id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
alkej-778	Baher , Karrar ; A. Atiyah , Qasim ; Abdulsahib, Imad A. 	تحليل الاهتزازات في الأعمدة الدوارة باستخدام طريقتين رايلي ودونكرلي	2022	14	.pdf	application/pdf	5179	274	59	Simply Supported Beam with finite nodes The uniform beam for the number of nodes is shown in figure 1, and the masses for the nodes are computed using the following equations [23]: ��� � ��/2 � � �� ��2 … 1� �� � � � �2 � � ��� ���2 … 2� where � � 1, 2, 3, . . . Deflections associated with :� � 1 and :# �:< � 0 are represented in the preceding matrix's first column.	cache/alkej-778.pdf	txt/alkej-778.txt