id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
fumecheng-12619	Hashemi Kachapi, Sayyid H.; Hashemi Kachapi, Sayyideh Gh.	COMPARISON OF NONCLASSICAL CONTROLLERS ON ‎NONLINEAR VIBRATIONS ANALYSIS OF PIEZOELECTRIC ‎NANORESONATOR	2025	24	.pdf	application/pdf	7258	323	46	= (1 − �̅� �̅�2) 𝜕2�̅� 𝜕𝜏2 , (8) (1 − �̅� �̅�2) ( 𝛼1𝑤 𝜕𝑢 𝜕𝜉 + 𝛼2𝑤 𝜕𝑢 𝜕𝜉 𝜕2�̅� 𝜕𝜉2 + 𝛼3𝑤 𝜕𝑢 𝜕𝜉 𝜕2�̅� 𝜕𝜃2 + 𝛼4𝑤 𝜕2𝑢 𝜕𝜉2 𝜕�̅� 𝜕𝜉 + 𝛼5𝑤 𝜕2𝑢 𝜕𝜉𝜕𝜃 𝜕�̅� 𝜕𝜃 +𝛼6𝑤 𝜕2𝑢 𝜕𝜉𝜕𝜃 𝜕�̅� 𝜕𝜃 + 𝛼7𝑤 𝜕𝑢 𝜕𝜃 𝜕2�̅� 𝜕𝜉𝜕𝜃 + 𝛼8𝑤 𝜕2𝑢 𝜕𝜃2 𝜕�̅� 𝜕𝜉 + 𝛼9𝑤 𝜕�̅� 𝜕𝜉 𝜕2�̅� 𝜕𝜉𝜕𝜃 +𝛼10𝑤 𝜕2�̅� 𝜕𝜉2 𝜕�̅� 𝜕𝜃 + 𝛼11𝑤 𝜕2�̅� 𝜕𝜉𝜕𝜃 𝜕�̅� 𝜕𝜉 + 𝛼12𝑤 𝜕�̅� 𝜕𝜃 + 𝛼13𝑤 𝜕�̅� 𝜕𝜃 𝜕2�̅� 𝜕𝜉2 +𝛼14𝑤 𝜕�̅� 𝜕𝜃 𝜕2�̅� 𝜕𝜃2 + 𝛼15𝑤 𝜕2�̅� 𝜕𝜃2 𝜕�̅� 𝜕𝜃 + 𝛼16𝑤�̅� + 𝛼17𝑤�̅� 𝜕2�̅� 𝜕𝜉2 + 𝛼18𝑤�̅� 𝜕2�̅� 𝜕𝜃2 +𝛼19𝑤 𝜕2�̅� 𝜕𝜉2 + 𝛼20𝑤 𝜕�̅� 𝜕𝜉 𝜕2�̅� 𝜕𝜉𝜕𝜃 𝜕�̅� 𝜕𝜃 + 𝛼21𝑤 𝜕2�̅� 𝜕𝜉2 ( 𝜕�̅� 𝜕𝜉 ) 2 + 𝛼22𝑤 𝜕2�̅� 𝜕𝜉2 ( 𝜕�̅� 𝜕𝜃 ) 2 +𝛼23𝑤 𝜕4�̅� 𝜕𝜉4 + 𝛼24𝑤 ( 𝜕�̅� 𝜕𝜉 ) 2 + 𝛼25𝑤 𝜕4�̅� 𝜕𝜉2𝜕𝜃2 + 𝛼26𝑤 ( 𝜕�̅� 𝜕𝜉 ) 2 𝜕2�̅� 𝜕𝜃2 +𝛼27𝑤 𝜕2�̅� 𝜕𝜃2 + 𝛼28𝑤 𝜕4�̅� 𝜕𝜃4 + 𝛼29𝑤 𝜕2�̅� 𝜕𝜃2 ( 𝜕�̅� 𝜕𝜃 ) 2 + 𝛼30𝑤 ( 𝜕�̅� 𝜕𝜃 ) 2 +𝛼31𝑤 𝜕4�̅� 𝜕𝜉2𝜕𝜏2 + 𝛼32𝑤 𝜕4�̅� 𝜕𝜃2𝜕𝜏2 + 𝛼33𝑤 ) (9) = (1 − �̅� �̅�2) ( 𝜕2�̅� 𝜕𝜏2 + 𝐶�̅� 𝜕�̅� 𝜕𝜏 + 𝐾𝑤�̅� − 𝐾𝑝�̅� 2�̅� − �̅�𝑒(�̅�𝐷𝐶 + �̅�𝐴𝐶 𝑐𝑜𝑠(�̅�𝜏)) 2 √(𝑚1�̅� − �̅�)(2𝑚4�̅� + 𝑚1�̅� − �̅�) Also, Figs. 17-22 present frequency response and stability analysis PENR for different values of direct (�̅�𝑫𝑪) and alternating (�̅�𝑨𝑪) voltages based on different theories of CT, NLT, SGT, GMSIT, GMSIT combined with NLT and SGT for CC boundary conditions.	cache/fumecheng-12619.pdf	txt/fumecheng-12619.txt