Natural frequencies of a functionally graded cracked beam using the differential quadrature method

Free Vibration Analysis of Multiple Cracked Functionally Graded Timoshenko Beams

“…Authors showed that the elastic foundation makes dynamic deflections of FGM beam more sensitive to the presence of cracks. Matbuly et al (2009) Banerjee, B. Panigrahi, G. Pohit 2015) was also used to calculate frequency paragraphs based on the location and size of cracks which is called frequency contours. These paragraphs were not only used to analysis changes of frequencies because of cracks but also employed to identify the crack in FGM beam by measuring natural frequencies.…”

Free vibration analysis of cracked functionally graded non-uniform beams

“…The use of FG materials eliminates interlaminar stress concentration and due to its unique properties provides strength and toughness of the structure [2]. A large number of studies related to vibration characteristics of intact and cracked FG uniform beams are available [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Furthermore the studies have been extended in mechanical analysis of small-sized structures [23][24][25][26][27][28][29][30][31].…”

Supercritical vibration of nonlinear coupled moving beams based on discrete Fourier transform

“…The analyses for vibration of finite axially moving beam models have been conducted via various solution techniques, such as the Galerkin method for the first three frequencies and modes [4], and the first two natural frequencies [5] under simple supported boundary conditions; the complex mode method for natural frequencies and modes in the cases of pinned-pinned ends [1,6] and clamped-clamped ends [7,8], and hybrid supports ends [9]; the perturbation technique for determining approximate natural frequencies in the subcritical speed ranges [10]; the artificial neural networks technique for the first two natural frequencies [11]; the differential quadrature method for determining natural frequencies and the mode shapes for cracked beam [12]. In all of the above literatures, the natural frequencies of axially moving beams were calculated from linear governing equation of transverse vibration.…”