scientific_journal-522 260 4 , , PUNCT american_scientific_journal-522 260 5 malik malik PROPN american_scientific_journal-522 260 6 and and CCONJ american_scientific_journal-522 260 7 bert bert PROPN american_scientific_journal-522 260 8 , , PUNCT american_scientific_journal-522 260 9 1998 1998 NUM american_scientific_journal-522 260 10 [ [ X american_scientific_journal-522 260 11 27 27 NUM american_scientific_journal-522 260 12 ] ] PUNCT american_scientific_journal-522 260 13 , , PUNCT american_scientific_journal-522 260 14 zhou zhou PROPN american_scientific_journal-522 260 15 and and CCONJ american_scientific_journal-522 260 16 his his PRON american_scientific_journal-522 260 17 colleagues colleague NOUN american_scientific_journal-522 261 1 [ [ X american_scientific_journal-522 261 2 20 20 NUM american_scientific_journal-522 261 3 ] ] PUNCT american_scientific_journal-522 261 4 , , PUNCT american_scientific_journal-522 261 5 very very ADV american_scientific_journal-522 261 6 good good ADJ american_scientific_journal-522 261 7 agreement agreement NOUN american_scientific_journal-522 261 8 can can AUX american_scientific_journal-522 261 9 be be AUX american_scientific_journal-522 261 10 observed observe VERB american_scientific_journal-522 261 11 , , PUNCT american_scientific_journal-522 261 12 in in ADP american_scientific_journal-522 261 13 the the DET american_scientific_journal-522 261 14 results result NOUN american_scientific_journal-522 261 15 with with ADP american_scientific_journal-522 261 16 concealment concealment NOUN american_scientific_journal-522 261 17 compare compare NOUN american_scientific_journal-522 261 18 of of ADP american_scientific_journal-522 261 19 nayak nayak PROPN american_scientific_journal-522 262 1 [ [ X american_scientific_journal-522 262 2 9 9 NUM american_scientific_journal-522 262 3 ] ] PUNCT american_scientific_journal-522 262 4 are be AUX american_scientific_journal-522 262 5 obtained obtain VERB american_scientific_journal-522 262 6 with with ADP american_scientific_journal-522 262 7 1245 1245 NUM american_scientific_journal-522 262 8 dof dof NOUN american_scientific_journal-522 262 9 , , PUNCT american_scientific_journal-522 262 10 or or CCONJ american_scientific_journal-522 262 11 ours ours PRON american_scientific_journal-522 262 12 are be AUX american_scientific_journal-522 262 13 obtained obtain VERB american_scientific_journal-522 262 14 with with ADP american_scientific_journal-522 262 15 480 480 NUM american_scientific_journal-522 262 16 dof dof NOUN american_scientific_journal-522 262 17 pθ pθ NOUN american_scientific_journal-522 262 18 = = PUNCT american_scientific_journal-522 262 19 pw pw PROPN american_scientific_journal-522 262 20 = = SYM american_scientific_journal-522 262 21 19 19 NUM american_scientific_journal-522 262 22 , , PUNCT american_scientific_journal-522 262 23 in in ADP american_scientific_journal-522 262 24 the the DET american_scientific_journal-522 262 25 example example NOUN american_scientific_journal-522 262 26 illustrated illustrate VERB american_scientific_journal-522 262 27 in in ADP american_scientific_journal-522 262 28 table table NOUN american_scientific_journal-522 262 29 6 6 NUM american_scientific_journal-522 262 30 , , PUNCT american_scientific_journal-522 262 31 a a DET american_scientific_journal-522 262 32 very very ADV american_scientific_journal-522 262 33 good good ADJ american_scientific_journal-522 262 34 accuracy accuracy NOUN american_scientific_journal-522 262 35 is be AUX american_scientific_journal-522 262 36 observed observe VERB american_scientific_journal-522 262 37 . . PUNCT american_scientific_journal-522 263 1 in in ADP american_scientific_journal-522 263 2 table table NOUN american_scientific_journal-522 263 3 7 7 NUM american_scientific_journal-522 263 4 , , PUNCT american_scientific_journal-522 263 5 good good ADJ american_scientific_journal-522 263 6 agreement agreement NOUN american_scientific_journal-522 263 7 is be AUX american_scientific_journal-522 263 8 achieved achieve VERB american_scientific_journal-522 263 9 by by ADP american_scientific_journal-522 263 10 comparing compare VERB american_scientific_journal-522 263 11 the the DET american_scientific_journal-522 263 12 present present ADJ american_scientific_journal-522 263 13 results result NOUN american_scientific_journal-522 263 14 with with ADP american_scientific_journal-522 263 15 those those PRON american_scientific_journal-522 263 16 obtained obtain VERB american_scientific_journal-522 263 17 by by ADP american_scientific_journal-522 263 18 wang wang PROPN american_scientific_journal-522 264 1 [ [ X american_scientific_journal-522 264 2 21 21 NUM american_scientific_journal-522 264 3 ] ] PUNCT american_scientific_journal-522 264 4 , , PUNCT american_scientific_journal-522 264 5 leissa leissa ADJ american_scientific_journal-522 264 6 [ [ X american_scientific_journal-522 264 7 17 17 NUM american_scientific_journal-522 264 8 ] ] PUNCT american_scientific_journal-522 264 9 , , PUNCT american_scientific_journal-522 264 10 lim lim PROPN american_scientific_journal-522 264 11 and and CCONJ american_scientific_journal-522 264 12 his his PRON american_scientific_journal-522 264 13 colleagues colleague NOUN american_scientific_journal-522 265 1 [ [ X american_scientific_journal-522 265 2 1 1 NUM american_scientific_journal-522 265 3 ] ] PUNCT american_scientific_journal-522 265 4 , , PUNCT american_scientific_journal-522 265 5 liew liew PROPN american_scientific_journal-522 265 6 and and CCONJ american_scientific_journal-522 265 7 his his PRON american_scientific_journal-522 265 8 colleagues colleague NOUN american_scientific_journal-522 266 1 [ [ X american_scientific_journal-522 266 2 23 23 NUM american_scientific_journal-522 266 3 ] ] PUNCT american_scientific_journal-522 266 4 , , PUNCT american_scientific_journal-522 266 5 wang wang PROPN american_scientific_journal-522 267 1 [ [ X american_scientific_journal-522 267 2 22 22 NUM american_scientific_journal-522 267 3 ] ] PUNCT american_scientific_journal-522 267 4 , , PUNCT american_scientific_journal-522 267 5 the the DET american_scientific_journal-522 267 6 first first ADJ american_scientific_journal-522 267 7 five five NUM american_scientific_journal-522 267 8 frequency frequency NOUN american_scientific_journal-522 267 9 parameters parameter NOUN american_scientific_journal-522 267 10 ω ω X american_scientific_journal-522 267 11 for for ADP american_scientific_journal-522 267 12 fully fully ADV american_scientific_journal-522 267 13 clamped clamp VERB american_scientific_journal-522 267 14 ( ( PUNCT american_scientific_journal-522 267 15 cccc cccc PROPN american_scientific_journal-522 267 16 ) ) PUNCT american_scientific_journal-522 267 17 square square ADJ american_scientific_journal-522 267 18 plates plate NOUN american_scientific_journal-522 267 19 with with ADP american_scientific_journal-522 267 20 different different ADJ american_scientific_journal-522 267 21 thickness thickness NOUN american_scientific_journal-522 267 22 - - PUNCT american_scientific_journal-522 267 23 side side NOUN american_scientific_journal-522 267 24 ratio ratio NOUN american_scientific_journal-522 267 25 h h PROPN american_scientific_journal-522 267 26 / / SYM american_scientific_journal-522 267 27 b b PROPN american_scientific_journal-522 267 28 = = SYM american_scientific_journal-522 267 29 0.001 0.001 NUM american_scientific_journal-522 267 30 , , PUNCT american_scientific_journal-522 267 31 0.1 0.1 NUM american_scientific_journal-522 267 32 , , PUNCT american_scientific_journal-522 267 33 0.2 0.2 NUM american_scientific_journal-522 267 34 , , PUNCT american_scientific_journal-522 267 35 0.5 0.5 NUM american_scientific_journal-522 267 36 . . NOUN american_scientific_journal-522 267 37 11 11 NUM american_scientific_journal-522 267 38 american american ADJ american_scientific_journal-522 267 39 scientific scientific ADJ american_scientific_journal-522 267 40 research research NOUN american_scientific_journal-522 267 41 journal journal NOUN american_scientific_journal-522 267 42 for for ADP american_scientific_journal-522 267 43 engineering engineering NOUN american_scientific_journal-522 267 44 , , PUNCT american_scientific_journal-522 267 45 technology technology NOUN american_scientific_journal-522 267 46 , , PUNCT american_scientific_journal-522 267 47 and and CCONJ american_scientific_journal-522 267 48 sciences science NOUN american_scientific_journal-522 267 49 ( ( PUNCT american_scientific_journal-522 267 50 asrjets asrjet NOUN american_scientific_journal-522 267 51 ) ) PUNCT american_scientific_journal-522 267 52 ( ( PUNCT american_scientific_journal-522 267 53 2014 2014 NUM american_scientific_journal-522 267 54 ) ) PUNCT american_scientific_journal-522 267 55 volume volume NOUN american_scientific_journal-522 267 56 9 9 NUM american_scientific_journal-522 267 57 , , PUNCT american_scientific_journal-522 267 58 no no DET american_scientific_journal-522 267 59 1 1 NUM american_scientific_journal-522 267 60 , , PUNCT american_scientific_journal-522 267 61 pp pp ADV american_scientific_journal-522 267 62 1 1 NUM american_scientific_journal-522 267 63 - - SYM american_scientific_journal-522 267 64 19 19 NUM american_scientific_journal-522 267 65 table table NOUN american_scientific_journal-522 267 66 6.comparison 6.comparison NUM american_scientific_journal-522 267 67 of of ADP american_scientific_journal-522 267 68 frequency frequency NOUN american_scientific_journal-522 267 69 parameters parameter NOUN american_scientific_journal-522 267 70 ω ω NOUN american_scientific_journal-522 267 71 = = SYM american_scientific_journal-522 267 72 ω ω PROPN american_scientific_journal-522 267 73 b2 b2 PROPN american_scientific_journal-522 267 74 π2 π2 PROPN american_scientific_journal-522 267 75 � � PROPN american_scientific_journal-522 267 76 ρ ρ PROPN american_scientific_journal-522 267 77 h h PROPN american_scientific_journal-522 267 78 d d NOUN american_scientific_journal-522 267 79 of of ADP american_scientific_journal-522 267 80 a a DET american_scientific_journal-522 267 81 ssss ssss NOUN american_scientific_journal-522 267 82 square square ADJ american_scientific_journal-522 267 83 plate plate NOUN american_scientific_journal-522 267 84 ( ( PUNCT american_scientific_journal-522 267 85 ν ν X american_scientific_journal-522 267 86 = = SYM american_scientific_journal-522 267 87 0.3 0.3 NUM american_scientific_journal-522 267 88 ) ) PUNCT american_scientific_journal-522 267 89 . . PUNCT american_scientific_journal-522 268 1 h h X american_scientific_journal-522 268 2 / / SYM american_scientific_journal-522 268 3 a a DET american_scientific_journal-522 268 4 solution solution NOUN american_scientific_journal-522 268 5 methods method NOUN american_scientific_journal-522 268 6 1 1 NUM american_scientific_journal-522 268 7 2 2 NUM american_scientific_journal-522 268 8 3 3 NUM american_scientific_journal-522 268 9 4 4 NUM american_scientific_journal-522 268 10 5 5 NUM american_scientific_journal-522 268 11 0.001 0.001 NUM american_scientific_journal-522 268 12 present present NOUN american_scientific_journal-522 268 13 ( ( PUNCT american_scientific_journal-522 268 14 pθ pθ NOUN american_scientific_journal-522 268 15 = = NOUN american_scientific_journal-522 268 16 pw=19 pw=19 ADJ american_scientific_journal-522 268 17 ) ) PUNCT american_scientific_journal-522 268 18 2,000 2,000 NUM american_scientific_journal-522 268 19 5,003 5,003 NUM american_scientific_journal-522 268 20 5,003 5,003 NUM american_scientific_journal-522 268 21 8,004 8,004 NUM american_scientific_journal-522 268 22 10,017 10,017 NUM american_scientific_journal-522 268 23 cpt cpt NOUN american_scientific_journal-522 268 24 - - NOUN american_scientific_journal-522 268 25 exact exact NOUN american_scientific_journal-522 268 26 [ [ X american_scientific_journal-522 268 27 17 17 NUM american_scientific_journal-522 268 28 ] ] SYM american_scientific_journal-522 268 29 2,000 2,000 NUM american_scientific_journal-522 268 30 5,000 5,000 NUM american_scientific_journal-522 268 31 5,000 5,000 NUM american_scientific_journal-522 268 32 8,000 8,000 NUM american_scientific_journal-522 268 33 10,000 10,000 NUM american_scientific_journal-522 268 34 0.1 0.1 NUM american_scientific_journal-522 268 35 present present ADJ american_scientific_journal-522 268 36 ( ( PUNCT american_scientific_journal-522 268 37 480 480 NUM american_scientific_journal-522 268 38 dofs dof NOUN american_scientific_journal-522 268 39 ) ) PUNCT american_scientific_journal-522 268 40 1,932 1,932 NUM american_scientific_journal-522 268 41 4,609 4,609 NUM american_scientific_journal-522 268 42 4,609 4,609 NUM american_scientific_journal-522 268 43 7.074 7.074 NUM american_scientific_journal-522 268 44 8.622 8.622 NUM american_scientific_journal-522 268 45 hsdt hsdt NOUN american_scientific_journal-522 268 46 fem fem NOUN american_scientific_journal-522 269 1 [ [ X american_scientific_journal-522 269 2 9 9 NUM american_scientific_journal-522 269 3 ] ] SYM american_scientific_journal-522 269 4 ( ( PUNCT american_scientific_journal-522 269 5 1245 1245 NUM american_scientific_journal-522 269 6 dofs dof NOUN american_scientific_journal-522 269 7 ) ) PUNCT american_scientific_journal-522 269 8 1,931 1,931 NUM american_scientific_journal-522 270 1 4,614 4,614 NUM american_scientific_journal-522 270 2 4,614 4,614 NUM american_scientific_journal-522 270 3 7.085 7.085 NUM american_scientific_journal-522 270 4 8.657 8.657 NUM american_scientific_journal-522 270 5 mindlintheory mindlintheory NOUN american_scientific_journal-522 271 1 [ [ X american_scientific_journal-522 271 2 2 2 NUM american_scientific_journal-522 271 3 ] ] PUNCT american_scientific_journal-522 271 4 1,931 1,931 NUM american_scientific_journal-522 271 5 4,605 4,605 NUM american_scientific_journal-522 271 6 4,605 4,605 NUM american_scientific_journal-522 271 7 7.064 7.064 NUM american_scientific_journal-522 271 8 8.607 8.607 NUM american_scientific_journal-522 271 9 hsdt hsdt NOUN american_scientific_journal-522 271 10 [ [ X american_scientific_journal-522 271 11 18 18 NUM american_scientific_journal-522 271 12 ] ] SYM american_scientific_journal-522 271 13 1,932 1,932 NUM american_scientific_journal-522 271 14 4,609 4,609 NUM american_scientific_journal-522 271 15 4,609 4,609 NUM american_scientific_journal-522 271 16 7.073 7.073 NUM american_scientific_journal-522 271 17 8.617 8.617 NUM american_scientific_journal-522 271 18 3 3 NUM american_scientific_journal-522 271 19 - - PUNCT american_scientific_journal-522 271 20 d d NOUN american_scientific_journal-522 271 21 exact exact NOUN american_scientific_journal-522 272 1 [ [ X american_scientific_journal-522 272 2 19 19 NUM american_scientific_journal-522 272 3 ] ] SYM american_scientific_journal-522 272 4 1,934 1,934 NUM american_scientific_journal-522 272 5 4,622 4,622 NUM american_scientific_journal-522 272 6 4,622 4,622 NUM american_scientific_journal-522 272 7 7.103 7.103 NUM american_scientific_journal-522 272 8 8.662 8.662 NUM american_scientific_journal-522 272 9 0.2 0.2 NUM american_scientific_journal-522 272 10 present present ADJ american_scientific_journal-522 272 11 ( ( PUNCT american_scientific_journal-522 272 12 pθ pθ ADP american_scientific_journal-522 272 13 = = SYM american_scientific_journal-522 272 14 pw=12 pw=12 NOUN american_scientific_journal-522 272 15 ) ) PUNCT american_scientific_journal-522 272 16 1,768 1,768 NUM american_scientific_journal-522 272 17 3.870 3.870 NUM american_scientific_journal-522 272 18 3.870 3.870 NUM american_scientific_journal-522 272 19 5.599 5.599 NUM american_scientific_journal-522 272 20 6.619 6.619 NUM american_scientific_journal-522 272 21 mindlintheory mindlintheory NOUN american_scientific_journal-522 272 22 [ [ X american_scientific_journal-522 272 23 2 2 NUM american_scientific_journal-522 272 24 ] ] PUNCT american_scientific_journal-522 272 25 1,766 1,766 NUM american_scientific_journal-522 272 26 3.858 3.858 NUM american_scientific_journal-522 272 27 3.858 3.858 NUM american_scientific_journal-522 272 28 5.573 5.573 NUM american_scientific_journal-522 272 29 3 3 NUM american_scientific_journal-522 272 30 - - PUNCT american_scientific_journal-522 272 31 d d NOUN american_scientific_journal-522 272 32 exact exact NOUN american_scientific_journal-522 272 33 [ [ X american_scientific_journal-522 272 34 19 19 NUM american_scientific_journal-522 272 35 ] ] SYM american_scientific_journal-522 272 36 1,756 1,756 NUM american_scientific_journal-522 272 37 3.899 3.899 NUM american_scientific_journal-522 272 38 3.899 3.899 NUM american_scientific_journal-522 272 39 5.653 5.653 NUM american_scientific_journal-522 272 40 0.5 0.5 NUM american_scientific_journal-522 272 41 present present NOUN american_scientific_journal-522 272 42 ( ( PUNCT american_scientific_journal-522 272 43 pθ pθ NOUN american_scientific_journal-522 272 44 = = PRON american_scientific_journal-522 272 45 pw=6 pw=6 NOUN american_scientific_journal-522 272 46 ) ) PUNCT american_scientific_journal-522 272 47 1,245 1,245 NUM american_scientific_journal-522 272 48 2.308 2.308 NUM american_scientific_journal-522 272 49 2.308 2.308 NUM american_scientific_journal-522 272 50 2.919 2.919 NUM american_scientific_journal-522 272 51 2.919 2.919 NUM american_scientific_journal-522 272 52 hsdt hsdt NOUN american_scientific_journal-522 272 53 [ [ X american_scientific_journal-522 272 54 18 18 NUM american_scientific_journal-522 272 55 ] ] SYM american_scientific_journal-522 272 56 1,245 1,245 NUM american_scientific_journal-522 272 57 2.308 2.308 NUM american_scientific_journal-522 272 58 2.308 2.308 NUM american_scientific_journal-522 272 59 2.917 2.917 NUM american_scientific_journal-522 272 60 2.917 2.917 NUM american_scientific_journal-522 272 61 3 3 NUM american_scientific_journal-522 272 62 - - PUNCT american_scientific_journal-522 272 63 d d NOUN american_scientific_journal-522 272 64 exact exact NOUN american_scientific_journal-522 273 1 [ [ X american_scientific_journal-522 273 2 19 19 NUM american_scientific_journal-522 273 3 ] ] SYM american_scientific_journal-522 273 4 1,259 1,259 NUM american_scientific_journal-522 273 5 3 3 NUM american_scientific_journal-522 273 6 - - SYM american_scientific_journal-522 273 7 d d PROPN american_scientific_journal-522 273 8 ritz ritz PROPN american_scientific_journal-522 273 9 [ [ X american_scientific_journal-522 273 10 20 20 NUM american_scientific_journal-522 273 11 ] ] SYM american_scientific_journal-522 273 12 1,259 1,259 NUM american_scientific_journal-522 273 13 2.331 2.331 NUM american_scientific_journal-522 273 14 2.331 2.331 NUM american_scientific_journal-522 273 15 table table NOUN american_scientific_journal-522 273 16 7.comparison 7.comparison NUM american_scientific_journal-522 273 17 of of ADP american_scientific_journal-522 273 18 frequency frequency NOUN american_scientific_journal-522 273 19 parameters parameter NOUN american_scientific_journal-522 273 20 ω ω NOUN american_scientific_journal-522 273 21 = = SYM american_scientific_journal-522 273 22 ω ω PROPN american_scientific_journal-522 273 23 b2 b2 PROPN american_scientific_journal-522 273 24 π2 π2 PROPN american_scientific_journal-522 273 25 � � PROPN american_scientific_journal-522 273 26 ρ ρ PROPN american_scientific_journal-522 273 27 h h PROPN american_scientific_journal-522 273 28 d d NOUN american_scientific_journal-522 273 29 of of ADP american_scientific_journal-522 273 30 a a DET american_scientific_journal-522 273 31 cccc cccc PROPN american_scientific_journal-522 273 32 square square ADJ american_scientific_journal-522 273 33 plate plate NOUN american_scientific_journal-522 273 34 ( ( PUNCT american_scientific_journal-522 273 35 ν ν X american_scientific_journal-522 273 36 = = SYM american_scientific_journal-522 273 37 0.3 0.3 NUM american_scientific_journal-522 273 38 ) ) PUNCT american_scientific_journal-522 273 39 . . PUNCT american_scientific_journal-522 274 1 h h X american_scientific_journal-522 274 2 / / SYM american_scientific_journal-522 274 3 a a DET american_scientific_journal-522 274 4 solution solution NOUN american_scientific_journal-522 274 5 methods method NOUN american_scientific_journal-522 274 6 1 1 NUM american_scientific_journal-522 274 7 2 2 NUM american_scientific_journal-522 274 8 3 3 NUM american_scientific_journal-522 274 9 4 4 NUM american_scientific_journal-522 274 10 5 5 NUM american_scientific_journal-522 274 11 0.001 0.001 NUM american_scientific_journal-522 274 12 present present NOUN american_scientific_journal-522 274 13 ( ( PUNCT american_scientific_journal-522 274 14 pθ pθ NOUN american_scientific_journal-522 274 15 = = NOUN american_scientific_journal-522 274 16 pw=24 pw=24 ADJ american_scientific_journal-522 274 17 ) ) PUNCT american_scientific_journal-522 274 18 3.674 3.674 NUM american_scientific_journal-522 274 19 7.506 7.506 NUM american_scientific_journal-522 274 20 7.506 7.506 NUM american_scientific_journal-522 274 21 11.162 11.162 NUM american_scientific_journal-522 274 22 13.488 13.488 NUM american_scientific_journal-522 274 23 cpt cpt PROPN american_scientific_journal-522 274 24 ritz ritz PROPN american_scientific_journal-522 274 25 ( ( PUNCT american_scientific_journal-522 274 26 s s PROPN american_scientific_journal-522 274 27 wang wang PROPN american_scientific_journal-522 274 28 ) ) PUNCT american_scientific_journal-522 275 1 [ [ X american_scientific_journal-522 275 2 21 21 NUM american_scientific_journal-522 275 3 ] ] PUNCT american_scientific_journal-522 275 4 3,646 3,646 NUM american_scientific_journal-522 275 5 7,436 7,436 NUM american_scientific_journal-522 275 6 7,436 7,436 NUM american_scientific_journal-522 275 7 10,945 10,945 NUM american_scientific_journal-522 275 8 13,332 13,332 NUM american_scientific_journal-522 275 9 cpt cpt PROPN american_scientific_journal-522 275 10 ritz ritz PROPN american_scientific_journal-522 275 11 [ [ X american_scientific_journal-522 275 12 17 17 NUM american_scientific_journal-522 275 13 ] ] PUNCT american_scientific_journal-522 275 14 3,647 3,647 NUM american_scientific_journal-522 275 15 7,438 7,438 NUM american_scientific_journal-522 275 16 7,438 7,438 NUM american_scientific_journal-522 275 17 10,970 10,970 NUM american_scientific_journal-522 275 18 13,338 13,338 NUM american_scientific_journal-522 275 19 0.1 0.1 NUM american_scientific_journal-522 275 20 present present ADJ american_scientific_journal-522 275 21 ( ( PUNCT american_scientific_journal-522 275 22 pθ pθ NOUN american_scientific_journal-522 275 23 = = NOUN american_scientific_journal-522 275 24 pw=22 pw=22 ADJ american_scientific_journal-522 275 25 ) ) PUNCT american_scientific_journal-522 275 26 3.306 3.306 NUM american_scientific_journal-522 275 27 6.323 6.323 NUM american_scientific_journal-522 275 28 6.323 6.323 NUM american_scientific_journal-522 275 29 8.879 8.879 NUM american_scientific_journal-522 275 30 10.477 10.477 NUM american_scientific_journal-522 275 31 hsdt hsdt NOUN american_scientific_journal-522 275 32 [ [ X american_scientific_journal-522 275 33 18 18 NUM american_scientific_journal-522 275 34 ] ] SYM american_scientific_journal-522 275 35 3,303 3,303 NUM american_scientific_journal-522 275 36 6,311 6,311 NUM american_scientific_journal-522 275 37 6,311 6,311 NUM american_scientific_journal-522 275 38 8,858 8,858 NUM american_scientific_journal-522 275 39 10,446 10,446 NUM american_scientific_journal-522 275 40 3 3 NUM american_scientific_journal-522 275 41 - - SYM american_scientific_journal-522 275 42 d d PROPN american_scientific_journal-522 275 43 ritz ritz PROPN american_scientific_journal-522 276 1 [ [ X american_scientific_journal-522 276 2 22 22 NUM american_scientific_journal-522 276 3 ] ] PUNCT american_scientific_journal-522 276 4 3,322 3,322 NUM american_scientific_journal-522 276 5 6,346 6,346 NUM american_scientific_journal-522 276 6 6,346 6,346 NUM american_scientific_journal-522 276 7 8,903 8,903 NUM american_scientific_journal-522 276 8 10,498 10,498 NUM american_scientific_journal-522 276 9 0.2 0.2 NUM american_scientific_journal-522 276 10 present present ADJ american_scientific_journal-522 276 11 ( ( PUNCT american_scientific_journal-522 276 12 pθ pθ NOUN american_scientific_journal-522 276 13 = = NOUN american_scientific_journal-522 276 14 pw=22 pw=22 ADJ american_scientific_journal-522 276 15 ) ) PUNCT american_scientific_journal-522 276 16 2.720 2.720 NUM american_scientific_journal-522 276 17 4.786 4.786 NUM american_scientific_journal-522 276 18 4.786 4.786 NUM american_scientific_journal-522 276 19 6.451 6.451 NUM american_scientific_journal-522 276 20 7.384 7.384 NUM american_scientific_journal-522 276 21 mindlintheory mindlintheory NOUN american_scientific_journal-522 276 22 [ [ X american_scientific_journal-522 276 23 23 23 NUM american_scientific_journal-522 276 24 ] ] PUNCT american_scientific_journal-522 276 25 2,681 2,681 NUM american_scientific_journal-522 276 26 4,675 4,675 NUM american_scientific_journal-522 276 27 4,675 4,675 NUM american_scientific_journal-522 276 28 0.5 0.5 NUM american_scientific_journal-522 276 29 present present NOUN american_scientific_journal-522 276 30 ( ( PUNCT american_scientific_journal-522 276 31 pθ pθ PROPN american_scientific_journal-522 276 32 = = NOUN american_scientific_journal-522 276 33 pw=14 pw=14 NOUN american_scientific_journal-522 276 34 ) ) PUNCT american_scientific_journal-522 276 35 1.593 1.593 NUM american_scientific_journal-522 276 36 2.550 2.550 NUM american_scientific_journal-522 276 37 2.550 2.550 NUM american_scientific_journal-522 276 38 3.358 3.358 NUM american_scientific_journal-522 276 39 3.685 3.685 NUM american_scientific_journal-522 276 40 12 12 NUM american_scientific_journal-522 276 41 american american ADJ american_scientific_journal-522 276 42 scientific scientific ADJ american_scientific_journal-522 276 43 research research NOUN american_scientific_journal-522 276 44 journal journal NOUN american_scientific_journal-522 276 45 for for ADP american_scientific_journal-522 276 46 engineering engineering NOUN american_scientific_journal-522 276 47 , , PUNCT american_scientific_journal-522 276 48 technology technology NOUN american_scientific_journal-522 276 49 , , PUNCT american_scientific_journal-522 276 50 and and CCONJ american_scientific_journal-522 276 51 sciences science NOUN american_scientific_journal-522 276 52 ( ( PUNCT american_scientific_journal-522 276 53 asrjets asrjet NOUN american_scientific_journal-522 276 54 ) ) PUNCT american_scientific_journal-522 276 55 ( ( PUNCT american_scientific_journal-522 276 56 2014 2014 NUM american_scientific_journal-522 276 57 ) ) PUNCT american_scientific_journal-522 276 58 volume volume NOUN american_scientific_journal-522 276 59 9 9 NUM american_scientific_journal-522 276 60 , , PUNCT american_scientific_journal-522 276 61 no no DET american_scientific_journal-522 276 62 1 1 NUM american_scientific_journal-522 276 63 , , PUNCT american_scientific_journal-522 276 64 pp pp ADV american_scientific_journal-522 276 65 1 1 NUM american_scientific_journal-522 276 66 - - SYM american_scientific_journal-522 276 67 19 19 NUM american_scientific_journal-522 276 68 hsdt hsdt NOUN american_scientific_journal-522 276 69 [ [ X american_scientific_journal-522 276 70 18 18 NUM american_scientific_journal-522 276 71 ] ] SYM american_scientific_journal-522 276 72 1,587 1,587 NUM american_scientific_journal-522 276 73 2.536 2.536 NUM american_scientific_journal-522 276 74 2.536 2.536 NUM american_scientific_journal-522 276 75 3.337 3.337 NUM american_scientific_journal-522 276 76 3.684 3.684 NUM american_scientific_journal-522 276 77 3 3 NUM american_scientific_journal-522 276 78 - - SYM american_scientific_journal-522 276 79 d d PROPN american_scientific_journal-522 276 80 ritz ritz PROPN american_scientific_journal-522 277 1 [ [ X american_scientific_journal-522 277 2 22 22 NUM american_scientific_journal-522 277 3 ] ] PUNCT american_scientific_journal-522 277 4 1,550 1,550 NUM american_scientific_journal-522 277 5 2,515 2,515 NUM american_scientific_journal-522 277 6 2,515 2,515 NUM american_scientific_journal-522 277 7 3,193 3,193 NUM american_scientific_journal-522 277 8 3.654 3.654 NUM american_scientific_journal-522 277 9 in in ADP american_scientific_journal-522 277 10 table table NOUN american_scientific_journal-522 277 11 8 8 NUM american_scientific_journal-522 277 12 , , PUNCT american_scientific_journal-522 277 13 good good ADJ american_scientific_journal-522 277 14 agreement agreement NOUN american_scientific_journal-522 277 15 is be AUX american_scientific_journal-522 277 16 achieved achieve VERB american_scientific_journal-522 277 17 by by ADP american_scientific_journal-522 277 18 comparing compare VERB american_scientific_journal-522 277 19 the the DET american_scientific_journal-522 277 20 present present ADJ american_scientific_journal-522 277 21 results result NOUN american_scientific_journal-522 277 22 with with ADP american_scientific_journal-522 277 23 those those PRON american_scientific_journal-522 277 24 obtained obtain VERB american_scientific_journal-522 277 25 by by ADP american_scientific_journal-522 277 26 , , PUNCT american_scientific_journal-522 277 27 liew liew PROPN american_scientific_journal-522 277 28 and and CCONJ american_scientific_journal-522 277 29 his his PRON american_scientific_journal-522 277 30 colleagues colleague NOUN american_scientific_journal-522 277 31 . . PUNCT american_scientific_journal-522 278 1 [ [ X american_scientific_journal-522 278 2 23 23 NUM american_scientific_journal-522 278 3 ] ] PUNCT american_scientific_journal-522 278 4 and and CCONJ american_scientific_journal-522 278 5 lim lim PROPN american_scientific_journal-522 278 6 and and CCONJ american_scientific_journal-522 278 7 his his PRON american_scientific_journal-522 278 8 colleagues colleague NOUN american_scientific_journal-522 278 9 [ [ X american_scientific_journal-522 278 10 18 18 NUM american_scientific_journal-522 278 11 ] ] PUNCT american_scientific_journal-522 278 12 , , PUNCT american_scientific_journal-522 278 13 the the DET american_scientific_journal-522 278 14 first first ADJ american_scientific_journal-522 278 15 five five NUM american_scientific_journal-522 278 16 frequency frequency NOUN american_scientific_journal-522 278 17 parameters parameter NOUN american_scientific_journal-522 278 18 ω ω X american_scientific_journal-522 278 19 for for ADP american_scientific_journal-522 278 20 combined combine VERB american_scientific_journal-522 278 21 boundary boundary ADJ american_scientific_journal-522 278 22 condition condition NOUN american_scientific_journal-522 278 23 ( ( PUNCT american_scientific_journal-522 278 24 cfcf cfcf NOUN american_scientific_journal-522 278 25 ) ) PUNCT american_scientific_journal-522 278 26 square square ADJ american_scientific_journal-522 278 27 plates plate NOUN american_scientific_journal-522 278 28 with with ADP american_scientific_journal-522 278 29 tree tree NOUN american_scientific_journal-522 278 30 different different ADJ american_scientific_journal-522 278 31 thickness thickness NOUN american_scientific_journal-522 278 32 - - PUNCT american_scientific_journal-522 278 33 side side NOUN american_scientific_journal-522 278 34 ratio ratio NOUN american_scientific_journal-522 278 35 h h PROPN american_scientific_journal-522 278 36 / / SYM american_scientific_journal-522 278 37 b b NOUN american_scientific_journal-522 278 38 = = NOUN american_scientific_journal-522 278 39 0.01 0.01 NUM american_scientific_journal-522 278 40 , , PUNCT american_scientific_journal-522 278 41 0.1 0.1 NUM american_scientific_journal-522 278 42 , , PUNCT american_scientific_journal-522 278 43 0.5 0.5 NUM american_scientific_journal-522 278 44 . . PUNCT american_scientific_journal-522 278 45 table table NOUN american_scientific_journal-522 278 46 8.comparison 8.comparison NUM american_scientific_journal-522 278 47 of of ADP american_scientific_journal-522 278 48 frequency frequency NOUN american_scientific_journal-522 278 49 parameters parameter NOUN american_scientific_journal-522 278 50 ω ω NOUN american_scientific_journal-522 278 51 = = SYM american_scientific_journal-522 278 52 ω ω PROPN american_scientific_journal-522 278 53 b2 b2 PROPN american_scientific_journal-522 278 54 π2 π2 PROPN american_scientific_journal-522 278 55 � � PROPN american_scientific_journal-522 278 56 ρ ρ PROPN american_scientific_journal-522 278 57 h h PROPN american_scientific_journal-522 279 1 d d NOUN american_scientific_journal-522 279 2 of of ADP american_scientific_journal-522 279 3 a a DET american_scientific_journal-522 279 4 cfcf cfcf ADJ american_scientific_journal-522 279 5 square square ADJ american_scientific_journal-522 279 6 plate plate NOUN american_scientific_journal-522 279 7 ( ( PUNCT american_scientific_journal-522 279 8 ν ν X american_scientific_journal-522 279 9 = = SYM american_scientific_journal-522 279 10 0.3 0.3 NUM american_scientific_journal-522 279 11 ) ) PUNCT american_scientific_journal-522 279 12 . . PUNCT american_scientific_journal-522 280 1 h h NOUN american_scientific_journal-522 280 2 / / SYM american_scientific_journal-522 280 3 b b NOUN american_scientific_journal-522 280 4 solution solution NOUN american_scientific_journal-522 280 5 methods method NOUN american_scientific_journal-522 280 6 1 1 NUM american_scientific_journal-522 280 7 2 2 NUM american_scientific_journal-522 280 8 3 3 NUM american_scientific_journal-522 280 9 4 4 NUM american_scientific_journal-522 280 10 5 5 NUM american_scientific_journal-522 280 11 0.01 0.01 NUM american_scientific_journal-522 280 12 present present ADJ american_scientific_journal-522 280 13 ( ( PUNCT american_scientific_journal-522 280 14 pθ pθ NOUN american_scientific_journal-522 280 15 = = NOUN american_scientific_journal-522 280 16 pw=22 pw=22 ADJ american_scientific_journal-522 280 17 ) ) PUNCT american_scientific_journal-522 280 18 2.245 2.245 NUM american_scientific_journal-522 280 19 2.673 2.673 NUM american_scientific_journal-522 280 20 4.410 4.410 NUM american_scientific_journal-522 280 21 6.189 6.189 NUM american_scientific_journal-522 280 22 6.795 6.795 NUM american_scientific_journal-522 280 23 3 3 NUM american_scientific_journal-522 280 24 - - SYM american_scientific_journal-522 280 25 d d PROPN american_scientific_journal-522 280 26 ritz ritz PROPN american_scientific_journal-522 281 1 [ [ X american_scientific_journal-522 281 2 22 22 NUM american_scientific_journal-522 281 3 ] ] PUNCT american_scientific_journal-522 281 4 2.248 2.248 NUM american_scientific_journal-522 281 5 2.674 2.674 NUM american_scientific_journal-522 281 6 4.408 4.408 NUM american_scientific_journal-522 281 7 6.197 6.197 NUM american_scientific_journal-522 281 8 6.799 6.799 NUM american_scientific_journal-522 281 9 0.1 0.1 NUM american_scientific_journal-522 281 10 present present ADJ american_scientific_journal-522 281 11 ( ( PUNCT american_scientific_journal-522 281 12 pθ pθ NOUN american_scientific_journal-522 281 13 = = NOUN american_scientific_journal-522 281 14 pw=22 pw=22 ADJ american_scientific_journal-522 281 15 ) ) PUNCT american_scientific_journal-522 281 16 2.095 2.095 NUM american_scientific_journal-522 281 17 2.441 2.441 NUM american_scientific_journal-522 281 18 3.920 3.920 NUM american_scientific_journal-522 281 19 5.366 5.366 NUM american_scientific_journal-522 281 20 5.813 5.813 NUM american_scientific_journal-522 281 21 hsdt hsdt NOUN american_scientific_journal-522 281 22 [ [ X american_scientific_journal-522 281 23 18 18 NUM american_scientific_journal-522 281 24 ] ] PUNCT american_scientific_journal-522 281 25 2.093 2.093 NUM american_scientific_journal-522 281 26 2.438 2.438 NUM american_scientific_journal-522 281 27 3.913 3.913 NUM american_scientific_journal-522 281 28 5.357 5.357 NUM american_scientific_journal-522 281 29 5.802 5.802 NUM american_scientific_journal-522 281 30 3 3 NUM american_scientific_journal-522 281 31 - - SYM american_scientific_journal-522 281 32 d d PROPN american_scientific_journal-522 281 33 ritz ritz PROPN american_scientific_journal-522 282 1 [ [ X american_scientific_journal-522 282 2 22 22 NUM american_scientific_journal-522 282 3 ] ] PUNCT american_scientific_journal-522 282 4 2.105 2.105 NUM american_scientific_journal-522 282 5 2.449 2.449 NUM american_scientific_journal-522 282 6 3.923 3.923 NUM american_scientific_journal-522 282 7 5.386 5.386 NUM american_scientific_journal-522 282 8 5.827 5.827 NUM american_scientific_journal-522 282 9 0.5 0.5 NUM american_scientific_journal-522 282 10 present present NOUN american_scientific_journal-522 282 11 ( ( PUNCT american_scientific_journal-522 282 12 pθ pθ ADP american_scientific_journal-522 282 13 = = NOUN american_scientific_journal-522 282 14 pw=17 pw=17 PROPN american_scientific_journal-522 282 15 ) ) PUNCT american_scientific_journal-522 282 16 1.098 1.098 NUM american_scientific_journal-522 282 17 1.192 1.192 NUM american_scientific_journal-522 282 18 1.894 1.894 NUM american_scientific_journal-522 282 19 2.192 2.192 NUM american_scientific_journal-522 282 20 2.376 2.376 NUM american_scientific_journal-522 282 21 hsdt hsdt NOUN american_scientific_journal-522 282 22 [ [ X american_scientific_journal-522 282 23 18 18 NUM american_scientific_journal-522 282 24 ] ] SYM american_scientific_journal-522 282 25 1.095 1.095 NUM american_scientific_journal-522 282 26 1.189 1.189 NUM american_scientific_journal-522 282 27 1.891 1.891 NUM american_scientific_journal-522 282 28 2.185 2.185 NUM american_scientific_journal-522 282 29 2.369 2.369 NUM american_scientific_journal-522 282 30 3 3 NUM american_scientific_journal-522 282 31 - - SYM american_scientific_journal-522 282 32 d d PROPN american_scientific_journal-522 282 33 ritz ritz PROPN american_scientific_journal-522 283 1 [ [ X american_scientific_journal-522 283 2 22 22 NUM american_scientific_journal-522 283 3 ] ] PUNCT american_scientific_journal-522 283 4 1.072 1.072 NUM american_scientific_journal-522 283 5 1.193 1.193 NUM american_scientific_journal-522 283 6 1.871 1.871 NUM american_scientific_journal-522 283 7 2.193 2.193 NUM american_scientific_journal-522 283 8 2.325 2.325 NUM american_scientific_journal-522 283 9 in in ADP american_scientific_journal-522 283 10 table table NOUN american_scientific_journal-522 283 11 9 9 NUM american_scientific_journal-522 283 12 , , PUNCT american_scientific_journal-522 283 13 shows show VERB american_scientific_journal-522 283 14 a a DET american_scientific_journal-522 283 15 comparison comparison NOUN american_scientific_journal-522 283 16 of of ADP american_scientific_journal-522 283 17 results result NOUN american_scientific_journal-522 283 18 for for ADP american_scientific_journal-522 283 19 square square ADJ american_scientific_journal-522 283 20 thin thin ADJ american_scientific_journal-522 283 21 and and CCONJ american_scientific_journal-522 283 22 thick thick ADJ american_scientific_journal-522 283 23 plates plate NOUN american_scientific_journal-522 283 24 by by ADP american_scientific_journal-522 283 25 , , PUNCT american_scientific_journal-522 283 26 houmat houmat PROPN american_scientific_journal-522 284 1 [ [ X american_scientific_journal-522 284 2 24 24 NUM american_scientific_journal-522 284 3 ] ] PUNCT american_scientific_journal-522 284 4 , , PUNCT american_scientific_journal-522 284 5 and and CCONJ american_scientific_journal-522 284 6 lim lim PROPN american_scientific_journal-522 284 7 and and CCONJ american_scientific_journal-522 284 8 his his PRON american_scientific_journal-522 284 9 colleagues colleague NOUN american_scientific_journal-522 284 10 [ [ X american_scientific_journal-522 284 11 18 18 NUM american_scientific_journal-522 284 12 ] ] PUNCT american_scientific_journal-522 284 13 , , PUNCT american_scientific_journal-522 284 14 the the DET american_scientific_journal-522 284 15 first first ADJ american_scientific_journal-522 284 16 five five NUM american_scientific_journal-522 284 17 frequency frequency NOUN american_scientific_journal-522 284 18 parameters parameter NOUN american_scientific_journal-522 284 19 ω ω X american_scientific_journal-522 284 20 for for ADP american_scientific_journal-522 284 21 free free ADJ american_scientific_journal-522 284 22 edges edge NOUN american_scientific_journal-522 284 23 ( ( PUNCT american_scientific_journal-522 284 24 ffff ffff NOUN american_scientific_journal-522 284 25 ) ) PUNCT american_scientific_journal-522 284 26 square square ADJ american_scientific_journal-522 284 27 plates plate NOUN american_scientific_journal-522 284 28 with with ADP american_scientific_journal-522 284 29 different different ADJ american_scientific_journal-522 284 30 thickness thickness NOUN american_scientific_journal-522 284 31 - - PUNCT american_scientific_journal-522 284 32 side side NOUN american_scientific_journal-522 284 33 ratio ratio NOUN american_scientific_journal-522 284 34 h h PROPN american_scientific_journal-522 284 35 / / SYM american_scientific_journal-522 284 36 b b PROPN american_scientific_journal-522 284 37 = = SYM american_scientific_journal-522 284 38 0.001 0.001 NUM american_scientific_journal-522 284 39 , , PUNCT american_scientific_journal-522 284 40 0.1 0.1 NUM american_scientific_journal-522 284 41 , , PUNCT american_scientific_journal-522 284 42 0.5 0.5 NUM american_scientific_journal-522 284 43 . . PUNCT american_scientific_journal-522 284 44 table table NOUN american_scientific_journal-522 284 45 9.comparison 9.comparison NUM american_scientific_journal-522 284 46 of of ADP american_scientific_journal-522 284 47 frequency frequency NOUN american_scientific_journal-522 284 48 parameters parameter NOUN american_scientific_journal-522 284 49 ω ω NOUN american_scientific_journal-522 284 50 = = SYM american_scientific_journal-522 284 51 ω ω PROPN american_scientific_journal-522 284 52 b2 b2 PROPN american_scientific_journal-522 284 53 π2 π2 PROPN american_scientific_journal-522 284 54 � � PROPN american_scientific_journal-522 284 55 ρ ρ PROPN american_scientific_journal-522 284 56 h h PROPN american_scientific_journal-522 285 1 d d NOUN american_scientific_journal-522 285 2 of of ADP american_scientific_journal-522 285 3 a a DET american_scientific_journal-522 285 4 ffff ffff ADJ american_scientific_journal-522 285 5 square square ADJ american_scientific_journal-522 285 6 plate plate NOUN american_scientific_journal-522 285 7 ( ( PUNCT american_scientific_journal-522 285 8 ν ν X american_scientific_journal-522 285 9 = = SYM american_scientific_journal-522 285 10 0.3 0.3 NUM american_scientific_journal-522 285 11 ) ) PUNCT american_scientific_journal-522 285 12 . . PUNCT american_scientific_journal-522 286 1 h h X american_scientific_journal-522 286 2 / / SYM american_scientific_journal-522 286 3 a a DET american_scientific_journal-522 286 4 solution solution NOUN american_scientific_journal-522 286 5 methods method NOUN american_scientific_journal-522 286 6 1 1 NUM american_scientific_journal-522 286 7 2 2 NUM american_scientific_journal-522 286 8 3 3 NUM american_scientific_journal-522 286 9 4 4 NUM american_scientific_journal-522 286 10 5 5 NUM american_scientific_journal-522 286 11 0.001 0.001 NUM american_scientific_journal-522 286 12 present present NOUN american_scientific_journal-522 286 13 ( ( PUNCT american_scientific_journal-522 286 14 pθ pθ NOUN american_scientific_journal-522 286 15 = = NOUN american_scientific_journal-522 286 16 pw=20 pw=20 NOUN american_scientific_journal-522 286 17 ) ) PUNCT american_scientific_journal-522 286 18 1,365 1,365 NUM american_scientific_journal-522 286 19 1,986 1,986 NUM american_scientific_journal-522 286 20 2,460 2,460 NUM american_scientific_journal-522 286 21 3,529 3,529 NUM american_scientific_journal-522 286 22 6,199 6,199 NUM american_scientific_journal-522 286 23 hfem hfem VERB american_scientific_journal-522 287 1 [ [ X american_scientific_journal-522 287 2 24 24 NUM american_scientific_journal-522 287 3 ] ] SYM american_scientific_journal-522 287 4 1,365 1,365 NUM american_scientific_journal-522 287 5 1,986 1,986 NUM american_scientific_journal-522 287 6 2,459 2,459 NUM american_scientific_journal-522 287 7 3,526 3,526 NUM american_scientific_journal-522 287 8 6,190 6,190 NUM american_scientific_journal-522 287 9 0.1 0.1 NUM american_scientific_journal-522 287 10 present present ADJ american_scientific_journal-522 287 11 ( ( PUNCT american_scientific_journal-522 287 12 pθ pθ NOUN american_scientific_journal-522 287 13 = = NOUN american_scientific_journal-522 287 14 pw=20 pw=20 NOUN american_scientific_journal-522 287 15 ) ) PUNCT american_scientific_journal-522 287 16 1,291 1,291 NUM american_scientific_journal-522 287 17 1,919 1,919 NUM american_scientific_journal-522 287 18 2,363 2,363 NUM american_scientific_journal-522 287 19 3,239 3,239 NUM american_scientific_journal-522 287 20 3,239 3,239 NUM american_scientific_journal-522 287 21 hsdt hsdt NOUN american_scientific_journal-522 287 22 [ [ X american_scientific_journal-522 287 23 18 18 NUM american_scientific_journal-522 287 24 ] ] SYM american_scientific_journal-522 287 25 1,289 1,289 NUM american_scientific_journal-522 287 26 1,919 1,919 NUM american_scientific_journal-522 287 27 2,363 2,363 NUM american_scientific_journal-522 287 28 3,235 3,235 NUM american_scientific_journal-522 287 29 3,235 3,235 NUM american_scientific_journal-522 287 30 0.5 0.5 NUM american_scientific_journal-522 287 31 present present NOUN american_scientific_journal-522 287 32 ( ( PUNCT american_scientific_journal-522 287 33 pθ pθ ADP american_scientific_journal-522 287 34 = = SYM american_scientific_journal-522 287 35 pw=12 pw=12 X american_scientific_journal-522 287 36 ) ) PUNCT american_scientific_journal-522 287 37 0,892 0,892 NUM american_scientific_journal-522 287 38 1,264 1,264 NUM american_scientific_journal-522 287 39 1,511 1,511 NUM american_scientific_journal-522 287 40 1.789 1.789 NUM american_scientific_journal-522 287 41 1.789 1.789 NUM american_scientific_journal-522 287 42 hsdt hsdt NOUN american_scientific_journal-522 287 43 [ [ X american_scientific_journal-522 287 44 18 18 NUM american_scientific_journal-522 287 45 ] ] SYM american_scientific_journal-522 287 46 0,891 0,891 NUM american_scientific_journal-522 287 47 1,264 1,264 NUM american_scientific_journal-522 287 48 1,511 1,511 NUM american_scientific_journal-522 287 49 1.788 1.788 NUM american_scientific_journal-522 287 50 1.788 1.788 NUM american_scientific_journal-522 287 51 13 13 NUM american_scientific_journal-522 287 52 american american ADJ american_scientific_journal-522 287 53 scientific scientific ADJ american_scientific_journal-522 287 54 research research NOUN american_scientific_journal-522 287 55 journal journal NOUN american_scientific_journal-522 287 56 for for ADP american_scientific_journal-522 287 57 engineering engineering NOUN american_scientific_journal-522 287 58 , , PUNCT american_scientific_journal-522 287 59 technology technology NOUN american_scientific_journal-522 287 60 , , PUNCT american_scientific_journal-522 287 61 and and CCONJ american_scientific_journal-522 287 62 sciences science NOUN american_scientific_journal-522 287 63 ( ( PUNCT american_scientific_journal-522 287 64 asrjets asrjet NOUN american_scientific_journal-522 287 65 ) ) PUNCT american_scientific_journal-522 287 66 ( ( PUNCT american_scientific_journal-522 287 67 2014 2014 NUM american_scientific_journal-522 287 68 ) ) PUNCT american_scientific_journal-522 287 69 volume volume NOUN american_scientific_journal-522 287 70 9 9 NUM american_scientific_journal-522 287 71 , , PUNCT american_scientific_journal-522 287 72 no no DET american_scientific_journal-522 287 73 1 1 NUM american_scientific_journal-522 287 74 , , PUNCT american_scientific_journal-522 287 75 pp pp ADV american_scientific_journal-522 287 76 1 1 NUM american_scientific_journal-522 287 77 - - SYM american_scientific_journal-522 287 78 19 19 NUM american_scientific_journal-522 287 79 in in ADP american_scientific_journal-522 287 80 table table NOUN american_scientific_journal-522 287 81 10 10 NUM american_scientific_journal-522 287 82 , , PUNCT american_scientific_journal-522 287 83 good good ADJ american_scientific_journal-522 287 84 agreement agreement NOUN american_scientific_journal-522 287 85 has have AUX american_scientific_journal-522 287 86 been be AUX american_scientific_journal-522 287 87 achieved achieve VERB american_scientific_journal-522 287 88 . . PUNCT american_scientific_journal-522 288 1 the the DET american_scientific_journal-522 288 2 attained attain VERB american_scientific_journal-522 288 3 accuracy accuracy NOUN american_scientific_journal-522 288 4 is be AUX american_scientific_journal-522 288 5 also also ADV american_scientific_journal-522 288 6 confirmed confirm VERB american_scientific_journal-522 288 7 by by ADP american_scientific_journal-522 288 8 comparing compare VERB american_scientific_journal-522 288 9 our our PRON american_scientific_journal-522 288 10 results result NOUN american_scientific_journal-522 288 11 , , PUNCT american_scientific_journal-522 288 12 leissa leissa ADJ american_scientific_journal-522 288 13 [ [ X american_scientific_journal-522 288 14 17 17 NUM american_scientific_journal-522 288 15 ] ] PUNCT american_scientific_journal-522 288 16 , , PUNCT american_scientific_journal-522 288 17 hosseini hosseini PROPN american_scientific_journal-522 288 18 and and CCONJ american_scientific_journal-522 288 19 his his PRON american_scientific_journal-522 288 20 colleagues colleague NOUN american_scientific_journal-522 288 21 [ [ X american_scientific_journal-522 288 22 25,26 25,26 NUM american_scientific_journal-522 288 23 ] ] PUNCT american_scientific_journal-522 288 24 , , PUNCT american_scientific_journal-522 288 25 malik malik PROPN american_scientific_journal-522 289 1 [ [ X american_scientific_journal-522 289 2 27 27 NUM american_scientific_journal-522 289 3 ] ] PUNCT american_scientific_journal-522 289 4 , , PUNCT american_scientific_journal-522 289 5 liew liew PROPN american_scientific_journal-522 289 6 and and CCONJ american_scientific_journal-522 289 7 his his PRON american_scientific_journal-522 289 8 colleagues colleague NOUN american_scientific_journal-522 290 1 [ [ X american_scientific_journal-522 290 2 23 23 NUM american_scientific_journal-522 290 3 ] ] PUNCT american_scientific_journal-522 290 4 , , PUNCT american_scientific_journal-522 290 5 the the DET american_scientific_journal-522 290 6 first first ADJ american_scientific_journal-522 290 7 five five NUM american_scientific_journal-522 290 8 frequency frequency NOUN american_scientific_journal-522 290 9 parameters parameter NOUN american_scientific_journal-522 290 10 ω ω NOUN american_scientific_journal-522 290 11 = = PROPN american_scientific_journal-522 290 12 ω ω PROPN american_scientific_journal-522 290 13 a2 a2 PROPN american_scientific_journal-522 290 14 � � PROPN american_scientific_journal-522 290 15 ρh ρh PROPN american_scientific_journal-522 290 16 / / SYM american_scientific_journal-522 290 17 d d PROPN american_scientific_journal-522 290 18 for for ADP american_scientific_journal-522 290 19 combined combine VERB american_scientific_journal-522 290 20 boundary boundary ADJ american_scientific_journal-522 290 21 condition condition NOUN american_scientific_journal-522 290 22 ( ( PUNCT american_scientific_journal-522 290 23 sfsf sfsf NOUN american_scientific_journal-522 290 24 ) ) PUNCT american_scientific_journal-522 290 25 square square ADJ american_scientific_journal-522 290 26 plates plate NOUN american_scientific_journal-522 290 27 with with ADP american_scientific_journal-522 290 28 different different ADJ american_scientific_journal-522 290 29 thickness thickness NOUN american_scientific_journal-522 290 30 - - PUNCT american_scientific_journal-522 290 31 side side NOUN american_scientific_journal-522 290 32 ratio ratio NOUN american_scientific_journal-522 290 33 h h PROPN american_scientific_journal-522 290 34 / / SYM american_scientific_journal-522 290 35 b b NOUN american_scientific_journal-522 290 36 = = SYM american_scientific_journal-522 290 37 0.001 0.001 NUM american_scientific_journal-522 290 38 , , PUNCT american_scientific_journal-522 290 39 0.1,0.2 0.1,0.2 PROPN american_scientific_journal-522 290 40 , , PUNCT american_scientific_journal-522 290 41 0.5 0.5 NUM american_scientific_journal-522 290 42 . . PUNCT american_scientific_journal-522 290 43 table table NOUN american_scientific_journal-522 290 44 10.comparison 10.comparison NUM american_scientific_journal-522 290 45 of of ADP american_scientific_journal-522 290 46 frequency frequency NOUN american_scientific_journal-522 290 47 parameters parameter NOUN american_scientific_journal-522 290 48 ω ω NOUN american_scientific_journal-522 290 49 = = PROPN american_scientific_journal-522 290 50 ω ω PROPN american_scientific_journal-522 290 51 a2 a2 PROPN american_scientific_journal-522 290 52 � � PROPN american_scientific_journal-522 290 53 ρh ρh PROPN american_scientific_journal-522 290 54 / / SYM american_scientific_journal-522 290 55 d d PROPN american_scientific_journal-522 290 56 of of ADP american_scientific_journal-522 290 57 a a DET american_scientific_journal-522 290 58 sfsf sfsf NOUN american_scientific_journal-522 290 59 square square ADJ american_scientific_journal-522 290 60 plate plate NOUN american_scientific_journal-522 290 61 ( ( PUNCT american_scientific_journal-522 290 62 ν ν X american_scientific_journal-522 290 63 = = SYM american_scientific_journal-522 290 64 0.3 0.3 NUM american_scientific_journal-522 290 65 ) ) PUNCT american_scientific_journal-522 290 66 . . PUNCT american_scientific_journal-522 291 1 h h X american_scientific_journal-522 291 2 / / SYM american_scientific_journal-522 291 3 a a DET american_scientific_journal-522 291 4 solution solution NOUN american_scientific_journal-522 291 5 methods method NOUN american_scientific_journal-522 291 6 1 1 NUM american_scientific_journal-522 291 7 2 2 NUM american_scientific_journal-522 291 8 3 3 NUM american_scientific_journal-522 291 9 4 4 NUM american_scientific_journal-522 291 10 5 5 NUM american_scientific_journal-522 291 11 0.001 0.001 NUM american_scientific_journal-522 291 12 present present NOUN american_scientific_journal-522 291 13 ( ( PUNCT american_scientific_journal-522 291 14 pθ pθ ADP american_scientific_journal-522 291 15 = = NOUN american_scientific_journal-522 291 16 pw=17 pw=17 PROPN american_scientific_journal-522 291 17 ) ) PUNCT american_scientific_journal-522 291 18 9.638 9.638 NUM american_scientific_journal-522 291 19 16.142 16.142 NUM american_scientific_journal-522 291 20 36.730 36.730 NUM american_scientific_journal-522 291 21 39.027 39.027 NUM american_scientific_journal-522 291 22 46.860 46.860 NUM american_scientific_journal-522 291 23 cpt cpt NOUN american_scientific_journal-522 291 24 - - NOUN american_scientific_journal-522 291 25 exact exact NOUN american_scientific_journal-522 291 26 [ [ X american_scientific_journal-522 291 27 17 17 NUM american_scientific_journal-522 291 28 ] ] SYM american_scientific_journal-522 291 29 9,631 9,631 NUM american_scientific_journal-522 291 30 16,135 16,135 NUM american_scientific_journal-522 291 31 36,726 36,726 NUM american_scientific_journal-522 291 32 38,945 38,945 NUM american_scientific_journal-522 291 33 46,738 46,738 NUM american_scientific_journal-522 291 34 hsdt hsdt NOUN american_scientific_journal-522 291 35 exact exact ADJ american_scientific_journal-522 291 36 [ [ X american_scientific_journal-522 291 37 25 25 NUM american_scientific_journal-522 291 38 ] ] PUNCT american_scientific_journal-522 291 39 9,631 9,631 NUM american_scientific_journal-522 291 40 16,131 16,131 NUM american_scientific_journal-522 291 41 36,716 36,716 NUM american_scientific_journal-522 291 42 38,943 38,943 NUM american_scientific_journal-522 291 43 46,732 46,732 NUM american_scientific_journal-522 291 44 0.1 0.1 NUM american_scientific_journal-522 291 45 present present ADJ american_scientific_journal-522 291 46 ( ( PUNCT american_scientific_journal-522 291 47 pθ pθ NOUN american_scientific_journal-522 291 48 = = NOUN american_scientific_journal-522 291 49 pw=20 pw=20 PROPN american_scientific_journal-522 291 50 ) ) PUNCT american_scientific_journal-522 291 51 9,442 9,442 NUM american_scientific_journal-522 291 52 15,401 15,401 NUM american_scientific_journal-522 291 53 33,896 33,896 NUM american_scientific_journal-522 291 54 36,367 36,367 NUM american_scientific_journal-522 291 55 42,821 42,821 NUM american_scientific_journal-522 291 56 exact exact ADJ american_scientific_journal-522 291 57 fsdt fsdt NOUN american_scientific_journal-522 292 1 [ [ X american_scientific_journal-522 292 2 26 26 NUM american_scientific_journal-522 292 3 ] ] SYM american_scientific_journal-522 292 4 9,446 9,446 NUM american_scientific_journal-522 292 5 15,405 15,405 NUM american_scientific_journal-522 292 6 33,916 33,916 NUM american_scientific_journal-522 292 7 36,425 36,425 NUM american_scientific_journal-522 292 8 42,887 42,887 NUM american_scientific_journal-522 292 9 3 3 NUM american_scientific_journal-522 292 10 - - SYM american_scientific_journal-522 292 11 d d ADJ american_scientific_journal-522 292 12 dqm dqm NOUN american_scientific_journal-522 292 13 [ [ X american_scientific_journal-522 292 14 27 27 NUM american_scientific_journal-522 292 15 ] ] SYM american_scientific_journal-522 292 16 9,446 9,446 NUM american_scientific_journal-522 292 17 15,400 15,400 NUM american_scientific_journal-522 292 18 33,911 33,911 NUM american_scientific_journal-522 292 19 36,437 36,437 NUM american_scientific_journal-522 292 20 42,887 42,887 NUM american_scientific_journal-522 292 21 3 3 NUM american_scientific_journal-522 292 22 - - SYM american_scientific_journal-522 292 23 d d PROPN american_scientific_journal-522 292 24 ritz ritz PROPN american_scientific_journal-522 293 1 [ [ X american_scientific_journal-522 293 2 22 22 NUM american_scientific_journal-522 293 3 ] ] SYM american_scientific_journal-522 293 4 9,446 9,446 NUM american_scientific_journal-522 293 5 15,400 15,400 NUM american_scientific_journal-522 293 6 33,913 33,913 NUM american_scientific_journal-522 293 7 36,438 36,438 NUM american_scientific_journal-522 293 8 42,887 42,887 NUM american_scientific_journal-522 293 9 hsdt hsdt NOUN american_scientific_journal-522 293 10 exact exact ADJ american_scientific_journal-522 293 11 [ [ X american_scientific_journal-522 293 12 25 25 NUM american_scientific_journal-522 293 13 ] ] SYM american_scientific_journal-522 293 14 9,446 9,446 NUM american_scientific_journal-522 293 15 15,392 15,392 NUM american_scientific_journal-522 293 16 33,868 33,868 NUM american_scientific_journal-522 293 17 36,349 36,349 NUM american_scientific_journal-522 293 18 42,801 42,801 NUM american_scientific_journal-522 293 19 0.2 0.2 NUM american_scientific_journal-522 293 20 present present ADJ american_scientific_journal-522 293 21 ( ( PUNCT american_scientific_journal-522 293 22 pθ pθ NOUN american_scientific_journal-522 293 23 = = NOUN american_scientific_journal-522 293 24 pw=20 pw=20 NOUN american_scientific_journal-522 293 25 ) ) PUNCT american_scientific_journal-522 293 26 8,984 8,984 NUM american_scientific_journal-522 293 27 14,104 14,104 NUM american_scientific_journal-522 293 28 29,170 29,170 NUM american_scientific_journal-522 293 29 31,296 31,296 NUM american_scientific_journal-522 293 30 36,006 36,006 NUM american_scientific_journal-522 293 31 exact exact ADJ american_scientific_journal-522 293 32 fsdt fsdt NOUN american_scientific_journal-522 293 33 [ [ X american_scientific_journal-522 293 34 26 26 NUM american_scientific_journal-522 293 35 ] ] SYM american_scientific_journal-522 293 36 9,000 9,000 NUM american_scientific_journal-522 293 37 14,134 14,134 NUM american_scientific_journal-522 293 38 29,256 29,256 NUM american_scientific_journal-522 293 39 31,434 31,434 NUM american_scientific_journal-522 293 40 36,165 36,165 NUM american_scientific_journal-522 293 41 3 3 NUM american_scientific_journal-522 293 42 - - PUNCT american_scientific_journal-522 293 43 d d ADJ american_scientific_journal-522 293 44 dqm dqm NOUN american_scientific_journal-522 293 45 [ [ X american_scientific_journal-522 293 46 27 27 NUM american_scientific_journal-522 293 47 ] ] SYM american_scientific_journal-522 293 48 9,001 9,001 NUM american_scientific_journal-522 293 49 14,123 14,123 NUM american_scientific_journal-522 293 50 29,263 29,263 NUM american_scientific_journal-522 293 51 31,472 31,472 NUM american_scientific_journal-522 293 52 36,173 36,173 NUM american_scientific_journal-522 293 53 3 3 NUM american_scientific_journal-522 293 54 - - SYM american_scientific_journal-522 293 55 d d PROPN american_scientific_journal-522 293 56 ritz ritz PROPN american_scientific_journal-522 294 1 [ [ X american_scientific_journal-522 294 2 22 22 NUM american_scientific_journal-522 294 3 ] ] SYM american_scientific_journal-522 294 4 9,001 9,001 NUM american_scientific_journal-522 294 5 14,122 14,122 NUM american_scientific_journal-522 294 6 29,263 29,263 NUM american_scientific_journal-522 294 7 31,472 31,472 NUM american_scientific_journal-522 294 8 36,173 36,173 NUM american_scientific_journal-522 294 9 hsdt hsdt NOUN american_scientific_journal-522 294 10 exact exact ADJ american_scientific_journal-522 295 1 [ [ X american_scientific_journal-522 295 2 25 25 NUM american_scientific_journal-522 295 3 ] ] SYM american_scientific_journal-522 295 4 8,984 8,984 NUM american_scientific_journal-522 295 5 14,101 14,101 NUM american_scientific_journal-522 295 6 29,162 29,162 NUM american_scientific_journal-522 295 7 31,293 31,293 NUM american_scientific_journal-522 295 8 35,999 35,999 NUM american_scientific_journal-522 295 9 0.5 0.5 NUM american_scientific_journal-522 295 10 present present NOUN american_scientific_journal-522 295 11 ( ( PUNCT american_scientific_journal-522 295 12 pθ pθ NOUN american_scientific_journal-522 295 13 = = NOUN american_scientific_journal-522 295 14 pw=20 pw=20 NOUN american_scientific_journal-522 295 15 ) ) PUNCT american_scientific_journal-522 295 16 7,121 7,121 NUM american_scientific_journal-522 295 17 10,070 10,070 NUM american_scientific_journal-522 295 18 18,196 18,196 NUM american_scientific_journal-522 295 19 19,470 19,470 NUM american_scientific_journal-522 295 20 21,628 21,628 NUM american_scientific_journal-522 295 21 3 3 NUM american_scientific_journal-522 295 22 - - SYM american_scientific_journal-522 295 23 d d PROPN american_scientific_journal-522 295 24 ritz ritz PROPN american_scientific_journal-522 296 1 [ [ X american_scientific_journal-522 296 2 22 22 NUM american_scientific_journal-522 296 3 ] ] SYM american_scientific_journal-522 296 4 7,166 7,166 NUM american_scientific_journal-522 296 5 10,100 10,100 NUM american_scientific_journal-522 296 6 18,210 18,210 NUM american_scientific_journal-522 296 7 19,613 19,613 NUM american_scientific_journal-522 296 8 21,652 21,652 NUM american_scientific_journal-522 296 9 hsdt hsdt NOUN american_scientific_journal-522 296 10 exact exact ADJ american_scientific_journal-522 297 1 [ [ X american_scientific_journal-522 297 2 25 25 NUM american_scientific_journal-522 297 3 ] ] SYM american_scientific_journal-522 297 4 7,121 7,121 NUM american_scientific_journal-522 297 5 10,069 10,069 NUM american_scientific_journal-522 297 6 18,194 18,194 NUM american_scientific_journal-522 297 7 19,469 19,469 NUM american_scientific_journal-522 297 8 21,626 21,626 NUM american_scientific_journal-522 297 9 in in ADP american_scientific_journal-522 297 10 table table NOUN american_scientific_journal-522 297 11 11 11 NUM american_scientific_journal-522 297 12 and and CCONJ american_scientific_journal-522 297 13 12 12 NUM american_scientific_journal-522 297 14 , , PUNCT american_scientific_journal-522 297 15 in in SCONJ american_scientific_journal-522 297 16 has have VERB american_scientific_journal-522 297 17 to to PART american_scientific_journal-522 297 18 study study VERB american_scientific_journal-522 297 19 the the DET american_scientific_journal-522 297 20 effect effect NOUN american_scientific_journal-522 297 21 of of ADP american_scientific_journal-522 297 22 the the DET american_scientific_journal-522 297 23 boundary boundary ADJ american_scientific_journal-522 297 24 conditions condition NOUN american_scientific_journal-522 297 25 , , PUNCT american_scientific_journal-522 297 26 thickness thickness NOUN american_scientific_journal-522 297 27 ratio ratio NOUN american_scientific_journal-522 297 28 and and CCONJ american_scientific_journal-522 297 29 rapport rapport VERB american_scientific_journal-522 297 30 a a DET american_scientific_journal-522 297 31 / / SYM american_scientific_journal-522 297 32 b b NOUN american_scientific_journal-522 297 33 on on ADP american_scientific_journal-522 297 34 frequency frequency NOUN american_scientific_journal-522 297 35 parameters parameter NOUN american_scientific_journal-522 297 36 ω ω NOUN american_scientific_journal-522 297 37 , , PUNCT american_scientific_journal-522 297 38 these these DET american_scientific_journal-522 297 39 tabulated tabulate VERB american_scientific_journal-522 297 40 frequency frequency NOUN american_scientific_journal-522 297 41 parameters parameter NOUN american_scientific_journal-522 297 42 should should AUX american_scientific_journal-522 297 43 be be AUX american_scientific_journal-522 297 44 useful useful ADJ american_scientific_journal-522 297 45 as as ADP american_scientific_journal-522 297 46 benchmark benchmark ADJ american_scientific_journal-522 297 47 solutions solution NOUN american_scientific_journal-522 297 48 for for ADP american_scientific_journal-522 297 49 researchers researcher NOUN american_scientific_journal-522 297 50 who who PRON american_scientific_journal-522 297 51 are be AUX american_scientific_journal-522 297 52 developing develop VERB american_scientific_journal-522 297 53 numerical numerical ADJ american_scientific_journal-522 297 54 techniques technique NOUN american_scientific_journal-522 297 55 and and CCONJ american_scientific_journal-522 297 56 software software NOUN american_scientific_journal-522 297 57 for for ADP american_scientific_journal-522 297 58 solving solve VERB american_scientific_journal-522 297 59 isotropic isotropic NOUN american_scientific_journal-522 297 60 hsdt hsdt NOUN american_scientific_journal-522 297 61 plate plate NOUN american_scientific_journal-522 297 62 vibration vibration NOUN american_scientific_journal-522 297 63 problems problem NOUN american_scientific_journal-522 297 64 . . PUNCT american_scientific_journal-522 298 1 14 14 NUM american_scientific_journal-522 298 2 american american ADJ american_scientific_journal-522 298 3 scientific scientific ADJ american_scientific_journal-522 298 4 research research NOUN american_scientific_journal-522 298 5 journal journal NOUN american_scientific_journal-522 298 6 for for ADP american_scientific_journal-522 298 7 engineering engineering NOUN american_scientific_journal-522 298 8 , , PUNCT american_scientific_journal-522 298 9 technology technology NOUN american_scientific_journal-522 298 10 , , PUNCT american_scientific_journal-522 298 11 and and CCONJ american_scientific_journal-522 298 12 sciences science NOUN american_scientific_journal-522 298 13 ( ( PUNCT american_scientific_journal-522 298 14 asrjets asrjet NOUN american_scientific_journal-522 298 15 ) ) PUNCT american_scientific_journal-522 298 16 ( ( PUNCT american_scientific_journal-522 298 17 2014 2014 NUM american_scientific_journal-522 298 18 ) ) PUNCT american_scientific_journal-522 298 19 volume volume NOUN american_scientific_journal-522 298 20 9 9 NUM american_scientific_journal-522 298 21 , , PUNCT american_scientific_journal-522 298 22 no no DET american_scientific_journal-522 298 23 1 1 NUM american_scientific_journal-522 298 24 , , PUNCT american_scientific_journal-522 298 25 pp pp ADV american_scientific_journal-522 298 26 1 1 NUM american_scientific_journal-522 298 27 - - SYM american_scientific_journal-522 298 28 19 19 NUM american_scientific_journal-522 298 29 table table NOUN american_scientific_journal-522 298 30 11.frequency 11.frequency NUM american_scientific_journal-522 298 31 parameter parameter NOUN american_scientific_journal-522 298 32 ω ω PROPN american_scientific_journal-522 298 33 = = SYM american_scientific_journal-522 298 34 ω ω PROPN american_scientific_journal-522 298 35 b2 b2 PROPN american_scientific_journal-522 298 36 π2 π2 PROPN american_scientific_journal-522 298 37 � � PROPN american_scientific_journal-522 298 38 ρ ρ PROPN american_scientific_journal-522 298 39 h h NOUN american_scientific_journal-522 298 40 d d NOUN american_scientific_journal-522 298 41 ( ( PUNCT american_scientific_journal-522 298 42 ν ν X american_scientific_journal-522 298 43 = = SYM american_scientific_journal-522 298 44 0.3 0.3 NUM american_scientific_journal-522 298 45 ) ) PUNCT american_scientific_journal-522 298 46 of of ADP american_scientific_journal-522 298 47 ffff ffff NOUN american_scientific_journal-522 298 48 , , PUNCT american_scientific_journal-522 298 49 cccc cccc NOUN american_scientific_journal-522 298 50 and and CCONJ american_scientific_journal-522 298 51 cfcf cfcf NOUN american_scientific_journal-522 298 52 plates plate NOUN american_scientific_journal-522 298 53 . . PUNCT american_scientific_journal-522 299 1 b.c b.c PROPN american_scientific_journal-522 299 2 a a PROPN american_scientific_journal-522 299 3 / / SYM american_scientific_journal-522 299 4 b b PROPN american_scientific_journal-522 299 5 h h PROPN american_scientific_journal-522 299 6 / / SYM american_scientific_journal-522 299 7 a a DET american_scientific_journal-522 299 8 1 1 NUM american_scientific_journal-522 299 9 2 2 NUM american_scientific_journal-522 299 10 3 3 NUM american_scientific_journal-522 299 11 4 4 NUM american_scientific_journal-522 299 12 5 5 NUM american_scientific_journal-522 299 13 ffff ffff NOUN american_scientific_journal-522 299 14 0.5 0.5 NUM american_scientific_journal-522 299 15 0.1 0.1 NUM american_scientific_journal-522 299 16 2.096 2.096 NUM american_scientific_journal-522 299 17 2.439 2.439 NUM american_scientific_journal-522 299 18 5.172 5.172 NUM american_scientific_journal-522 299 19 5.466 5.466 NUM american_scientific_journal-522 299 20 7.850 7.850 NUM american_scientific_journal-522 299 21 0.2 0.2 NUM american_scientific_journal-522 299 22 1.917 1.917 NUM american_scientific_journal-522 299 23 2.090 2.090 NUM american_scientific_journal-522 299 24 4.219 4.219 NUM american_scientific_journal-522 299 25 4.477 4.477 NUM american_scientific_journal-522 299 26 6.220 6.220 NUM american_scientific_journal-522 299 27 0.5 0.5 NUM american_scientific_journal-522 299 28 1.201 1.201 NUM american_scientific_journal-522 299 29 1.365 1.365 NUM american_scientific_journal-522 299 30 2.278 2.278 NUM american_scientific_journal-522 299 31 2.408 2.408 NUM american_scientific_journal-522 299 32 2.772 2.772 NUM american_scientific_journal-522 299 33 1 1 NUM american_scientific_journal-522 299 34 0.1 0.1 NUM american_scientific_journal-522 299 35 1.291 1.291 NUM american_scientific_journal-522 299 36 1.919 1.919 NUM american_scientific_journal-522 299 37 2.363 2.363 NUM american_scientific_journal-522 299 38 3.239 3.239 NUM american_scientific_journal-522 299 39 3.239 3.239 NUM american_scientific_journal-522 299 40 0.2 0.2 NUM american_scientific_journal-522 299 41 1.187 1.187 NUM american_scientific_journal-522 299 42 1.763 1.763 NUM american_scientific_journal-522 299 43 2.148 2.148 NUM american_scientific_journal-522 299 44 2.798 2.798 NUM american_scientific_journal-522 299 45 2.798 2.798 NUM american_scientific_journal-522 299 46 0.5 0.5 NUM american_scientific_journal-522 299 47 0.892 0.892 NUM american_scientific_journal-522 299 48 1.264 1.264 NUM american_scientific_journal-522 299 49 1.511 1.511 NUM american_scientific_journal-522 299 50 1.789 1.789 NUM american_scientific_journal-522 299 51 1.789 1.789 NUM american_scientific_journal-522 299 52 1.5 1.5 NUM american_scientific_journal-522 299 53 0.1 0.1 NUM american_scientific_journal-522 299 54 0.865 0.865 NUM american_scientific_journal-522 299 55 0.948 0.948 NUM american_scientific_journal-522 299 56 1.963 1.963 NUM american_scientific_journal-522 299 57 2.166 2.166 NUM american_scientific_journal-522 299 58 2.463 2.463 NUM american_scientific_journal-522 299 59 0.2 0.2 NUM american_scientific_journal-522 299 60 0.809 0.809 NUM american_scientific_journal-522 299 61 0.906 0.906 NUM american_scientific_journal-522 299 62 1.766 1.766 NUM american_scientific_journal-522 299 63 1.978 1.978 NUM american_scientific_journal-522 299 64 2.196 2.196 NUM american_scientific_journal-522 299 65 0.5 0.5 NUM american_scientific_journal-522 299 66 0.630 0.630 NUM american_scientific_journal-522 299 67 0.731 0.731 NUM american_scientific_journal-522 299 68 1.243 1.243 NUM american_scientific_journal-522 299 69 1.402 1.402 NUM american_scientific_journal-522 299 70 1.451 1.451 NUM american_scientific_journal-522 299 71 2 2 NUM american_scientific_journal-522 299 72 0.1 0.1 NUM american_scientific_journal-522 299 73 0.538 0.538 NUM american_scientific_journal-522 299 74 0.646 0.646 NUM american_scientific_journal-522 299 75 1.409 1.409 NUM american_scientific_journal-522 299 76 1.467 1.467 NUM american_scientific_journal-522 299 77 2.149 2.149 NUM american_scientific_journal-522 299 78 0.2 0.2 NUM american_scientific_journal-522 299 79 0.524 0.524 NUM american_scientific_journal-522 299 80 0.609 0.609 NUM american_scientific_journal-522 299 81 1.293 1.293 NUM american_scientific_journal-522 299 82 1.367 1.367 NUM american_scientific_journal-522 299 83 1.962 1.962 NUM american_scientific_journal-522 299 84 0.5 0.5 NUM american_scientific_journal-522 299 85 0.538 0.538 NUM american_scientific_journal-522 299 86 0.646 0.646 NUM american_scientific_journal-522 299 87 1.409 1.409 NUM american_scientific_journal-522 299 88 1.467 1.467 NUM american_scientific_journal-522 299 89 2.149 2.149 NUM american_scientific_journal-522 299 90 0.5 0.5 NUM american_scientific_journal-522 299 91 0.1 0.1 NUM american_scientific_journal-522 299 92 7.872 7.872 NUM american_scientific_journal-522 299 93 9.913 9.913 NUM american_scientific_journal-522 299 94 13.323 13.323 NUM american_scientific_journal-522 299 95 17.15 17.15 NUM american_scientific_journal-522 299 96 17.739 17.739 NUM american_scientific_journal-522 299 97 0.2 0.2 NUM american_scientific_journal-522 299 98 5.569 5.569 NUM american_scientific_journal-522 299 99 6.925 6.925 NUM american_scientific_journal-522 299 100 9.039 9.039 NUM american_scientific_journal-522 299 101 10.885 10.885 NUM american_scientific_journal-522 299 102 11.631 11.631 NUM american_scientific_journal-522 299 103 0.5 0.5 NUM american_scientific_journal-522 299 104 2.863 2.863 NUM american_scientific_journal-522 299 105 3.510 3.510 NUM american_scientific_journal-522 299 106 4.331 4.331 NUM american_scientific_journal-522 299 107 4.541 4.541 NUM american_scientific_journal-522 299 108 4.959 4.959 NUM american_scientific_journal-522 299 109 1 1 NUM american_scientific_journal-522 299 110 0.1 0.1 NUM american_scientific_journal-522 299 111 3.306 3.306 NUM american_scientific_journal-522 299 112 6.323 6.323 NUM american_scientific_journal-522 299 113 6.323 6.323 NUM american_scientific_journal-522 299 114 8.879 8.879 NUM american_scientific_journal-522 299 115 10.477 10.477 NUM american_scientific_journal-522 299 116 0.2 0.2 NUM american_scientific_journal-522 299 117 2.720 2.720 NUM american_scientific_journal-522 299 118 4.786 4.786 NUM american_scientific_journal-522 299 119 4.786 4.786 NUM american_scientific_journal-522 299 120 6.451 6.451 NUM american_scientific_journal-522 299 121 7.384 7.384 NUM american_scientific_journal-522 299 122 0.5 0.5 NUM american_scientific_journal-522 299 123 1.593 1.593 NUM american_scientific_journal-522 299 124 2.550 2.550 NUM american_scientific_journal-522 299 125 2.550 2.550 NUM american_scientific_journal-522 299 126 3.358 3.358 NUM american_scientific_journal-522 299 127 3.685 3.685 NUM american_scientific_journal-522 299 128 cfcf cfcf NOUN american_scientific_journal-522 299 129 1.5 1.5 NUM american_scientific_journal-522 299 130 0.1 0.1 NUM american_scientific_journal-522 299 131 2.531 2.531 NUM american_scientific_journal-522 299 132 3.811 3.811 NUM american_scientific_journal-522 299 133 5.767 5.767 NUM american_scientific_journal-522 299 134 5.858 5.858 NUM american_scientific_journal-522 299 135 6.831 6.831 NUM american_scientific_journal-522 299 136 0.2 0.2 NUM american_scientific_journal-522 299 137 2.140 2.140 NUM american_scientific_journal-522 299 138 3.111 3.111 NUM american_scientific_journal-522 299 139 4.407 4.407 NUM american_scientific_journal-522 299 140 4.553 4.553 NUM american_scientific_journal-522 299 141 5.149 5.149 NUM american_scientific_journal-522 299 142 0.5 0.5 NUM american_scientific_journal-522 299 143 1.303 1.303 NUM american_scientific_journal-522 299 144 1.804 1.804 NUM american_scientific_journal-522 299 145 2.363 2.363 NUM american_scientific_journal-522 299 146 2.508 2.508 NUM american_scientific_journal-522 299 147 2.755 2.755 NUM american_scientific_journal-522 299 148 2 2 NUM american_scientific_journal-522 299 149 0.1 0.1 NUM american_scientific_journal-522 299 150 2.314 2.314 NUM american_scientific_journal-522 299 151 2.960 2.960 NUM american_scientific_journal-522 299 152 4.086 4.086 NUM american_scientific_journal-522 299 153 5.599 5.599 NUM american_scientific_journal-522 299 154 5.632 5.632 NUM american_scientific_journal-522 299 155 0.2 0.2 NUM american_scientific_journal-522 299 156 1.968 1.968 NUM american_scientific_journal-522 299 157 2.478 2.478 NUM american_scientific_journal-522 299 158 3.331 3.331 NUM american_scientific_journal-522 299 159 4.287 4.287 NUM american_scientific_journal-522 299 160 4.435 4.435 NUM american_scientific_journal-522 299 161 0.5 0.5 NUM american_scientific_journal-522 299 162 1.203 1.203 NUM american_scientific_journal-522 299 163 1.493 1.493 NUM american_scientific_journal-522 299 164 1.939 1.939 NUM american_scientific_journal-522 299 165 2.298 2.298 NUM american_scientific_journal-522 299 166 2.476 2.476 NUM american_scientific_journal-522 299 167 0.5 0.5 NUM american_scientific_journal-522 299 168 0.1 0.1 NUM american_scientific_journal-522 299 169 2.080 2.080 NUM american_scientific_journal-522 299 170 3.152 3.152 NUM american_scientific_journal-522 299 171 5.328 5.328 NUM american_scientific_journal-522 299 172 6.852 6.852 NUM american_scientific_journal-522 299 173 9.214 9.214 NUM american_scientific_journal-522 299 174 0.2 0.2 NUM american_scientific_journal-522 299 175 1.782 1.782 NUM american_scientific_journal-522 299 176 2.473 2.473 NUM american_scientific_journal-522 299 177 4.098 4.098 NUM american_scientific_journal-522 299 178 5.074 5.074 NUM american_scientific_journal-522 299 179 6.851 6.851 NUM american_scientific_journal-522 299 180 0.5 0.5 NUM american_scientific_journal-522 299 181 1.095 1.095 NUM american_scientific_journal-522 299 182 1.253 1.253 NUM american_scientific_journal-522 299 183 2.186 2.186 NUM american_scientific_journal-522 299 184 2.513 2.513 NUM american_scientific_journal-522 299 185 3.434 3.434 NUM american_scientific_journal-522 299 186 1 1 NUM american_scientific_journal-522 299 187 0.1 0.1 NUM american_scientific_journal-522 299 188 2.095 2.095 NUM american_scientific_journal-522 299 189 2.441 2.441 NUM american_scientific_journal-522 299 190 3.920 3.920 NUM american_scientific_journal-522 299 191 5.366 5.366 NUM american_scientific_journal-522 299 192 5.813 5.813 NUM american_scientific_journal-522 299 193 0.2 0.2 NUM american_scientific_journal-522 299 194 1.793 1.793 NUM american_scientific_journal-522 299 195 2.036 2.036 NUM american_scientific_journal-522 299 196 3.194 3.194 NUM american_scientific_journal-522 299 197 4.120 4.120 NUM american_scientific_journal-522 299 198 4.430 4.430 NUM american_scientific_journal-522 299 199 0.5 0.5 NUM american_scientific_journal-522 299 200 1.098 1.098 NUM american_scientific_journal-522 299 201 1.192 1.192 NUM american_scientific_journal-522 299 202 1.894 1.894 NUM american_scientific_journal-522 299 203 2.192 2.192 NUM american_scientific_journal-522 299 204 2.376 2.376 NUM american_scientific_journal-522 299 205 15 15 NUM american_scientific_journal-522 299 206 american american ADJ american_scientific_journal-522 299 207 scientific scientific ADJ american_scientific_journal-522 299 208 research research NOUN american_scientific_journal-522 299 209 journal journal NOUN american_scientific_journal-522 299 210 for for ADP american_scientific_journal-522 299 211 engineering engineering NOUN american_scientific_journal-522 299 212 , , PUNCT american_scientific_journal-522 299 213 technology technology NOUN american_scientific_journal-522 299 214 , , PUNCT american_scientific_journal-522 299 215 and and CCONJ american_scientific_journal-522 299 216 sciences science NOUN american_scientific_journal-522 299 217 ( ( PUNCT american_scientific_journal-522 299 218 asrjets asrjet NOUN american_scientific_journal-522 299 219 ) ) PUNCT american_scientific_journal-522 299 220 ( ( PUNCT american_scientific_journal-522 299 221 2014 2014 NUM american_scientific_journal-522 299 222 ) ) PUNCT american_scientific_journal-522 299 223 volume volume NOUN american_scientific_journal-522 299 224 9 9 NUM american_scientific_journal-522 299 225 , , PUNCT american_scientific_journal-522 299 226 no no DET american_scientific_journal-522 299 227 1 1 NUM american_scientific_journal-522 299 228 , , PUNCT american_scientific_journal-522 299 229 pp pp ADV american_scientific_journal-522 299 230 1 1 NUM american_scientific_journal-522 299 231 - - SYM american_scientific_journal-522 299 232 19 19 NUM american_scientific_journal-522 299 233 1.5 1.5 NUM american_scientific_journal-522 299 234 0.1 0.1 NUM american_scientific_journal-522 299 235 2.101 2.101 NUM american_scientific_journal-522 299 236 2.264 2.264 NUM american_scientific_journal-522 299 237 2.907 2.907 NUM american_scientific_journal-522 299 238 4.225 4.225 NUM american_scientific_journal-522 299 239 5.381 5.381 NUM american_scientific_journal-522 299 240 0.2 0.2 NUM american_scientific_journal-522 299 241 1.798 1.798 NUM american_scientific_journal-522 299 242 1.915 1.915 NUM american_scientific_journal-522 299 243 2.41 2.41 NUM american_scientific_journal-522 299 244 3.446 3.446 NUM american_scientific_journal-522 299 245 4.13 4.13 NUM american_scientific_journal-522 299 246 0.5 0.5 NUM american_scientific_journal-522 299 247 1.099 1.099 NUM american_scientific_journal-522 299 248 1.150 1.150 NUM american_scientific_journal-522 299 249 1.443 1.443 NUM american_scientific_journal-522 299 250 1.990 1.990 NUM american_scientific_journal-522 299 251 2.198 2.198 NUM american_scientific_journal-522 299 252 2 2 NUM american_scientific_journal-522 299 253 0.1 0.1 NUM american_scientific_journal-522 299 254 2.105 2.105 NUM american_scientific_journal-522 299 255 2.198 2.198 NUM american_scientific_journal-522 299 256 2.555 2.555 NUM american_scientific_journal-522 299 257 3.265 3.265 NUM american_scientific_journal-522 299 258 4.400 4.400 NUM american_scientific_journal-522 299 259 0.2 0.2 NUM american_scientific_journal-522 299 260 1.800 1.800 NUM american_scientific_journal-522 299 261 1.867 1.867 NUM american_scientific_journal-522 299 262 2.140 2.140 NUM american_scientific_journal-522 299 263 2.703 2.703 NUM american_scientific_journal-522 299 264 3.589 3.589 NUM american_scientific_journal-522 299 265 0.5 0.5 NUM american_scientific_journal-522 299 266 1.100 1.100 NUM american_scientific_journal-522 299 267 1.131 1.131 NUM american_scientific_journal-522 299 268 1.285 1.285 NUM american_scientific_journal-522 299 269 1.619 1.619 NUM american_scientific_journal-522 299 270 2.084 2.084 NUM american_scientific_journal-522 299 271 table table NOUN american_scientific_journal-522 299 272 12.frequency 12.frequency NUM american_scientific_journal-522 299 273 parameter parameter NOUN american_scientific_journal-522 299 274 ω ω PROPN american_scientific_journal-522 299 275 = = SYM american_scientific_journal-522 299 276 ω ω PROPN american_scientific_journal-522 299 277 b2 b2 PROPN american_scientific_journal-522 299 278 π2 π2 PROPN american_scientific_journal-522 299 279 � � PROPN american_scientific_journal-522 300 1 ρ ρ PROPN american_scientific_journal-522 301 1 h h NOUN american_scientific_journal-522 302 1 d d NOUN american_scientific_journal-522 302 2 ( ( PUNCT american_scientific_journal-522 302 3 ν ν X american_scientific_journal-522 302 4 = = SYM american_scientific_journal-522 302 5 0.3 0.3 NUM american_scientific_journal-522 302 6 ) ) PUNCT american_scientific_journal-522 302 7 of of ADP american_scientific_journal-522 302 8 cfff cfff PROPN american_scientific_journal-522 302 9 , , PUNCT american_scientific_journal-522 302 10 cscs cscs PROPN american_scientific_journal-522 302 11 and and CCONJ american_scientific_journal-522 302 12 sfsf sfsf NOUN american_scientific_journal-522 302 13 plates plate NOUN american_scientific_journal-522 302 14 . . PUNCT american_scientific_journal-522 303 1 b.c b.c PROPN american_scientific_journal-522 303 2 a a PROPN american_scientific_journal-522 303 3 / / SYM american_scientific_journal-522 303 4 b b PROPN american_scientific_journal-522 303 5 h h PROPN american_scientific_journal-522 303 6 / / SYM american_scientific_journal-522 303 7 a a DET american_scientific_journal-522 303 8 1 1 NUM american_scientific_journal-522 303 9 2 2 NUM american_scientific_journal-522 303 10 3 3 NUM american_scientific_journal-522 303 11 4 4 NUM american_scientific_journal-522 303 12 5 5 NUM american_scientific_journal-522 303 13 cfff cfff NOUN american_scientific_journal-522 303 14 0.5 0.5 NUM american_scientific_journal-522 303 15 0.1 0.1 NUM american_scientific_journal-522 303 16 1.367 1.367 NUM american_scientific_journal-522 303 17 1.997 1.997 NUM american_scientific_journal-522 303 18 3.658 3.658 NUM american_scientific_journal-522 303 19 6.611 6.611 NUM american_scientific_journal-522 303 20 7.332 7.332 NUM american_scientific_journal-522 303 21 0.2 0.2 NUM american_scientific_journal-522 303 22 1.257 1.257 NUM american_scientific_journal-522 303 23 1.730 1.730 NUM american_scientific_journal-522 303 24 3.018 3.018 NUM american_scientific_journal-522 303 25 5.120 5.120 NUM american_scientific_journal-522 303 26 5.321 5.321 NUM american_scientific_journal-522 303 27 0.5 0.5 NUM american_scientific_journal-522 303 28 0.908 0.908 NUM american_scientific_journal-522 303 29 1.120 1.120 NUM american_scientific_journal-522 303 30 1.834 1.834 NUM american_scientific_journal-522 303 31 2.339 2.339 NUM american_scientific_journal-522 303 32 2.499 2.499 NUM american_scientific_journal-522 303 33 1 1 NUM american_scientific_journal-522 303 34 0.1 0.1 NUM american_scientific_journal-522 303 35 0.348 0.348 NUM american_scientific_journal-522 303 36 0.818 0.818 NUM american_scientific_journal-522 303 37 2.038 2.038 NUM american_scientific_journal-522 303 38 2.586 2.586 NUM american_scientific_journal-522 303 39 2.868 2.868 NUM american_scientific_journal-522 303 40 0.2 0.2 NUM american_scientific_journal-522 303 41 0.339 0.339 NUM american_scientific_journal-522 303 42 0.747 0.747 NUM american_scientific_journal-522 303 43 1.790 1.790 NUM american_scientific_journal-522 303 44 2.282 2.282 NUM american_scientific_journal-522 303 45 2.435 2.435 NUM american_scientific_journal-522 303 46 0.5 0.5 NUM american_scientific_journal-522 303 47 0.296 0.296 NUM american_scientific_journal-522 303 48 0.531 0.531 NUM american_scientific_journal-522 303 49 1.125 1.125 NUM american_scientific_journal-522 303 50 1.502 1.502 NUM american_scientific_journal-522 303 51 1.523 1.523 NUM american_scientific_journal-522 303 52 1.5 1.5 NUM american_scientific_journal-522 303 53 0.1 0.1 NUM american_scientific_journal-522 303 54 0.155 0.155 NUM american_scientific_journal-522 303 55 0.502 0.502 NUM american_scientific_journal-522 303 56 0.941 0.941 NUM american_scientific_journal-522 303 57 1.666 1.666 NUM american_scientific_journal-522 303 58 2.294 2.294 NUM american_scientific_journal-522 303 59 0.2 0.2 NUM american_scientific_journal-522 303 60 0.152 0.152 NUM american_scientific_journal-522 303 61 0.467 0.467 NUM american_scientific_journal-522 303 62 0.879 0.879 NUM american_scientific_journal-522 303 63 1.490 1.490 NUM american_scientific_journal-522 303 64 2.057 2.057 NUM american_scientific_journal-522 303 65 0.5 0.5 NUM american_scientific_journal-522 303 66 0.142 0.142 NUM american_scientific_journal-522 303 67 0.346 0.346 NUM american_scientific_journal-522 303 68 0.649 0.649 NUM american_scientific_journal-522 303 69 1.023 1.023 NUM american_scientific_journal-522 303 70 1.380 1.380 NUM american_scientific_journal-522 303 71 2 2 NUM american_scientific_journal-522 303 72 0.1 0.1 NUM american_scientific_journal-522 303 73 0.087 0.087 NUM american_scientific_journal-522 303 74 0.360 0.360 NUM american_scientific_journal-522 303 75 0.534 0.534 NUM american_scientific_journal-522 303 76 1.161 1.161 NUM american_scientific_journal-522 303 77 1.471 1.471 NUM american_scientific_journal-522 303 78 0.2 0.2 NUM american_scientific_journal-522 303 79 0.086 0.086 NUM american_scientific_journal-522 303 80 0.337 0.337 NUM american_scientific_journal-522 303 81 0.513 0.513 NUM american_scientific_journal-522 303 82 1.062 1.062 NUM american_scientific_journal-522 303 83 1.349 1.349 NUM american_scientific_journal-522 303 84 0.5 0.5 NUM american_scientific_journal-522 303 85 0.082 0.082 NUM american_scientific_journal-522 303 86 0.256 0.256 NUM american_scientific_journal-522 303 87 0.417 0.417 NUM american_scientific_journal-522 303 88 0.766 0.766 NUM american_scientific_journal-522 303 89 0.958 0.958 NUM american_scientific_journal-522 303 90 cscs cscs PROPN american_scientific_journal-522 303 91 0.5 0.5 NUM american_scientific_journal-522 303 92 0.1 0.1 NUM american_scientific_journal-522 303 93 7.867 7.867 NUM american_scientific_journal-522 303 94 9.898 9.898 NUM american_scientific_journal-522 303 95 13.297 13.297 NUM american_scientific_journal-522 303 96 17.142 17.142 NUM american_scientific_journal-522 303 97 17.706 17.706 NUM american_scientific_journal-522 303 98 0.2 0.2 NUM american_scientific_journal-522 303 99 5.565 5.565 NUM american_scientific_journal-522 303 100 6.913 6.913 NUM american_scientific_journal-522 303 101 9.023 9.023 NUM american_scientific_journal-522 303 102 10.87 10.87 NUM american_scientific_journal-522 303 103 11.616 11.616 NUM american_scientific_journal-522 303 104 0.5 0.5 NUM american_scientific_journal-522 303 105 2.859 2.859 NUM american_scientific_journal-522 303 106 3.504 3.504 NUM american_scientific_journal-522 303 107 4.319 4.319 NUM american_scientific_journal-522 303 108 4.535 4.535 NUM american_scientific_journal-522 303 109 4.898 4.898 NUM american_scientific_journal-522 303 110 1 1 NUM american_scientific_journal-522 303 111 0.1 0.1 NUM american_scientific_journal-522 303 112 3.302 3.302 NUM american_scientific_journal-522 303 113 6.312 6.312 NUM american_scientific_journal-522 303 114 6.314 6.314 NUM american_scientific_journal-522 303 115 8.854 8.854 NUM american_scientific_journal-522 303 116 10.461 10.461 NUM american_scientific_journal-522 303 117 0.2 0.2 NUM american_scientific_journal-522 303 118 2.710 2.710 NUM american_scientific_journal-522 303 119 4.769 4.769 NUM american_scientific_journal-522 303 120 4.770 4.770 NUM american_scientific_journal-522 303 121 6.412 6.412 NUM american_scientific_journal-522 303 122 7.358 7.358 NUM american_scientific_journal-522 303 123 0.5 0.5 NUM american_scientific_journal-522 303 124 1.586 1.586 NUM american_scientific_journal-522 303 125 2.512 2.512 NUM american_scientific_journal-522 303 126 2.542 2.542 NUM american_scientific_journal-522 303 127 3.260 3.260 NUM american_scientific_journal-522 303 128 3.512 3.512 NUM american_scientific_journal-522 303 129 1.5 1.5 NUM american_scientific_journal-522 303 130 0.1 0.1 NUM american_scientific_journal-522 303 131 2.528 2.528 NUM american_scientific_journal-522 303 132 3.804 3.804 NUM american_scientific_journal-522 303 133 5.762 5.762 NUM american_scientific_journal-522 303 134 5.848 5.848 NUM american_scientific_journal-522 303 135 6.814 6.814 NUM american_scientific_journal-522 303 136 0.2 0.2 NUM american_scientific_journal-522 303 137 2.132 2.132 NUM american_scientific_journal-522 303 138 3.093 3.093 NUM american_scientific_journal-522 303 139 4.395 4.395 NUM american_scientific_journal-522 303 140 4.533 4.533 NUM american_scientific_journal-522 303 141 5.115 5.115 NUM american_scientific_journal-522 303 142 0.5 0.5 NUM american_scientific_journal-522 303 143 1.295 1.295 NUM american_scientific_journal-522 303 144 1.779 1.779 NUM american_scientific_journal-522 303 145 2.359 2.359 NUM american_scientific_journal-522 303 146 2.491 2.491 NUM american_scientific_journal-522 303 147 2.728 2.728 NUM american_scientific_journal-522 303 148 2 2 NUM american_scientific_journal-522 303 149 0.1 0.1 NUM american_scientific_journal-522 303 150 2.313 2.313 NUM american_scientific_journal-522 303 151 2.955 2.955 NUM american_scientific_journal-522 303 152 4.078 4.078 NUM american_scientific_journal-522 303 153 5.596 5.596 NUM american_scientific_journal-522 303 154 5.622 5.622 NUM american_scientific_journal-522 303 155 0.2 0.2 NUM american_scientific_journal-522 303 156 1.962 1.962 NUM american_scientific_journal-522 303 157 2.462 2.462 NUM american_scientific_journal-522 303 158 3.310 3.310 NUM american_scientific_journal-522 303 159 4.279 4.279 NUM american_scientific_journal-522 303 160 4.413 4.413 NUM american_scientific_journal-522 303 161 0.5 0.5 NUM american_scientific_journal-522 303 162 1.194 1.194 NUM american_scientific_journal-522 303 163 1.470 1.470 NUM american_scientific_journal-522 303 164 1.917 1.917 NUM american_scientific_journal-522 303 165 2.294 2.294 NUM american_scientific_journal-522 303 166 2.453 2.453 NUM american_scientific_journal-522 303 167 sfsf sfsf NOUN american_scientific_journal-522 303 168 0.5 0.5 NUM american_scientific_journal-522 303 169 0.1 0.1 NUM american_scientific_journal-522 303 170 0.945 0.945 NUM american_scientific_journal-522 303 171 2.527 2.527 NUM american_scientific_journal-522 303 172 3.641 3.641 NUM american_scientific_journal-522 303 173 5.716 5.716 NUM american_scientific_journal-522 303 174 7.698 7.698 NUM american_scientific_journal-522 303 175 0.2 0.2 NUM american_scientific_journal-522 303 176 0.900 0.900 NUM american_scientific_journal-522 303 177 2.155 2.155 NUM american_scientific_journal-522 303 178 3.137 3.137 NUM american_scientific_journal-522 303 179 4.575 4.575 NUM american_scientific_journal-522 303 180 6.006 6.006 NUM american_scientific_journal-522 303 181 0.5 0.5 NUM american_scientific_journal-522 303 182 0.718 0.718 NUM american_scientific_journal-522 303 183 1.202 1.202 NUM american_scientific_journal-522 303 184 1.963 1.963 NUM american_scientific_journal-522 303 185 2.414 2.414 NUM american_scientific_journal-522 303 186 2.611 2.611 NUM american_scientific_journal-522 303 187 1 1 NUM american_scientific_journal-522 303 188 0.1 0.1 NUM american_scientific_journal-522 303 189 0.957 0.957 NUM american_scientific_journal-522 303 190 1.560 1.560 NUM american_scientific_journal-522 303 191 3.434 3.434 NUM american_scientific_journal-522 303 192 3.685 3.685 NUM american_scientific_journal-522 303 193 4.338 4.338 NUM american_scientific_journal-522 303 194 0.2 0.2 NUM american_scientific_journal-522 303 195 0.910 0.910 NUM american_scientific_journal-522 303 196 1.429 1.429 NUM american_scientific_journal-522 303 197 2.955 2.955 NUM american_scientific_journal-522 303 198 3.171 3.171 NUM american_scientific_journal-522 303 199 3.648 3.648 NUM american_scientific_journal-522 303 200 0.5 0.5 NUM american_scientific_journal-522 303 201 0.722 0.722 NUM american_scientific_journal-522 303 202 1.020 1.020 NUM american_scientific_journal-522 303 203 1.844 1.844 NUM american_scientific_journal-522 303 204 1.973 1.973 NUM american_scientific_journal-522 303 205 2.191 2.191 NUM american_scientific_journal-522 303 206 1.5 1.5 NUM american_scientific_journal-522 303 207 0.1 0.1 NUM american_scientific_journal-522 303 208 0.964 0.964 NUM american_scientific_journal-522 303 209 1.274 1.274 NUM american_scientific_journal-522 303 210 2.204 2.204 NUM american_scientific_journal-522 303 211 3.702 3.702 NUM american_scientific_journal-522 303 212 3.777 3.777 NUM american_scientific_journal-522 303 213 0.2 0.2 NUM american_scientific_journal-522 303 214 0.917 0.917 NUM american_scientific_journal-522 303 215 1.188 1.188 NUM american_scientific_journal-522 303 216 1.977 1.977 NUM american_scientific_journal-522 303 217 3.185 3.185 NUM american_scientific_journal-522 303 218 3.225 3.225 NUM american_scientific_journal-522 303 219 0.5 0.5 NUM american_scientific_journal-522 303 220 0.726 0.726 NUM american_scientific_journal-522 303 221 0.892 0.892 NUM american_scientific_journal-522 303 222 1.343 1.343 NUM american_scientific_journal-522 303 223 1.945 1.945 NUM american_scientific_journal-522 303 224 1.98 1.98 NUM american_scientific_journal-522 303 225 2 2 NUM american_scientific_journal-522 303 226 0.1 0.1 NUM american_scientific_journal-522 303 227 0.968 0.968 NUM american_scientific_journal-522 303 228 1.153 1.153 NUM american_scientific_journal-522 303 229 1.721 1.721 NUM american_scientific_journal-522 303 230 2.655 2.655 NUM american_scientific_journal-522 303 231 3.711 3.711 NUM american_scientific_journal-522 303 232 0.2 0.2 NUM american_scientific_journal-522 303 233 0.921 0.921 NUM american_scientific_journal-522 303 234 1.085 1.085 NUM american_scientific_journal-522 303 235 1.576 1.576 NUM american_scientific_journal-522 303 236 2.349 2.349 NUM american_scientific_journal-522 303 237 3.193 3.193 NUM american_scientific_journal-522 303 238 0.5 0.5 NUM american_scientific_journal-522 303 239 0.729 0.729 NUM american_scientific_journal-522 303 240 0.831 0.831 NUM american_scientific_journal-522 303 241 1.124 1.124 NUM american_scientific_journal-522 303 242 1.540 1.540 NUM american_scientific_journal-522 303 243 1.984 1.984 NUM american_scientific_journal-522 303 244 16 16 NUM american_scientific_journal-522 303 245 american american ADJ american_scientific_journal-522 303 246 scientific scientific ADJ american_scientific_journal-522 303 247 research research NOUN american_scientific_journal-522 303 248 journal journal NOUN american_scientific_journal-522 303 249 for for ADP american_scientific_journal-522 303 250 engineering engineering NOUN american_scientific_journal-522 303 251 , , PUNCT american_scientific_journal-522 303 252 technology technology NOUN american_scientific_journal-522 303 253 , , PUNCT american_scientific_journal-522 303 254 and and CCONJ american_scientific_journal-522 303 255 sciences science NOUN american_scientific_journal-522 303 256 ( ( PUNCT american_scientific_journal-522 303 257 asrjets asrjet NOUN american_scientific_journal-522 303 258 ) ) PUNCT american_scientific_journal-522 303 259 ( ( PUNCT american_scientific_journal-522 303 260 2014 2014 NUM american_scientific_journal-522 303 261 ) ) PUNCT american_scientific_journal-522 303 262 volume volume NOUN american_scientific_journal-522 303 263 9 9 NUM american_scientific_journal-522 303 264 , , PUNCT american_scientific_journal-522 303 265 no no DET american_scientific_journal-522 303 266 1 1 NUM american_scientific_journal-522 303 267 , , PUNCT american_scientific_journal-522 303 268 pp pp ADV american_scientific_journal-522 303 269 1 1 NUM american_scientific_journal-522 303 270 - - SYM american_scientific_journal-522 303 271 19 19 NUM american_scientific_journal-522 303 272 4 4 NUM american_scientific_journal-522 303 273 . . PUNCT american_scientific_journal-522 303 274 conclusion conclusion NOUN american_scientific_journal-522 303 275 an an DET american_scientific_journal-522 303 276 hierarchical hierarchical ADJ american_scientific_journal-522 303 277 finite finite ADJ american_scientific_journal-522 303 278 element element NOUN american_scientific_journal-522 303 279 formulation formulation NOUN american_scientific_journal-522 303 280 is be AUX american_scientific_journal-522 303 281 presented present VERB american_scientific_journal-522 303 282 based base VERB american_scientific_journal-522 303 283 on on ADP american_scientific_journal-522 303 284 an an DET american_scientific_journal-522 303 285 higher high ADJ american_scientific_journal-522 303 286 - - PUNCT american_scientific_journal-522 303 287 order order NOUN american_scientific_journal-522 303 288 shear shear NOUN american_scientific_journal-522 303 289 plates plate NOUN american_scientific_journal-522 303 290 theory theory NOUN american_scientific_journal-522 303 291 for for ADP american_scientific_journal-522 303 292 homogeneous homogeneous ADJ american_scientific_journal-522 303 293 thick thick ADJ american_scientific_journal-522 303 294 plates plate NOUN american_scientific_journal-522 303 295 , , PUNCT american_scientific_journal-522 303 296 a a DET american_scientific_journal-522 303 297 computer computer NOUN american_scientific_journal-522 303 298 program program NOUN american_scientific_journal-522 303 299 is be AUX american_scientific_journal-522 303 300 developed develop VERB american_scientific_journal-522 303 301 , , PUNCT american_scientific_journal-522 303 302 a a DET american_scientific_journal-522 303 303 p p NOUN american_scientific_journal-522 303 304 - - PUNCT american_scientific_journal-522 303 305 version version NOUN american_scientific_journal-522 303 306 , , PUNCT american_scientific_journal-522 303 307 hierarchical hierarchical ADJ american_scientific_journal-522 303 308 finite finite ADJ american_scientific_journal-522 303 309 element element NOUN american_scientific_journal-522 303 310 was be AUX american_scientific_journal-522 303 311 presented present VERB american_scientific_journal-522 303 312 and and CCONJ american_scientific_journal-522 303 313 applied apply VERB american_scientific_journal-522 303 314 to to ADP american_scientific_journal-522 303 315 thick thick ADJ american_scientific_journal-522 303 316 plate plate NOUN american_scientific_journal-522 303 317 with with ADP american_scientific_journal-522 303 318 trigonometric trigonometric ADJ american_scientific_journal-522 303 319 hierarchical hierarchical ADJ american_scientific_journal-522 303 320 shape shape NOUN american_scientific_journal-522 303 321 functions function NOUN american_scientific_journal-522 303 322 . . PUNCT american_scientific_journal-522 304 1 1based 1base VERB american_scientific_journal-522 304 2 on on ADP american_scientific_journal-522 304 3 the the DET american_scientific_journal-522 304 4 reddy reddy PROPN american_scientific_journal-522 304 5 ’s ’s PART american_scientific_journal-522 304 6 higher high ADJ american_scientific_journal-522 304 7 - - PUNCT american_scientific_journal-522 304 8 order order NOUN american_scientific_journal-522 304 9 theory theory NOUN american_scientific_journal-522 304 10 , , PUNCT american_scientific_journal-522 304 11 these these DET american_scientific_journal-522 304 12 elements element NOUN american_scientific_journal-522 304 13 have have AUX american_scientific_journal-522 304 14 been be AUX american_scientific_journal-522 304 15 implemented implement VERB american_scientific_journal-522 304 16 with with ADP american_scientific_journal-522 304 17 a a DET american_scientific_journal-522 304 18 very very ADV american_scientific_journal-522 304 19 simple simple ADJ american_scientific_journal-522 304 20 and and CCONJ american_scientific_journal-522 304 21 understandable understandable ADJ american_scientific_journal-522 304 22 mathematical mathematical ADJ american_scientific_journal-522 304 23 framework framework NOUN american_scientific_journal-522 304 24 and and CCONJ american_scientific_journal-522 304 25 are be AUX american_scientific_journal-522 304 26 easily easily ADV american_scientific_journal-522 304 27 programmed program VERB american_scientific_journal-522 304 28 . . PUNCT american_scientific_journal-522 305 1 2high 2high NUM american_scientific_journal-522 305 2 accuracy accuracy NOUN american_scientific_journal-522 305 3 , , PUNCT american_scientific_journal-522 305 4 stable stable ADJ american_scientific_journal-522 305 5 numerical numerical ADJ american_scientific_journal-522 305 6 computation computation NOUN american_scientific_journal-522 305 7 and and CCONJ american_scientific_journal-522 305 8 rapid rapid ADJ american_scientific_journal-522 305 9 convergence convergence NOUN american_scientific_journal-522 305 10 have have AUX american_scientific_journal-522 305 11 been be AUX american_scientific_journal-522 305 12 observed observe VERB american_scientific_journal-522 305 13 in in ADP american_scientific_journal-522 305 14 the the DET american_scientific_journal-522 305 15 analysis analysis NOUN american_scientific_journal-522 305 16 . . PUNCT american_scientific_journal-522 306 1 3the 3the DET american_scientific_journal-522 306 2 results result NOUN american_scientific_journal-522 306 3 are be AUX american_scientific_journal-522 306 4 compared compare VERB american_scientific_journal-522 306 5 with with ADP american_scientific_journal-522 306 6 other other ADJ american_scientific_journal-522 306 7 shear shear NOUN american_scientific_journal-522 306 8 deformation deformation NOUN american_scientific_journal-522 306 9 theories theory NOUN american_scientific_journal-522 306 10 and and CCONJ american_scientific_journal-522 306 11 exact exact ADJ american_scientific_journal-522 306 12 elasticity elasticity NOUN american_scientific_journal-522 306 13 solutions solution NOUN american_scientific_journal-522 306 14 . . PUNCT american_scientific_journal-522 307 1 good good ADJ american_scientific_journal-522 307 2 agreement agreement NOUN american_scientific_journal-522 307 3 may may AUX american_scientific_journal-522 307 4 be be AUX american_scientific_journal-522 307 5 noted note VERB american_scientific_journal-522 307 6 . . PUNCT american_scientific_journal-522 308 1 several several ADJ american_scientific_journal-522 308 2 examples example NOUN american_scientific_journal-522 308 3 are be AUX american_scientific_journal-522 308 4 solved solve VERB american_scientific_journal-522 308 5 . . PUNCT american_scientific_journal-522 309 1 the the DET american_scientific_journal-522 309 2 effect effect NOUN american_scientific_journal-522 309 3 of of ADP american_scientific_journal-522 309 4 boundary boundary ADJ american_scientific_journal-522 309 5 condition condition NOUN american_scientific_journal-522 309 6 and and CCONJ american_scientific_journal-522 309 7 ratio ratio NOUN american_scientific_journal-522 309 8 a a DET american_scientific_journal-522 309 9 / / SYM american_scientific_journal-522 309 10 b b NOUN american_scientific_journal-522 309 11 and and CCONJ american_scientific_journal-522 309 12 h h NOUN american_scientific_journal-522 309 13 / / SYM american_scientific_journal-522 309 14 a a PRON american_scientific_journal-522 309 15 the the DET american_scientific_journal-522 309 16 analyzes analyze NOUN american_scientific_journal-522 309 17 is be AUX american_scientific_journal-522 309 18 also also ADV american_scientific_journal-522 309 19 studied study VERB american_scientific_journal-522 309 20 . . PUNCT american_scientific_journal-522 310 1 references reference NOUN american_scientific_journal-522 310 2 [ [ X american_scientific_journal-522 310 3 1 1 NUM american_scientific_journal-522 310 4 ] ] PUNCT american_scientific_journal-522 310 5 a. a. PROPN american_scientific_journal-522 310 6 e. e. PROPN american_scientific_journal-522 310 7 h. h. PROPN american_scientific_journal-522 310 8 love love PROPN american_scientific_journal-522 310 9 . . PUNCT american_scientific_journal-522 311 1 ( ( PUNCT american_scientific_journal-522 311 2 1888 1888 NUM american_scientific_journal-522 311 3 ) ) PUNCT american_scientific_journal-522 311 4 on on ADP american_scientific_journal-522 311 5 the the DET american_scientific_journal-522 311 6 small small ADJ american_scientific_journal-522 311 7 free free ADJ american_scientific_journal-522 311 8 vibrations vibration NOUN american_scientific_journal-522 311 9 and and CCONJ american_scientific_journal-522 311 10 deformations deformation NOUN american_scientific_journal-522 311 11 of of ADP american_scientific_journal-522 311 12 elastic elastic ADJ american_scientific_journal-522 311 13 shells shell NOUN american_scientific_journal-522 311 14 , , PUNCT american_scientific_journal-522 311 15 philosophical philosophical ADJ american_scientific_journal-522 311 16 trans tran NOUN american_scientific_journal-522 311 17 . . PROPN american_scientific_journal-522 312 1 of of ADP american_scientific_journal-522 312 2 the the DET american_scientific_journal-522 312 3 royal royal ADJ american_scientific_journal-522 312 4 society society NOUN american_scientific_journal-522 312 5 ( ( PUNCT american_scientific_journal-522 312 6 london london PROPN american_scientific_journal-522 312 7 ) ) PUNCT american_scientific_journal-522 312 8 , , PUNCT american_scientific_journal-522 312 9 17 17 NUM american_scientific_journal-522 312 10 491–549 491–549 NUM american_scientific_journal-522 312 11 . . PUNCT american_scientific_journal-522 313 1 available available ADJ american_scientific_journal-522 313 2 : : PUNCT american_scientific_journal-522 314 1 http://www.jstor.org/stable/90527 http://www.jstor.org/stable/90527 X american_scientific_journal-522 315 1 [ [ X american_scientific_journal-522 315 2 2 2 NUM american_scientific_journal-522 315 3 ] ] X american_scientific_journal-522 315 4 mindlin mindlin NOUN american_scientific_journal-522 315 5 , , PUNCT american_scientific_journal-522 315 6 r.d r.d PROPN american_scientific_journal-522 315 7 . . PROPN american_scientific_journal-522 315 8 schacknow schacknow PROPN american_scientific_journal-522 315 9 , , PUNCT american_scientific_journal-522 315 10 a. a. NOUN american_scientific_journal-522 315 11 deresiewicz deresiewicz PROPN american_scientific_journal-522 315 12 ( ( PUNCT american_scientific_journal-522 315 13 1955 1955 NUM american_scientific_journal-522 315 14 , , PUNCT american_scientific_journal-522 315 15 jun jun PROPN american_scientific_journal-522 315 16 ) ) PUNCT american_scientific_journal-522 315 17 , , PUNCT american_scientific_journal-522 315 18 flexural flexural ADJ american_scientific_journal-522 315 19 vibrations vibration NOUN american_scientific_journal-522 315 20 of of ADP american_scientific_journal-522 315 21 rectangular rectangular ADJ american_scientific_journal-522 315 22 plates plate NOUN american_scientific_journal-522 315 23 , , PUNCT american_scientific_journal-522 315 24 asme asme PROPN american_scientific_journal-522 315 25 j. j. PROPN american_scientific_journal-522 315 26 appl appl PROPN american_scientific_journal-522 315 27 . . PROPN american_scientific_journal-522 315 28 mec mec PROPN american_scientific_journal-522 315 29 , , PUNCT american_scientific_journal-522 315 30 23 23 NUM american_scientific_journal-522 315 31 ( ( PUNCT american_scientific_journal-522 315 32 1956 1956 NUM american_scientific_journal-522 315 33 ) ) PUNCT american_scientific_journal-522 315 34 430–436 430–436 NUM american_scientific_journal-522 315 35 . . PUNCT american_scientific_journal-522 316 1 [ [ X american_scientific_journal-522 316 2 3 3 X american_scientific_journal-522 316 3 ] ] X american_scientific_journal-522 316 4 r.b r.b PROPN american_scientific_journal-522 316 5 . . PROPN american_scientific_journal-522 316 6 nelson nelson PROPN american_scientific_journal-522 316 7 , , PUNCT american_scientific_journal-522 316 8 dr dr PROPN american_scientific_journal-522 316 9 . . PROPN american_scientific_journal-522 316 10 lorch lorch PROPN american_scientific_journal-522 316 11 . . PUNCT american_scientific_journal-522 317 1 ( ( PUNCT american_scientific_journal-522 317 2 1974 1974 NUM american_scientific_journal-522 317 3 , , PUNCT american_scientific_journal-522 317 4 mar mar PROPN american_scientific_journal-522 317 5 ) ) PUNCT american_scientific_journal-522 317 6 , , PUNCT american_scientific_journal-522 317 7 a a DET american_scientific_journal-522 317 8 refined refined ADJ american_scientific_journal-522 317 9 theory theory NOUN american_scientific_journal-522 317 10 for for ADP american_scientific_journal-522 317 11 laminated laminate VERB american_scientific_journal-522 317 12 orthotropic orthotropic ADJ american_scientific_journal-522 317 13 plates plate NOUN american_scientific_journal-522 317 14 . . PUNCT american_scientific_journal-522 318 1 asme asme PROPN american_scientific_journal-522 318 2 , , PUNCT american_scientific_journal-522 318 3 j. j. PROPN american_scientific_journal-522 318 4 appl appl PROPN american_scientific_journal-522 318 5 . . PROPN american_scientific_journal-522 318 6 mech mech PROPN american_scientific_journal-522 318 7 , , PUNCT american_scientific_journal-522 318 8 41 41 NUM american_scientific_journal-522 318 9 177 177 NUM american_scientific_journal-522 318 10 - - SYM american_scientific_journal-522 318 11 183.available 183.available NUM american_scientific_journal-522 318 12 : : PUNCT american_scientific_journal-522 318 13 http://appliedmechanics.asmedigitalcollection.asme.org.scihub.org http://appliedmechanics.asmedigitalcollection.asme.org.scihub.org ADJ american_scientific_journal-522 318 14 / / SYM american_scientific_journal-522 318 15 article.aspx?articleid=1401537 article.aspx?articleid=1401537 PROPN american_scientific_journal-522 319 1 [ [ X american_scientific_journal-522 319 2 4 4 X american_scientific_journal-522 319 3 ] ] X american_scientific_journal-522 319 4 k.h k.h PROPN american_scientific_journal-522 319 5 lo lo PROPN american_scientific_journal-522 319 6 , , PUNCT american_scientific_journal-522 319 7 r.m r.m PROPN american_scientific_journal-522 319 8 . . PROPN american_scientific_journal-522 319 9 christen christen PROPN american_scientific_journal-522 319 10 , , PUNCT american_scientific_journal-522 319 11 e.m e.m PROPN american_scientific_journal-522 319 12 wu wu PROPN american_scientific_journal-522 319 13 . . PUNCT american_scientific_journal-522 320 1 ( ( PUNCT american_scientific_journal-522 320 2 1977 1977 NUM american_scientific_journal-522 320 3 , , PUNCT american_scientific_journal-522 320 4 dec dec PROPN american_scientific_journal-522 320 5 ) ) PUNCT american_scientific_journal-522 320 6 , , PUNCT american_scientific_journal-522 320 7 a a DET american_scientific_journal-522 320 8 higher high ADJ american_scientific_journal-522 320 9 order order NOUN american_scientific_journal-522 320 10 rheory rheory NOUN american_scientific_journal-522 320 11 of of ADP american_scientific_journal-522 320 12 plate plate NOUN american_scientific_journal-522 320 13 deformation deformation NOUN american_scientific_journal-522 320 14 – – PUNCT american_scientific_journal-522 320 15 part part NOUN american_scientific_journal-522 320 16 1 1 NUM american_scientific_journal-522 320 17 : : PUNCT american_scientific_journal-522 320 18 homogeneous homogeneous ADJ american_scientific_journal-522 320 19 plates plate NOUN american_scientific_journal-522 320 20 , , PUNCT american_scientific_journal-522 320 21 asme asme PROPN american_scientific_journal-522 320 22 , , PUNCT american_scientific_journal-522 320 23 j. j. PROPN american_scientific_journal-522 320 24 appl appl PROPN american_scientific_journal-522 320 25 . . PROPN american_scientific_journal-522 320 26 mech mech PROPN american_scientific_journal-522 320 27 , , PUNCT american_scientific_journal-522 320 28 44 44 NUM american_scientific_journal-522 320 29 663 663 NUM american_scientific_journal-522 320 30 - - SYM american_scientific_journal-522 320 31 668 668 NUM american_scientific_journal-522 320 32 . . PUNCT american_scientific_journal-522 320 33 available available ADJ american_scientific_journal-522 320 34 : : PUNCT american_scientific_journal-522 320 35 http://appliedmechanics.asmedigitalcollection.asme.org http://appliedmechanics.asmedigitalcollection.asme.org PROPN american_scientific_journal-522 320 36 / / SYM american_scientific_journal-522 320 37 article.aspx?articleid=1403567 article.aspx?articleid=1403567 PROPN american_scientific_journal-522 321 1 [ [ X american_scientific_journal-522 321 2 5 5 NUM american_scientific_journal-522 321 3 ] ] PUNCT american_scientific_journal-522 321 4 m. m. NOUN american_scientific_journal-522 321 5 levinson levinson PROPN american_scientific_journal-522 321 6 . . PUNCT american_scientific_journal-522 322 1 ( ( PUNCT american_scientific_journal-522 322 2 1980 1980 NUM american_scientific_journal-522 322 3 ) ) PUNCT american_scientific_journal-522 322 4 , , PUNCT american_scientific_journal-522 322 5 an an DET american_scientific_journal-522 322 6 accurate accurate ADJ american_scientific_journal-522 322 7 simple simple ADJ american_scientific_journal-522 322 8 theory theory NOUN american_scientific_journal-522 322 9 of of ADP american_scientific_journal-522 322 10 the the DET american_scientific_journal-522 322 11 statics static NOUN american_scientific_journal-522 322 12 and and CCONJ american_scientific_journal-522 322 13 dynamics dynamic NOUN american_scientific_journal-522 322 14 of of ADP american_scientific_journal-522 322 15 elastic elastic ADJ american_scientific_journal-522 322 16 plates plate NOUN american_scientific_journal-522 322 17 , , PUNCT american_scientific_journal-522 322 18 mech mech NOUN american_scientific_journal-522 322 19 . . PUNCT american_scientific_journal-522 323 1 res re NOUN american_scientific_journal-522 323 2 . . PUNCT american_scientific_journal-522 324 1 commun commun PROPN american_scientific_journal-522 324 2 . . PUNCT american_scientific_journal-522 325 1 7 7 NUM american_scientific_journal-522 325 2 343 343 NUM american_scientific_journal-522 325 3 - - SYM american_scientific_journal-522 325 4 350 350 NUM american_scientific_journal-522 325 5 . . PUNCT american_scientific_journal-522 326 1 [ [ X american_scientific_journal-522 326 2 6 6 NUM american_scientific_journal-522 326 3 ] ] SYM american_scientific_journal-522 326 4 m.v.v m.v.v NOUN american_scientific_journal-522 326 5 . . PUNCT american_scientific_journal-522 326 6 murty murty PROPN american_scientific_journal-522 326 7 . . PUNCT american_scientific_journal-522 327 1 ( ( PUNCT american_scientific_journal-522 327 2 1981 1981 NUM american_scientific_journal-522 327 3 ) ) PUNCT american_scientific_journal-522 327 4 , , PUNCT american_scientific_journal-522 327 5 an an DET american_scientific_journal-522 327 6 improved improved ADJ american_scientific_journal-522 327 7 transverse transverse NOUN american_scientific_journal-522 327 8 shear shear NOUN american_scientific_journal-522 327 9 deformation deformation NOUN american_scientific_journal-522 327 10 theory theory NOUN american_scientific_journal-522 327 11 for for ADP american_scientific_journal-522 327 12 laminated laminate VERB american_scientific_journal-522 327 13 anistropic anistropic ADJ american_scientific_journal-522 327 14 plates plate NOUN american_scientific_journal-522 327 15 . . PUNCT american_scientific_journal-522 328 1 nasa nasa PROPN american_scientific_journal-522 328 2 technical technical PROPN american_scientific_journal-522 328 3 paper paper PROPN american_scientific_journal-522 328 4 1903 1903 NUM american_scientific_journal-522 328 5 . . PUNCT american_scientific_journal-522 329 1 [ [ X american_scientific_journal-522 329 2 7 7 X american_scientific_journal-522 329 3 ] ] PUNCT american_scientific_journal-522 329 4 j. j. PROPN american_scientific_journal-522 329 5 n. n. PROPN american_scientific_journal-522 329 6 reddy.(1984 reddy.(1984 PROPN american_scientific_journal-522 329 7 , , PUNCT american_scientific_journal-522 329 8 dec dec PROPN american_scientific_journal-522 329 9 ) ) PUNCT american_scientific_journal-522 329 10 , , PUNCT american_scientific_journal-522 329 11 a a DET american_scientific_journal-522 329 12 simple simple ADJ american_scientific_journal-522 329 13 higher high ADJ american_scientific_journal-522 329 14 - - PUNCT american_scientific_journal-522 329 15 order order NOUN american_scientific_journal-522 329 16 theory theory NOUN american_scientific_journal-522 329 17 for for ADP american_scientific_journal-522 329 18 laminated laminated ADJ american_scientific_journal-522 329 19 composite composite ADJ american_scientific_journal-522 329 20 plates plate NOUN american_scientific_journal-522 329 21 , , PUNCT american_scientific_journal-522 329 22 asme asme PROPN american_scientific_journal-522 329 23 j. j. PROPN american_scientific_journal-522 329 24 appl appl PROPN american_scientific_journal-522 329 25 . . PROPN american_scientific_journal-522 329 26 mech mech PROPN american_scientific_journal-522 329 27 . . PUNCT american_scientific_journal-522 330 1 51 51 NUM american_scientific_journal-522 330 2 745 745 NUM american_scientific_journal-522 330 3 - - PUNCT american_scientific_journal-522 330 4 752.available 752.available NUM american_scientific_journal-522 330 5 : : PUNCT american_scientific_journal-522 330 6 http://appliedmechanics.asmedigitalcollection.asme.org http://appliedmechanics.asmedigitalcollection.asme.org PROPN american_scientific_journal-522 330 7 /article.aspx?articleid=1407769 /article.aspx?articleid=1407769 PUNCT american_scientific_journal-522 331 1 [ [ X american_scientific_journal-522 331 2 8 8 X american_scientific_journal-522 331 3 ] ] X american_scientific_journal-522 331 4 t. t. PROPN american_scientific_journal-522 331 5 kant kant PROPN american_scientific_journal-522 331 6 , , PUNCT american_scientific_journal-522 331 7 j.h j.h PROPN american_scientific_journal-522 331 8 . . PROPN american_scientific_journal-522 331 9 varaiya varaiya PROPN american_scientific_journal-522 331 10 , , PUNCT american_scientific_journal-522 331 11 c.p c.p PROPN american_scientific_journal-522 331 12 . . PROPN american_scientific_journal-522 331 13 arora arora PROPN american_scientific_journal-522 331 14 , , PUNCT american_scientific_journal-522 331 15 finite finite PROPN american_scientific_journal-522 331 16 element element NOUN american_scientific_journal-522 331 17 transient transient NOUN american_scientific_journal-522 331 18 analysis analysis NOUN american_scientific_journal-522 331 19 of of ADP american_scientific_journal-522 331 20 composite composite ADJ american_scientific_journal-522 331 21 and and CCONJ american_scientific_journal-522 331 22 sandwich sandwich NOUN american_scientific_journal-522 331 23 plates plate NOUN american_scientific_journal-522 331 24 based base VERB american_scientific_journal-522 331 25 a a DET american_scientific_journal-522 331 26 refined refined ADJ american_scientific_journal-522 331 27 theory theory NOUN american_scientific_journal-522 331 28 and and CCONJ american_scientific_journal-522 331 29 implicit implicit ADJ american_scientific_journal-522 331 30 time time NOUN american_scientific_journal-522 331 31 integration integration NOUN american_scientific_journal-522 331 32 shemes sheme NOUN american_scientific_journal-522 331 33 , , PUNCT american_scientific_journal-522 331 34 comput comput NOUN american_scientific_journal-522 331 35 . . PUNCT american_scientific_journal-522 332 1 struct struct NOUN american_scientific_journal-522 332 2 , , PUNCT american_scientific_journal-522 332 3 36 36 NUM american_scientific_journal-522 332 4 ( ( PUNCT american_scientific_journal-522 332 5 1990 1990 NUM american_scientific_journal-522 332 6 ) ) PUNCT american_scientific_journal-522 332 7 401420.available 401420.available NUM american_scientific_journal-522 332 8 : : PUNCT american_scientific_journal-522 332 9 http://www.sciencedirect.com http://www.sciencedirect.com NUM american_scientific_journal-522 332 10 / / SYM american_scientific_journal-522 332 11 science science NOUN american_scientific_journal-522 332 12 / / SYM american_scientific_journal-522 332 13 article article NOUN american_scientific_journal-522 332 14 / / SYM american_scientific_journal-522 332 15 pii/004579499090279b pii/004579499090279b PROPN american_scientific_journal-522 332 16 17 17 NUM american_scientific_journal-522 332 17 http://appliedmechanics.asmedigitalcollection.asme.org.sci-hub.org/article.aspx?articleid=1401537 http://appliedmechanics.asmedigitalcollection.asme.org.sci-hub.org/article.aspx?articleid=1401537 NUM american_scientific_journal-522 332 18 http://appliedmechanics.asmedigitalcollection.asme.org.sci-hub.org/article.aspx?articleid=1401537 http://appliedmechanics.asmedigitalcollection.asme.org.sci-hub.org/article.aspx?articleid=1401537 NOUN american_scientific_journal-522 332 19 http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=1403567 http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=1403567 PROPN american_scientific_journal-522 332 20 http://www.sciencedirect.com/science/article/pii/004579499090279b http://www.sciencedirect.com/science/article/pii/004579499090279b NOUN american_scientific_journal-522 332 21 american american PROPN american_scientific_journal-522 332 22 scientific scientific PROPN american_scientific_journal-522 332 23 research research PROPN american_scientific_journal-522 332 24 journal journal NOUN american_scientific_journal-522 332 25 for for ADP american_scientific_journal-522 332 26 engineering engineering NOUN american_scientific_journal-522 332 27 , , PUNCT american_scientific_journal-522 332 28 technology technology NOUN american_scientific_journal-522 332 29 , , PUNCT american_scientific_journal-522 332 30 and and CCONJ american_scientific_journal-522 332 31 sciences science NOUN american_scientific_journal-522 332 32 ( ( PUNCT american_scientific_journal-522 332 33 asrjets asrjet NOUN american_scientific_journal-522 332 34 ) ) PUNCT american_scientific_journal-522 332 35 ( ( PUNCT american_scientific_journal-522 332 36 2014 2014 NUM american_scientific_journal-522 332 37 ) ) PUNCT american_scientific_journal-522 332 38 volume volume NOUN american_scientific_journal-522 332 39 9 9 NUM american_scientific_journal-522 332 40 , , PUNCT american_scientific_journal-522 332 41 no no DET american_scientific_journal-522 332 42 1 1 NUM american_scientific_journal-522 332 43 , , PUNCT american_scientific_journal-522 332 44 pp pp ADV american_scientific_journal-522 332 45 1 1 NUM american_scientific_journal-522 332 46 - - SYM american_scientific_journal-522 332 47 19 19 NUM american_scientific_journal-522 333 1 [ [ X american_scientific_journal-522 333 2 9 9 NUM american_scientific_journal-522 333 3 ] ] X american_scientific_journal-522 333 4 a.k a.k PROPN american_scientific_journal-522 333 5 . . PROPN american_scientific_journal-522 333 6 nayak nayak PROPN american_scientific_journal-522 333 7 , , PUNCT american_scientific_journal-522 333 8 s.s.j s.s.j NOUN american_scientific_journal-522 333 9 . . PUNCT american_scientific_journal-522 333 10 moy moy PROPN american_scientific_journal-522 333 11 , , PUNCT american_scientific_journal-522 333 12 r.a r.a PROPN american_scientific_journal-522 333 13 . . PROPN american_scientific_journal-522 333 14 shenoi shenoi PROPN american_scientific_journal-522 333 15 , , PUNCT american_scientific_journal-522 333 16 free free ADJ american_scientific_journal-522 333 17 vibration vibration NOUN american_scientific_journal-522 333 18 analysis analysis NOUN american_scientific_journal-522 333 19 of of ADP american_scientific_journal-522 333 20 composite composite ADJ american_scientific_journal-522 333 21 sandwich sandwich NOUN american_scientific_journal-522 333 22 plates plate NOUN american_scientific_journal-522 333 23 based base VERB american_scientific_journal-522 333 24 on on ADP american_scientific_journal-522 333 25 reddy reddy PROPN american_scientific_journal-522 333 26 's 's PART american_scientific_journal-522 333 27 higherorder higherorder NOUN american_scientific_journal-522 333 28 theory theory NOUN american_scientific_journal-522 333 29 , , PUNCT american_scientific_journal-522 333 30 composites composite VERB american_scientific_journal-522 333 31 part part NOUN american_scientific_journal-522 333 32 b b NOUN american_scientific_journal-522 333 33 : : PUNCT american_scientific_journal-522 333 34 engineering engineering NOUN american_scientific_journal-522 333 35 . . PUNCT american_scientific_journal-522 334 1 33 33 NUM american_scientific_journal-522 334 2 ( ( PUNCT american_scientific_journal-522 334 3 7 7 NUM american_scientific_journal-522 334 4 ) ) PUNCT american_scientific_journal-522 334 5 ( ( PUNCT american_scientific_journal-522 334 6 2002 2002 NUM american_scientific_journal-522 334 7 ) ) PUNCT american_scientific_journal-522 334 8 505 505 NUM american_scientific_journal-522 334 9 - - SYM american_scientific_journal-522 334 10 519 519 NUM american_scientific_journal-522 334 11 . . PUNCT american_scientific_journal-522 334 12 available available ADJ american_scientific_journal-522 334 13 : : PUNCT american_scientific_journal-522 335 1 http://www.sciencedirect.com/science/article/pii/s1359836802000355 http://www.sciencedirect.com/science/article/pii/s1359836802000355 PROPN american_scientific_journal-522 336 1 [ [ X american_scientific_journal-522 336 2 10 10 NUM american_scientific_journal-522 336 3 ] ] X american_scientific_journal-522 336 4 a.k a.k PROPN american_scientific_journal-522 336 5 . . PROPN american_scientific_journal-522 336 6 nayak nayak PROPN american_scientific_journal-522 336 7 , , PUNCT american_scientific_journal-522 336 8 r.a r.a PROPN american_scientific_journal-522 336 9 . . PROPN american_scientific_journal-522 336 10 shenoi shenoi PROPN american_scientific_journal-522 336 11 , , PUNCT american_scientific_journal-522 336 12 s.s.j s.s.j NOUN american_scientific_journal-522 336 13 moy moy NOUN american_scientific_journal-522 336 14 , , PUNCT american_scientific_journal-522 336 15 transient transient ADJ american_scientific_journal-522 336 16 response response NOUN american_scientific_journal-522 336 17 of of ADP american_scientific_journal-522 336 18 composite composite ADJ american_scientific_journal-522 336 19 sandwich sandwich NOUN american_scientific_journal-522 336 20 plates plate NOUN american_scientific_journal-522 336 21 , , PUNCT american_scientific_journal-522 336 22 comput comput NOUN american_scientific_journal-522 336 23 . . PUNCT american_scientific_journal-522 336 24 struct struct NOUN american_scientific_journal-522 336 25 , , PUNCT american_scientific_journal-522 336 26 64 64 NUM american_scientific_journal-522 336 27 ( ( PUNCT american_scientific_journal-522 336 28 2004 2004 NUM american_scientific_journal-522 336 29 ) ) PUNCT american_scientific_journal-522 336 30 249 249 NUM american_scientific_journal-522 336 31 - - SYM american_scientific_journal-522 336 32 267 267 NUM american_scientific_journal-522 336 33 . . PUNCT american_scientific_journal-522 337 1 available available ADJ american_scientific_journal-522 337 2 : : PUNCT american_scientific_journal-522 337 3 http://www.sciencedirect.com/science/article/pii/s0263822303001351 http://www.sciencedirect.com/science/article/pii/s0263822303001351 X american_scientific_journal-522 338 1 [ [ X american_scientific_journal-522 338 2 11 11 NUM american_scientific_journal-522 338 3 ] ] X american_scientific_journal-522 338 4 a.h a.h PROPN american_scientific_journal-522 338 5 . . PROPN american_scientific_journal-522 338 6 sheikh sheikh PROPN american_scientific_journal-522 338 7 , , PUNCT american_scientific_journal-522 338 8 a. a. NOUN american_scientific_journal-522 338 9 chakrabarti chakrabarti PROPN american_scientific_journal-522 338 10 , , PUNCT american_scientific_journal-522 338 11 a a DET american_scientific_journal-522 338 12 new new ADJ american_scientific_journal-522 338 13 plate plate NOUN american_scientific_journal-522 338 14 bending bend VERB american_scientific_journal-522 338 15 element element NOUN american_scientific_journal-522 338 16 based base VERB american_scientific_journal-522 338 17 on on ADP american_scientific_journal-522 338 18 higher high ADJ american_scientific_journal-522 338 19 order order NOUN american_scientific_journal-522 338 20 shear shear ADJ american_scientific_journal-522 338 21 deformation deformation NOUN american_scientific_journal-522 338 22 theory theory NOUN american_scientific_journal-522 338 23 for for ADP american_scientific_journal-522 338 24 the the DET american_scientific_journal-522 338 25 analysis analysis NOUN american_scientific_journal-522 338 26 of of ADP american_scientific_journal-522 338 27 composite composite ADJ american_scientific_journal-522 338 28 plates plate NOUN american_scientific_journal-522 338 29 , , PUNCT american_scientific_journal-522 338 30 finite finite NOUN american_scientific_journal-522 338 31 . . PROPN american_scientific_journal-522 338 32 elem elem NOUN american_scientific_journal-522 338 33 . . PUNCT american_scientific_journal-522 339 1 anal anal PROPN american_scientific_journal-522 339 2 . . PUNCT american_scientific_journal-522 340 1 des des PROPN american_scientific_journal-522 340 2 , , PUNCT american_scientific_journal-522 340 3 39 39 NUM american_scientific_journal-522 340 4 ( ( PUNCT american_scientific_journal-522 340 5 2003 2003 NUM american_scientific_journal-522 340 6 ) ) PUNCT american_scientific_journal-522 340 7 137 137 NUM american_scientific_journal-522 340 8 - - SYM american_scientific_journal-522 340 9 155 155 NUM american_scientific_journal-522 340 10 . . PUNCT american_scientific_journal-522 341 1 vailable vailable PROPN american_scientific_journal-522 341 2 : : PUNCT american_scientific_journal-522 341 3 http://www.sciencedirect.com http://www.sciencedirect.com X american_scientific_journal-522 341 4 / / SYM american_scientific_journal-522 341 5 science science NOUN american_scientific_journal-522 341 6 / / SYM american_scientific_journal-522 341 7 article article NOUN american_scientific_journal-522 341 8 / / SYM american_scientific_journal-522 341 9 pii pii PROPN american_scientific_journal-522 341 10 / / SYM american_scientific_journal-522 341 11 s0168874x02001373 s0168874x02001373 NOUN american_scientific_journal-522 342 1 [ [ X american_scientific_journal-522 342 2 12 12 NUM american_scientific_journal-522 342 3 ] ] X american_scientific_journal-522 342 4 r.c r.c PROPN american_scientific_journal-522 342 5 . . PROPN american_scientific_journal-522 342 6 batra batra PROPN american_scientific_journal-522 342 7 , , PUNCT american_scientific_journal-522 342 8 s. s. PROPN american_scientific_journal-522 342 9 aimmanee aimmanee PROPN american_scientific_journal-522 342 10 , , PUNCT american_scientific_journal-522 342 11 vibrations vibration NOUN american_scientific_journal-522 342 12 of of ADP american_scientific_journal-522 342 13 thick thick ADJ american_scientific_journal-522 342 14 isotropic isotropic ADJ american_scientific_journal-522 342 15 plates plate NOUN american_scientific_journal-522 342 16 with with ADP american_scientific_journal-522 342 17 higher high ADJ american_scientific_journal-522 342 18 order order NOUN american_scientific_journal-522 342 19 shear shear NOUN american_scientific_journal-522 342 20 and and CCONJ american_scientific_journal-522 342 21 normal normal ADJ american_scientific_journal-522 342 22 deformable deformable ADJ american_scientific_journal-522 342 23 plate plate NOUN american_scientific_journal-522 342 24 theories theory NOUN american_scientific_journal-522 342 25 , , PUNCT american_scientific_journal-522 342 26 comput comput NOUN american_scientific_journal-522 342 27 . . PUNCT american_scientific_journal-522 343 1 struct struct NOUN american_scientific_journal-522 343 2 , , PUNCT american_scientific_journal-522 343 3 83 83 NUM american_scientific_journal-522 343 4 ( ( PUNCT american_scientific_journal-522 343 5 2005 2005 NUM american_scientific_journal-522 343 6 ) ) PUNCT american_scientific_journal-522 343 7 934 934 NUM american_scientific_journal-522 343 8 - - SYM american_scientific_journal-522 343 9 955 955 NUM american_scientific_journal-522 343 10 . . PUNCT american_scientific_journal-522 344 1 available available ADJ american_scientific_journal-522 344 2 : : PUNCT american_scientific_journal-522 345 1 http://www.sciencedirect.com/science/article/pii/s0045794905000507?np=y http://www.sciencedirect.com/science/article/pii/s0045794905000507?np=y PROPN american_scientific_journal-522 345 2 [ [ X american_scientific_journal-522 345 3 13 13 NUM american_scientific_journal-522 345 4 ] ] PUNCT american_scientific_journal-522 345 5 s. s. PROPN american_scientific_journal-522 345 6 kapuria kapuria PROPN american_scientific_journal-522 345 7 , , PUNCT american_scientific_journal-522 345 8 sd sd ADP american_scientific_journal-522 345 9 kulkarni kulkarni PROPN american_scientific_journal-522 345 10 , , PUNCT american_scientific_journal-522 345 11 an an DET american_scientific_journal-522 345 12 improved improve VERB american_scientific_journal-522 345 13 discrete discrete ADJ american_scientific_journal-522 345 14 kirchhoff kirchhoff NOUN american_scientific_journal-522 345 15 quadrilateral quadrilateral PROPN american_scientific_journal-522 345 16 element element NOUN american_scientific_journal-522 345 17 based base VERB american_scientific_journal-522 345 18 on on ADP american_scientific_journal-522 345 19 third third ADJ american_scientific_journal-522 345 20 - - PUNCT american_scientific_journal-522 345 21 order order NOUN american_scientific_journal-522 345 22 zigzag zigzag NOUN american_scientific_journal-522 345 23 theory theory NOUN american_scientific_journal-522 345 24 for for ADP american_scientific_journal-522 345 25 static static ADJ american_scientific_journal-522 345 26 analysis analysis NOUN american_scientific_journal-522 345 27 of of ADP american_scientific_journal-522 345 28 composite composite ADJ american_scientific_journal-522 345 29 and and CCONJ american_scientific_journal-522 345 30 sandwich sandwich NOUN american_scientific_journal-522 345 31 plates plate NOUN american_scientific_journal-522 345 32 , , PUNCT american_scientific_journal-522 345 33 j. j. PROPN american_scientific_journal-522 345 34 numer numer PROPN american_scientific_journal-522 345 35 . . PROPN american_scientific_journal-522 345 36 method method PROPN american_scientific_journal-522 345 37 . . PUNCT american_scientific_journal-522 346 1 eng eng PROPN american_scientific_journal-522 346 2 , , PUNCT american_scientific_journal-522 346 3 69 69 NUM american_scientific_journal-522 346 4 ( ( PUNCT american_scientific_journal-522 346 5 2007)1948 2007)1948 NUM american_scientific_journal-522 346 6 - - SYM american_scientific_journal-522 346 7 1981 1981 NUM american_scientific_journal-522 346 8 . . PUNCT american_scientific_journal-522 347 1 available available ADJ american_scientific_journal-522 347 2 : : PUNCT american_scientific_journal-522 347 3 http://onlinelibrary.wiley.com/doi/10.1002/nme.1836/abstract http://onlinelibrary.wiley.com/doi/10.1002/nme.1836/abstract PROPN american_scientific_journal-522 348 1 [ [ X american_scientific_journal-522 348 2 14 14 NUM american_scientific_journal-522 348 3 ] ] X american_scientific_journal-522 348 4 b.a b.a PROPN american_scientific_journal-522 348 5 . . PROPN american_scientific_journal-522 348 6 szabo szabo PROPN american_scientific_journal-522 348 7 , , PUNCT american_scientific_journal-522 348 8 and and CCONJ american_scientific_journal-522 348 9 g.j g.j PROPN american_scientific_journal-522 348 10 . . PROPN american_scientific_journal-522 348 11 sahrmann sahrmann PROPN american_scientific_journal-522 348 12 , , PUNCT american_scientific_journal-522 348 13 hierarchical hierarchical ADJ american_scientific_journal-522 348 14 plate plate NOUN american_scientific_journal-522 348 15 and and CCONJ american_scientific_journal-522 348 16 shells shell NOUN american_scientific_journal-522 348 17 models model NOUN american_scientific_journal-522 348 18 based base VERB american_scientific_journal-522 348 19 on on ADP american_scientific_journal-522 348 20 p p PROPN american_scientific_journal-522 348 21 extension extension NOUN american_scientific_journal-522 348 22 , , PUNCT american_scientific_journal-522 348 23 int int NOUN american_scientific_journal-522 348 24 . . PUNCT american_scientific_journal-522 349 1 j. j. PROPN american_scientific_journal-522 349 2 numer.method numer.method PROPN american_scientific_journal-522 349 3 . . PROPN american_scientific_journal-522 350 1 eng eng PROPN american_scientific_journal-522 350 2 , , PUNCT american_scientific_journal-522 350 3 26 26 NUM american_scientific_journal-522 350 4 ( ( PUNCT american_scientific_journal-522 350 5 1988 1988 NUM american_scientific_journal-522 350 6 ) ) PUNCT american_scientific_journal-522 350 7 1855 1855 NUM american_scientific_journal-522 350 8 - - SYM american_scientific_journal-522 350 9 1881 1881 NUM american_scientific_journal-522 350 10 . . PUNCT american_scientific_journal-522 351 1 available available ADJ american_scientific_journal-522 351 2 : : PUNCT american_scientific_journal-522 351 3 http://onlinelibrary.wiley.com http://onlinelibrary.wiley.com X american_scientific_journal-522 351 4 / / SYM american_scientific_journal-522 351 5 doi/10.1002 doi/10.1002 NOUN american_scientific_journal-522 351 6 / / SYM american_scientific_journal-522 351 7 nme.1620260812 nme.1620260812 NOUN american_scientific_journal-522 351 8 / / SYM american_scientific_journal-522 351 9 abstract;jsessionid=3dcb6a45626b110 abstract;jsessionid=3dcb6a45626b110 PROPN american_scientific_journal-522 351 10 6e11ab1a7f34b4282.f04t04 6e11ab1a7f34b4282.f04t04 NUM american_scientific_journal-522 352 1 [ [ X american_scientific_journal-522 352 2 15 15 NUM american_scientific_journal-522 352 3 ] ] X american_scientific_journal-522 352 4 b.a b.a PROPN american_scientific_journal-522 352 5 . . PROPN american_scientific_journal-522 352 6 szabo szabo PROPN american_scientific_journal-522 352 7 , , PUNCT american_scientific_journal-522 352 8 i. i. PROPN american_scientific_journal-522 352 9 babuska babuska PROPN american_scientific_journal-522 352 10 . . PUNCT american_scientific_journal-522 352 11 , , PUNCT american_scientific_journal-522 352 12 finite finite VERB american_scientific_journal-522 352 13 element element NOUN american_scientific_journal-522 352 14 analysis analysis NOUN american_scientific_journal-522 352 15 , , PUNCT american_scientific_journal-522 352 16 ( ( PUNCT american_scientific_journal-522 352 17 1990 1990 NUM american_scientific_journal-522 352 18 ) ) PUNCT american_scientific_journal-522 352 19 wiley wiley NOUN american_scientific_journal-522 352 20 - - PUNCT american_scientific_journal-522 352 21 lnterscience lnterscience NOUN american_scientific_journal-522 352 22 , , PUNCT american_scientific_journal-522 352 23 new new PROPN american_scientific_journal-522 352 24 york york PROPN american_scientific_journal-522 352 25 , , PUNCT american_scientific_journal-522 352 26 1991 1991 NUM american_scientific_journal-522 352 27 . . PUNCT american_scientific_journal-522 353 1 [ [ X american_scientific_journal-522 353 2 on on ADP american_scientific_journal-522 353 3 - - PUNCT american_scientific_journal-522 353 4 line line NOUN american_scientific_journal-522 353 5 ] ] PUNCT american_scientific_journal-522 353 6 . . PUNCT american_scientific_journal-522 354 1 http://eu.wiley.com/wileycda/wileytitle/productcd-0471502731.html http://eu.wiley.com/wileycda/wileytitle/productcd-0471502731.html PROPN american_scientific_journal-522 355 1 [ [ X american_scientific_journal-522 355 2 16 16 NUM american_scientific_journal-522 355 3 ] ] PUNCT american_scientific_journal-522 355 4 s. s. PROPN american_scientific_journal-522 355 5 m. m. PROPN american_scientific_journal-522 355 6 hamza hamza PROPN american_scientific_journal-522 355 7 - - PUNCT american_scientific_journal-522 355 8 cherif cherif PROPN american_scientific_journal-522 355 9 , , PUNCT american_scientific_journal-522 355 10 free free ADJ american_scientific_journal-522 355 11 vibration vibration NOUN american_scientific_journal-522 355 12 analysis analysis NOUN american_scientific_journal-522 355 13 of of ADP american_scientific_journal-522 355 14 rotating rotate VERB american_scientific_journal-522 355 15 cantilever cantilever NOUN american_scientific_journal-522 355 16 plates plate NOUN american_scientific_journal-522 355 17 using use VERB american_scientific_journal-522 355 18 the the DET american_scientific_journal-522 355 19 p p NOUN american_scientific_journal-522 355 20 - - PUNCT american_scientific_journal-522 355 21 version version NOUN american_scientific_journal-522 355 22 of of ADP american_scientific_journal-522 355 23 the the DET american_scientific_journal-522 355 24 finite finite PROPN american_scientific_journal-522 355 25 element element NOUN american_scientific_journal-522 355 26 method method NOUN american_scientific_journal-522 355 27 , , PUNCT american_scientific_journal-522 355 28 structural structural ADJ american_scientific_journal-522 355 29 engineering engineering NOUN american_scientific_journal-522 355 30 and and CCONJ american_scientific_journal-522 355 31 mechanics mechanic NOUN american_scientific_journal-522 355 32 , , PUNCT american_scientific_journal-522 355 33 22 22 NUM american_scientific_journal-522 355 34 ( ( PUNCT american_scientific_journal-522 355 35 2006 2006 NUM american_scientific_journal-522 355 36 ) ) PUNCT american_scientific_journal-522 355 37 151 151 NUM american_scientific_journal-522 355 38 - - SYM american_scientific_journal-522 355 39 167 167 NUM american_scientific_journal-522 355 40 . . PUNCT american_scientific_journal-522 356 1 [ [ X american_scientific_journal-522 356 2 17 17 NUM american_scientific_journal-522 356 3 ] ] X american_scientific_journal-522 356 4 a.w a.w PROPN american_scientific_journal-522 356 5 . . PROPN american_scientific_journal-522 356 6 leissa leissa PROPN american_scientific_journal-522 356 7 , , PUNCT american_scientific_journal-522 356 8 the the DET american_scientific_journal-522 356 9 free free ADJ american_scientific_journal-522 356 10 vibration vibration NOUN american_scientific_journal-522 356 11 of of ADP american_scientific_journal-522 356 12 rectangular rectangular ADJ american_scientific_journal-522 356 13 plates plate NOUN american_scientific_journal-522 356 14 , , PUNCT american_scientific_journal-522 356 15 j. j. PROPN american_scientific_journal-522 356 16 sound sound PROPN american_scientific_journal-522 356 17 vib vib PROPN american_scientific_journal-522 356 18 . . PROPN american_scientific_journal-522 356 19 31 31 NUM american_scientific_journal-522 356 20 ( ( PUNCT american_scientific_journal-522 356 21 1973 1973 NUM american_scientific_journal-522 356 22 ) ) PUNCT american_scientific_journal-522 356 23 257–293 257–293 NUM american_scientific_journal-522 356 24 . . PUNCT american_scientific_journal-522 357 1 available available ADJ american_scientific_journal-522 357 2 : : PUNCT american_scientific_journal-522 358 1 http://www.sciencedirect.com/science/article/pii/s0022460x73803712 http://www.sciencedirect.com/science/article/pii/s0022460x73803712 PROPN american_scientific_journal-522 358 2 [ [ X american_scientific_journal-522 358 3 18 18 NUM american_scientific_journal-522 358 4 ] ] X american_scientific_journal-522 358 5 c. c. PROPN american_scientific_journal-522 358 6 w. w. PROPN american_scientific_journal-522 358 7 lim lim PROPN american_scientific_journal-522 359 1 a a PROPN american_scientific_journal-522 359 2 , , PUNCT american_scientific_journal-522 359 3 k.m k.m PROPN american_scientific_journal-522 359 4 . . PROPN american_scientific_journal-522 359 5 liew liew PROPN american_scientific_journal-522 359 6 b b PROPN american_scientific_journal-522 359 7 , , PUNCT american_scientific_journal-522 359 8 s. s. PROPN american_scientific_journal-522 359 9 kitipornchai kitipornchai PROPN american_scientific_journal-522 359 10 , , PUNCT american_scientific_journal-522 359 11 a a DET american_scientific_journal-522 359 12 numerical numerical ADJ american_scientific_journal-522 359 13 aspects aspect NOUN american_scientific_journal-522 359 14 for for ADP american_scientific_journal-522 359 15 free free ADJ american_scientific_journal-522 359 16 vibration vibration NOUN american_scientific_journal-522 359 17 of of ADP american_scientific_journal-522 359 18 thick thick ADJ american_scientific_journal-522 359 19 part part NOUN american_scientific_journal-522 360 1 i i NOUN american_scientific_journal-522 360 2 : : PUNCT american_scientific_journal-522 360 3 formulation formulation NOUN american_scientific_journal-522 360 4 and and CCONJ american_scientific_journal-522 360 5 verification verification NOUN american_scientific_journal-522 360 6 plates plate NOUN american_scientific_journal-522 360 7 , , PUNCT american_scientific_journal-522 360 8 comput comput NOUN american_scientific_journal-522 360 9 . . PUNCT american_scientific_journal-522 361 1 methods method NOUN american_scientific_journal-522 361 2 appl appl PROPN american_scientific_journal-522 361 3 . . PROPN american_scientific_journal-522 361 4 mech mech PROPN american_scientific_journal-522 361 5 . . PUNCT american_scientific_journal-522 362 1 eng eng PROPN american_scientific_journal-522 362 2 , , PUNCT american_scientific_journal-522 362 3 156 156 NUM american_scientific_journal-522 362 4 ( ( PUNCT american_scientific_journal-522 362 5 1998 1998 NUM american_scientific_journal-522 362 6 ) ) PUNCT american_scientific_journal-522 362 7 15 15 NUM american_scientific_journal-522 362 8 - - SYM american_scientific_journal-522 362 9 29 29 NUM american_scientific_journal-522 362 10 . . PUNCT american_scientific_journal-522 363 1 available available ADJ american_scientific_journal-522 363 2 : : PUNCT american_scientific_journal-522 364 1 http://www.sciencedirect.com/science/article/pii/s0045782597001977 http://www.sciencedirect.com/science/article/pii/s0045782597001977 X american_scientific_journal-522 364 2 [ [ X american_scientific_journal-522 364 3 19 19 NUM american_scientific_journal-522 364 4 ] ] PUNCT american_scientific_journal-522 364 5 s. s. PROPN american_scientific_journal-522 364 6 srinivas srinivas PROPN american_scientific_journal-522 364 7 , , PUNCT american_scientific_journal-522 364 8 c.v c.v PROPN american_scientific_journal-522 364 9 . . PROPN american_scientific_journal-522 364 10 jogarao jogarao PROPN american_scientific_journal-522 364 11 , , PUNCT american_scientific_journal-522 364 12 a.k a.k PROPN american_scientific_journal-522 364 13 . . PROPN american_scientific_journal-522 364 14 rao rao PROPN american_scientific_journal-522 364 15 , , PUNCT american_scientific_journal-522 364 16 an an DET american_scientific_journal-522 364 17 exact exact ADJ american_scientific_journal-522 364 18 analysis analysis NOUN american_scientific_journal-522 364 19 for for ADP american_scientific_journal-522 364 20 vibration vibration NOUN american_scientific_journal-522 364 21 of of ADP american_scientific_journal-522 364 22 simply simply ADV american_scientific_journal-522 364 23 - - PUNCT american_scientific_journal-522 364 24 supported support VERB american_scientific_journal-522 364 25 homogeneous homogeneous ADJ american_scientific_journal-522 364 26 and and CCONJ american_scientific_journal-522 364 27 laminated laminate VERB american_scientific_journal-522 364 28 thick thick ADJ american_scientific_journal-522 364 29 rectangular rectangular ADJ american_scientific_journal-522 364 30 plates plate NOUN american_scientific_journal-522 364 31 , , PUNCT american_scientific_journal-522 364 32 j. j. PROPN american_scientific_journal-522 364 33 sound sound PROPN american_scientific_journal-522 364 34 vib vib PROPN american_scientific_journal-522 364 35 . . PUNCT american_scientific_journal-522 365 1 12(2 12(2 NUM american_scientific_journal-522 365 2 ) ) PUNCT american_scientific_journal-522 366 1 ( ( PUNCT american_scientific_journal-522 366 2 1970 1970 NUM american_scientific_journal-522 366 3 ) ) PUNCT american_scientific_journal-522 366 4 187 187 NUM american_scientific_journal-522 366 5 - - SYM american_scientific_journal-522 366 6 199 199 NUM american_scientific_journal-522 366 7 . . PUNCT american_scientific_journal-522 367 1 available available ADJ american_scientific_journal-522 367 2 : : PUNCT american_scientific_journal-522 368 1 http://www.sciencedirect.com/science/article/pii/0022460x70900891 http://www.sciencedirect.com/science/article/pii/0022460x70900891 X american_scientific_journal-522 368 2 18 18 NUM american_scientific_journal-522 368 3 http://www.sciencedirect.com/science/article/pii/s1359836802000355 http://www.sciencedirect.com/science/article/pii/s1359836802000355 PROPN american_scientific_journal-522 368 4 http://www.sciencedirect.com/science/article/pii/s1359836802000355 http://www.sciencedirect.com/science/article/pii/s1359836802000355 PROPN american_scientific_journal-522 368 5 http://www.sciencedirect.com/science/article/pii/s1359836802000355 http://www.sciencedirect.com/science/article/pii/s1359836802000355 PROPN american_scientific_journal-522 368 6 http://www.sciencedirect.com/science/article/pii/s1359836802000355 http://www.sciencedirect.com/science/article/pii/s1359836802000355 PROPN american_scientific_journal-522 368 7 http://www.sciencedirect.com/science/article/pii/s0263822303001351 http://www.sciencedirect.com/science/article/pii/s0263822303001351 NOUN american_scientific_journal-522 368 8 http://www.sciencedirect.com/science/article/pii/s0168874x02001373 http://www.sciencedirect.com/science/article/pii/s0168874x02001373 NOUN american_scientific_journal-522 368 9 http://www.sciencedirect.com/science/article/pii/s0045794905000507 http://www.sciencedirect.com/science/article/pii/s0045794905000507 NOUN american_scientific_journal-522 368 10 http://www.sciencedirect.com/science/article/pii/s0045794905000507 http://www.sciencedirect.com/science/article/pii/s0045794905000507 NOUN american_scientific_journal-522 368 11 http://www.sciencedirect.com/science/article/pii/s0045794905000507?np=y http://www.sciencedirect.com/science/article/pii/s0045794905000507?np=y PROPN american_scientific_journal-522 368 12 http://onlinelibrary.wiley.com/doi/10.1002/nme.1836/abstract http://onlinelibrary.wiley.com/doi/10.1002/nme.1836/abstract PROPN american_scientific_journal-522 368 13 http://onlinelibrary.wiley.com/doi/10.1002/nme.1836/abstract http://onlinelibrary.wiley.com/doi/10.1002/nme.1836/abstract VERB american_scientific_journal-522 368 14 http://onlinelibrary.wiley.com/doi/10.1002/nme.1836/abstract http://onlinelibrary.wiley.com/doi/10.1002/nme.1836/abstract PROPN american_scientific_journal-522 368 15 http://www.sciencedirect.com/science/article/pii/s0022460x73803712 http://www.sciencedirect.com/science/article/pii/s0022460x73803712 PROPN american_scientific_journal-522 368 16 http://www.sciencedirect.com/science/article/pii/s0045782597001977 http://www.sciencedirect.com/science/article/pii/s0045782597001977 CCONJ american_scientific_journal-522 368 17 http://www.sciencedirect.com/science/article/pii/0022460x70900891 http://www.sciencedirect.com/science/article/pii/0022460x70900891 ADJ american_scientific_journal-522 368 18 american american ADJ american_scientific_journal-522 368 19 scientific scientific ADJ american_scientific_journal-522 368 20 research research NOUN american_scientific_journal-522 368 21 journal journal NOUN american_scientific_journal-522 368 22 for for ADP american_scientific_journal-522 368 23 engineering engineering NOUN american_scientific_journal-522 368 24 , , PUNCT american_scientific_journal-522 368 25 technology technology NOUN american_scientific_journal-522 368 26 , , PUNCT american_scientific_journal-522 368 27 and and CCONJ american_scientific_journal-522 368 28 sciences science NOUN american_scientific_journal-522 368 29 ( ( PUNCT american_scientific_journal-522 368 30 asrjets asrjet NOUN american_scientific_journal-522 368 31 ) ) PUNCT american_scientific_journal-522 368 32 ( ( PUNCT american_scientific_journal-522 368 33 2014 2014 NUM american_scientific_journal-522 368 34 ) ) PUNCT american_scientific_journal-522 368 35 volume volume NOUN american_scientific_journal-522 368 36 9 9 NUM american_scientific_journal-522 368 37 , , PUNCT american_scientific_journal-522 368 38 no no DET american_scientific_journal-522 368 39 1 1 NUM american_scientific_journal-522 368 40 , , PUNCT american_scientific_journal-522 368 41 pp pp ADV american_scientific_journal-522 368 42 1 1 NUM american_scientific_journal-522 368 43 - - SYM american_scientific_journal-522 368 44 19 19 NUM american_scientific_journal-522 369 1 [ [ SYM american_scientific_journal-522 369 2 20 20 NUM american_scientific_journal-522 369 3 ] ] PUNCT american_scientific_journal-522 369 4 d. d. PROPN american_scientific_journal-522 369 5 zhou zhou PROPN american_scientific_journal-522 370 1 a a PROPN american_scientific_journal-522 370 2 , , PUNCT american_scientific_journal-522 370 3 y.k y.k PROPN american_scientific_journal-522 370 4 . . PROPN american_scientific_journal-522 370 5 cheung cheung PROPN american_scientific_journal-522 370 6 , , PUNCT american_scientific_journal-522 370 7 f.t.k f.t.k PROPN american_scientific_journal-522 370 8 . . PUNCT american_scientific_journal-522 370 9 au au PROPN american_scientific_journal-522 370 10 , , PUNCT american_scientific_journal-522 370 11 s.h s.h PROPN american_scientific_journal-522 370 12 . . PROPN american_scientific_journal-522 370 13 lo lo PROPN american_scientific_journal-522 370 14 , , PUNCT american_scientific_journal-522 370 15 three three NUM american_scientific_journal-522 370 16 - - PUNCT american_scientific_journal-522 370 17 dimensional dimensional ADJ american_scientific_journal-522 370 18 vibration vibration NOUN american_scientific_journal-522 370 19 analysis analysis NOUN american_scientific_journal-522 370 20 of of ADP american_scientific_journal-522 370 21 thick thick ADJ american_scientific_journal-522 370 22 rectangular rectangular ADJ american_scientific_journal-522 370 23 plates plate NOUN american_scientific_journal-522 370 24 using use VERB american_scientific_journal-522 370 25 chebyshev chebyshev NOUN american_scientific_journal-522 370 26 polynomial polynomial ADJ american_scientific_journal-522 370 27 and and CCONJ american_scientific_journal-522 370 28 ritz ritz PROPN american_scientific_journal-522 370 29 method method NOUN american_scientific_journal-522 370 30 , , PUNCT american_scientific_journal-522 370 31 int int NOUN american_scientific_journal-522 370 32 . . PUNCT american_scientific_journal-522 371 1 j. j. PROPN american_scientific_journal-522 371 2 solids solids PROPN american_scientific_journal-522 371 3 struct struct NOUN american_scientific_journal-522 371 4 , , PUNCT american_scientific_journal-522 371 5 63(2002 63(2002 NUM american_scientific_journal-522 371 6 ) ) PUNCT american_scientific_journal-522 371 7 39 39 NUM american_scientific_journal-522 371 8 – – PUNCT american_scientific_journal-522 371 9 6353.available 6353.available NOUN american_scientific_journal-522 371 10 : : PUNCT american_scientific_journal-522 371 11 http://www.sciencedirect.com http://www.sciencedirect.com NUM american_scientific_journal-522 371 12 / / SYM american_scientific_journal-522 371 13 science science NOUN american_scientific_journal-522 371 14 / / SYM american_scientific_journal-522 371 15 article article NOUN american_scientific_journal-522 371 16 / / SYM american_scientific_journal-522 371 17 pii pii PROPN american_scientific_journal-522 371 18 / / SYM american_scientific_journal-522 371 19 s0020768302004602 s0020768302004602 PROPN american_scientific_journal-522 372 1 [ [ X american_scientific_journal-522 372 2 21 21 NUM american_scientific_journal-522 372 3 ] ] X american_scientific_journal-522 372 4 s. s. PROPN american_scientific_journal-522 372 5 wang wang PROPN american_scientific_journal-522 372 6 , , PUNCT american_scientific_journal-522 372 7 vibration vibration NOUN american_scientific_journal-522 372 8 of of ADP american_scientific_journal-522 372 9 thin thin ADJ american_scientific_journal-522 372 10 skew skew ADJ american_scientific_journal-522 372 11 fiber fiber NOUN american_scientific_journal-522 372 12 reinforced reinforce VERB american_scientific_journal-522 372 13 composite composite ADJ american_scientific_journal-522 372 14 laminates laminate NOUN american_scientific_journal-522 372 15 , , PUNCT american_scientific_journal-522 372 16 j. j. PROPN american_scientific_journal-522 372 17 sound sound PROPN american_scientific_journal-522 372 18 . . PUNCT american_scientific_journal-522 373 1 vib vib PROPN american_scientific_journal-522 373 2 . . PUNCT american_scientific_journal-522 374 1 201(3 201(3 NUM american_scientific_journal-522 374 2 ) ) PUNCT american_scientific_journal-522 374 3 ( ( PUNCT american_scientific_journal-522 374 4 1997 1997 NUM american_scientific_journal-522 374 5 ) ) PUNCT american_scientific_journal-522 374 6 335 335 NUM american_scientific_journal-522 374 7 – – PUNCT american_scientific_journal-522 374 8 352.available 352.available NUM american_scientific_journal-522 374 9 : : PUNCT american_scientific_journal-522 374 10 http://www.sciencedirect.com http://www.sciencedirect.com NUM american_scientific_journal-522 374 11 / / SYM american_scientific_journal-522 374 12 science science NOUN american_scientific_journal-522 374 13 / / SYM american_scientific_journal-522 374 14 article article NOUN american_scientific_journal-522 374 15 / / SYM american_scientific_journal-522 374 16 pii pii PROPN american_scientific_journal-522 374 17 / / SYM american_scientific_journal-522 374 18 s0022460x96907452 s0022460x96907452 NOUN american_scientific_journal-522 374 19 [ [ X american_scientific_journal-522 374 20 22 22 NUM american_scientific_journal-522 374 21 ] ] PUNCT american_scientific_journal-522 374 22 s. s. PROPN american_scientific_journal-522 374 23 wang wang PROPN american_scientific_journal-522 374 24 , , PUNCT american_scientific_journal-522 374 25 free free ADJ american_scientific_journal-522 374 26 vibration vibration NOUN american_scientific_journal-522 374 27 analysis analysis NOUN american_scientific_journal-522 374 28 of of ADP american_scientific_journal-522 374 29 skew skew ADJ american_scientific_journal-522 374 30 fiber fiber NOUN american_scientific_journal-522 374 31 - - PUNCT american_scientific_journal-522 374 32 reinforced reinforce VERB american_scientific_journal-522 374 33 composite composite ADJ american_scientific_journal-522 374 34 laminates laminate NOUN american_scientific_journal-522 374 35 based base VERB american_scientific_journal-522 374 36 on on ADP american_scientific_journal-522 374 37 first first ADJ american_scientific_journal-522 374 38 - - PUNCT american_scientific_journal-522 374 39 order order NOUN american_scientific_journal-522 374 40 shear shear NOUN american_scientific_journal-522 374 41 deformation deformation NOUN american_scientific_journal-522 374 42 plate plate NOUN american_scientific_journal-522 374 43 theory theory NOUN american_scientific_journal-522 374 44 , , PUNCT american_scientific_journal-522 375 1 comput comput NOUN american_scientific_journal-522 375 2 . . PUNCT american_scientific_journal-522 375 3 struct struct NOUN american_scientific_journal-522 375 4 , , PUNCT american_scientific_journal-522 375 5 63 63 NUM american_scientific_journal-522 375 6 ( ( PUNCT american_scientific_journal-522 375 7 3 3 NUM american_scientific_journal-522 375 8 ) ) PUNCT american_scientific_journal-522 375 9 ( ( PUNCT american_scientific_journal-522 375 10 1997 1997 NUM american_scientific_journal-522 375 11 ) ) PUNCT american_scientific_journal-522 375 12 525 525 NUM american_scientific_journal-522 375 13 - - SYM american_scientific_journal-522 375 14 538 538 NUM american_scientific_journal-522 375 15 . . PUNCT american_scientific_journal-522 376 1 available available ADJ american_scientific_journal-522 376 2 : : PUNCT american_scientific_journal-522 376 3 http://www.sciencedirect.com http://www.sciencedirect.com NUM american_scientific_journal-522 376 4 / / SYM american_scientific_journal-522 376 5 science science NOUN american_scientific_journal-522 376 6 / / SYM american_scientific_journal-522 376 7 article article NOUN american_scientific_journal-522 376 8 / / SYM american_scientific_journal-522 376 9 pii pii PROPN american_scientific_journal-522 376 10 / / SYM american_scientific_journal-522 376 11 s0045794996003574 s0045794996003574 PROPN american_scientific_journal-522 377 1 [ [ X american_scientific_journal-522 377 2 23 23 NUM american_scientific_journal-522 377 3 ] ] X american_scientific_journal-522 377 4 k.m k.m PROPN american_scientific_journal-522 377 5 . . PROPN american_scientific_journal-522 377 6 liew liew PROPN american_scientific_journal-522 377 7 , , PUNCT american_scientific_journal-522 377 8 k.c k.c PROPN american_scientific_journal-522 377 9 . . PROPN american_scientific_journal-522 377 10 hung hung PROPN american_scientific_journal-522 377 11 , , PUNCT american_scientific_journal-522 377 12 m.k m.k PROPN american_scientific_journal-522 377 13 . . PUNCT american_scientific_journal-522 377 14 lim lim PROPN american_scientific_journal-522 377 15 , , PUNCT american_scientific_journal-522 377 16 a a DET american_scientific_journal-522 377 17 continuum continuum ADJ american_scientific_journal-522 377 18 three three NUM american_scientific_journal-522 377 19 - - PUNCT american_scientific_journal-522 377 20 dimensional dimensional ADJ american_scientific_journal-522 377 21 vibration vibration NOUN american_scientific_journal-522 377 22 analysis analysis NOUN american_scientific_journal-522 377 23 of of ADP american_scientific_journal-522 377 24 thick thick ADJ american_scientific_journal-522 377 25 rectangular rectangular ADJ american_scientific_journal-522 377 26 plates plate NOUN american_scientific_journal-522 377 27 , , PUNCT american_scientific_journal-522 377 28 int int NOUN american_scientific_journal-522 377 29 . . PUNCT american_scientific_journal-522 378 1 j. j. PROPN american_scientific_journal-522 378 2 solids solids PROPN american_scientific_journal-522 378 3 struct struct NOUN american_scientific_journal-522 378 4 . . PUNCT american_scientific_journal-522 379 1 30 30 NUM american_scientific_journal-522 379 2 ( ( PUNCT american_scientific_journal-522 379 3 24 24 NUM american_scientific_journal-522 379 4 ) ) PUNCT american_scientific_journal-522 379 5 ( ( PUNCT american_scientific_journal-522 379 6 1993 1993 NUM american_scientific_journal-522 379 7 ) ) PUNCT american_scientific_journal-522 379 8 3357 3357 NUM american_scientific_journal-522 379 9 - - SYM american_scientific_journal-522 379 10 3379 3379 NUM american_scientific_journal-522 379 11 . . PUNCT american_scientific_journal-522 380 1 available available ADJ american_scientific_journal-522 380 2 : : PUNCT american_scientific_journal-522 380 3 http://www.sciencedirect.com http://www.sciencedirect.com NUM american_scientific_journal-522 380 4 / / SYM american_scientific_journal-522 380 5 science science NOUN american_scientific_journal-522 380 6 / / SYM american_scientific_journal-522 380 7 article article NOUN american_scientific_journal-522 380 8 / / SYM american_scientific_journal-522 380 9 pii/002076839390089p pii/002076839390089p PROPN american_scientific_journal-522 380 10 [ [ X american_scientific_journal-522 380 11 24 24 NUM american_scientific_journal-522 380 12 ] ] PUNCT american_scientific_journal-522 380 13 a. a. NOUN american_scientific_journal-522 380 14 houmat houmat PROPN american_scientific_journal-522 380 15 , , PUNCT american_scientific_journal-522 380 16 an an DET american_scientific_journal-522 380 17 alternative alternative ADJ american_scientific_journal-522 380 18 hierarchical hierarchical ADJ american_scientific_journal-522 380 19 finite finite ADJ american_scientific_journal-522 380 20 element element NOUN american_scientific_journal-522 380 21 formulation formulation NOUN american_scientific_journal-522 380 22 applied apply VERB american_scientific_journal-522 380 23 to to ADP american_scientific_journal-522 380 24 plate plate NOUN american_scientific_journal-522 380 25 vibrations vibration NOUN american_scientific_journal-522 380 26 , , PUNCT american_scientific_journal-522 380 27 j. j. PROPN american_scientific_journal-522 380 28 sound sound PROPN american_scientific_journal-522 380 29 vib vib PROPN american_scientific_journal-522 380 30 . . PUNCT american_scientific_journal-522 381 1 ( ( PUNCT american_scientific_journal-522 381 2 1997 1997 NUM american_scientific_journal-522 381 3 ) ) PUNCT american_scientific_journal-522 381 4 206 206 NUM american_scientific_journal-522 381 5 ( ( PUNCT american_scientific_journal-522 381 6 2 2 NUM american_scientific_journal-522 381 7 ) ) PUNCT american_scientific_journal-522 381 8 201 201 NUM american_scientific_journal-522 381 9 - - SYM american_scientific_journal-522 381 10 215 215 NUM american_scientific_journal-522 381 11 . . PUNCT american_scientific_journal-522 382 1 available available ADJ american_scientific_journal-522 382 2 : : PUNCT american_scientific_journal-522 383 1 http://www.sciencedirect.com/science/article/pii/s0022460x97910762 http://www.sciencedirect.com/science/article/pii/s0022460x97910762 PROPN american_scientific_journal-522 384 1 [ [ X american_scientific_journal-522 384 2 25 25 NUM american_scientific_journal-522 384 3 ] ] PUNCT american_scientific_journal-522 384 4 s. s. PROPN american_scientific_journal-522 384 5 hosseini hosseini PROPN american_scientific_journal-522 384 6 - - PUNCT american_scientific_journal-522 384 7 hashemi hashemi PROPN american_scientific_journal-522 384 8 , , PUNCT american_scientific_journal-522 384 9 m. m. NOUN american_scientific_journal-522 384 10 fadaee fadaee PROPN american_scientific_journal-522 384 11 , , PUNCT american_scientific_journal-522 384 12 h. h. PROPN american_scientific_journal-522 384 13 roknidamavanditaher roknidamavanditaher PROPN american_scientific_journal-522 384 14 , , PUNCT american_scientific_journal-522 384 15 exact exact ADJ american_scientific_journal-522 384 16 solutions solution NOUN american_scientific_journal-522 384 17 for for ADP american_scientific_journal-522 384 18 free free ADJ american_scientific_journal-522 384 19 flexural flexural ADJ american_scientific_journal-522 384 20 vibration vibration NOUN american_scientific_journal-522 384 21 of of ADP american_scientific_journal-522 384 22 lévy lévy ADJ american_scientific_journal-522 384 23 - - PUNCT american_scientific_journal-522 384 24 type type NOUN american_scientific_journal-522 384 25 rectangular rectangular ADJ american_scientific_journal-522 384 26 thick thick ADJ american_scientific_journal-522 384 27 plates plate NOUN american_scientific_journal-522 384 28 via via ADP american_scientific_journal-522 384 29 third third ADJ american_scientific_journal-522 384 30 - - PUNCT american_scientific_journal-522 384 31 order order NOUN american_scientific_journal-522 384 32 shear shear NOUN american_scientific_journal-522 384 33 deformation deformation NOUN american_scientific_journal-522 384 34 plate plate NOUN american_scientific_journal-522 384 35 theory theory NOUN american_scientific_journal-522 384 36 , , PUNCT american_scientific_journal-522 384 37 appl appl PROPN american_scientific_journal-522 384 38 . . PROPN american_scientific_journal-522 384 39 math math NOUN american_scientific_journal-522 384 40 . . PUNCT american_scientific_journal-522 385 1 model.35 model.35 INTJ american_scientific_journal-522 385 2 ( ( PUNCT american_scientific_journal-522 385 3 2011 2011 NUM american_scientific_journal-522 385 4 ) ) PUNCT american_scientific_journal-522 386 1 708–727 708–727 NUM american_scientific_journal-522 386 2 . . PUNCT american_scientific_journal-522 387 1 available available ADJ american_scientific_journal-522 387 2 : : PUNCT american_scientific_journal-522 388 1 http://www.sciencedirect.com/science/article/pii/s0307904x10002775 http://www.sciencedirect.com/science/article/pii/s0307904x10002775 NOUN american_scientific_journal-522 388 2 [ [ X american_scientific_journal-522 388 3 26 26 NUM american_scientific_journal-522 388 4 ] ] PUNCT american_scientific_journal-522 388 5 s. s. PROPN american_scientific_journal-522 388 6 hosseini hosseini PROPN american_scientific_journal-522 388 7 - - PUNCT american_scientific_journal-522 388 8 hashemi hashemi PROPN american_scientific_journal-522 388 9 , , PUNCT american_scientific_journal-522 388 10 m. m. NOUN american_scientific_journal-522 388 11 arsanjani arsanjani PROPN american_scientific_journal-522 388 12 , , PUNCT american_scientific_journal-522 388 13 exact exact ADJ american_scientific_journal-522 388 14 characteristic characteristic ADJ american_scientific_journal-522 388 15 equations equation NOUN american_scientific_journal-522 388 16 for for ADP american_scientific_journal-522 388 17 some some PRON american_scientific_journal-522 388 18 of of ADP american_scientific_journal-522 388 19 classical classical ADJ american_scientific_journal-522 388 20 boundary boundary ADJ american_scientific_journal-522 388 21 conditions condition NOUN american_scientific_journal-522 388 22 of of ADP american_scientific_journal-522 388 23 vibrating vibrate VERB american_scientific_journal-522 388 24 moderately moderately ADV american_scientific_journal-522 388 25 thick thick ADJ american_scientific_journal-522 388 26 rectangular rectangular ADJ american_scientific_journal-522 388 27 plates plate NOUN american_scientific_journal-522 388 28 , , PUNCT american_scientific_journal-522 388 29 int int NOUN american_scientific_journal-522 388 30 . . PUNCT american_scientific_journal-522 389 1 j. j. PROPN american_scientific_journal-522 389 2 solids solids PROPN american_scientific_journal-522 389 3 . . PUNCT american_scientific_journal-522 389 4 struct struct NOUN american_scientific_journal-522 389 5 . . PUNCT american_scientific_journal-522 390 1 47 47 NUM american_scientific_journal-522 390 2 ( ( PUNCT american_scientific_journal-522 390 3 2005 2005 NUM american_scientific_journal-522 390 4 ) ) PUNCT american_scientific_journal-522 390 5 819–853 819–853 NUM american_scientific_journal-522 390 6 . . PUNCT american_scientific_journal-522 391 1 available available ADJ american_scientific_journal-522 391 2 : : PUNCT american_scientific_journal-522 391 3 http://www.sciencedirect.com http://www.sciencedirect.com NUM american_scientific_journal-522 391 4 / / SYM american_scientific_journal-522 391 5 science science NOUN american_scientific_journal-522 391 6 / / SYM american_scientific_journal-522 391 7 article article NOUN american_scientific_journal-522 391 8 / / SYM american_scientific_journal-522 391 9 pii pii PROPN american_scientific_journal-522 391 10 / / SYM american_scientific_journal-522 391 11 s0020768304003671 s0020768304003671 PROPN american_scientific_journal-522 392 1 [ [ X american_scientific_journal-522 392 2 27 27 NUM american_scientific_journal-522 392 3 ] ] PUNCT american_scientific_journal-522 392 4 m. m. NOUN american_scientific_journal-522 392 5 malik malik PROPN american_scientific_journal-522 392 6 , , PUNCT american_scientific_journal-522 392 7 c.w c.w PROPN american_scientific_journal-522 392 8 . . PROPN american_scientific_journal-522 392 9 bert bert PROPN american_scientific_journal-522 392 10 , , PUNCT american_scientific_journal-522 392 11 three three NUM american_scientific_journal-522 392 12 - - PUNCT american_scientific_journal-522 392 13 dimensional dimensional ADJ american_scientific_journal-522 392 14 elasticity elasticity NOUN american_scientific_journal-522 392 15 solutions solution NOUN american_scientific_journal-522 392 16 for for ADP american_scientific_journal-522 392 17 free free ADJ american_scientific_journal-522 392 18 vibrations vibration NOUN american_scientific_journal-522 392 19 of of ADP american_scientific_journal-522 392 20 rectangular rectangular ADJ american_scientific_journal-522 392 21 plates plate NOUN american_scientific_journal-522 392 22 by by ADP american_scientific_journal-522 392 23 the the DET american_scientific_journal-522 392 24 differential differential ADJ american_scientific_journal-522 392 25 quadrature quadrature NOUN american_scientific_journal-522 392 26 method method NOUN american_scientific_journal-522 392 27 , , PUNCT american_scientific_journal-522 392 28 int int NOUN american_scientific_journal-522 392 29 . . PUNCT american_scientific_journal-522 393 1 j. j. PROPN american_scientific_journal-522 393 2 solids solids PROPN american_scientific_journal-522 393 3 . . PUNCT american_scientific_journal-522 394 1 struct struct NOUN american_scientific_journal-522 394 2 . . PUNCT american_scientific_journal-522 395 1 35 35 NUM american_scientific_journal-522 395 2 ( ( PUNCT american_scientific_journal-522 395 3 1998 1998 NUM american_scientific_journal-522 395 4 ) ) PUNCT american_scientific_journal-522 396 1 299–318 299–318 NUM american_scientific_journal-522 396 2 . . PUNCT american_scientific_journal-522 397 1 available available ADJ american_scientific_journal-522 397 2 : : PUNCT american_scientific_journal-522 397 3 http://www.sciencedirect.com/science/article/pii/s0020768397000735 http://www.sciencedirect.com/science/article/pii/s0020768397000735 NUM american_scientific_journal-522 397 4 19 19 NUM american_scientific_journal-522 397 5 http://www.sciencedirect.com/science/article/pii/s0020768302004602 http://www.sciencedirect.com/science/article/pii/s0020768302004602 PROPN american_scientific_journal-522 397 6 http://www.sciencedirect.com/science/article/pii/s0022460x96907452 http://www.sciencedirect.com/science/article/pii/s0022460x96907452 VERB american_scientific_journal-522 397 7 http://www.sciencedirect.com/science/article/pii/s0045794996003574 http://www.sciencedirect.com/science/article/pii/s0045794996003574 NOUN american_scientific_journal-522 397 8 http://www.sciencedirect.com/science/article/pii/002076839390089p http://www.sciencedirect.com/science/article/pii/002076839390089p NOUN american_scientific_journal-522 397 9 http://www.sciencedirect.com/science/article/pii/s0022460x97910762 http://www.sciencedirect.com/science/article/pii/s0022460x97910762 PROPN american_scientific_journal-522 397 10 http://www.sciencedirect.com/science/article/pii/s0307904x10002775 http://www.sciencedirect.com/science/article/pii/s0307904x10002775 PROPN american_scientific_journal-522 397 11 http://www.sciencedirect.com/science/article/pii/s0020768304003671 http://www.sciencedirect.com/science/article/pii/s0020768304003671 PROPN american_scientific_journal-522 397 12 http://www.sciencedirect.com/science/article/pii/s0020768397000735 http://www.sciencedirect.com/science/article/pii/s0020768397000735 PROPN