title: Vibration analysis of structural elements using differential quadrature method.
abstract: The method of differential quadrature is employed to analyze the free vibration of a cracked cantilever beam resting on elastic foundation. The beam is made of a functionally graded material and rests on a Winkler-Pasternak foundation. The crack action is simulated by a line spring model. Also, the differential quadrature method with a geometric mapping are applied to study the free vibration of irregular plates. The obtained results agreed with the previous studies in the literature. Further, a parametric study is introduced to investigate the effects of geometric and elastic characteristics of the problem on the natural frequencies.
authors: Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza, Egypt.
authors: Mohamed
authors: M
authors: Nassar
authors: Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, P.O. 44519, Zagazig, Egypt.
authors: Mohamed S
authors: MS
authors: Matbuly
authors: Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, P.O. 44519, Zagazig, Egypt.
authors: Ola
authors: O
authors: Ragb
keywords: Crack; Differential quadrature; Irregular boundaries; Vibration