Free vibration analysis of edge cracked symmetric functionally graded sandwich beams

Free vibration analysis of cracked functionally graded non-uniform beams

“…Young's modulus and the density of each layer of the beam for the upper half of the beam are given by the exponential and power law equations [10]:…”

“…To verify the modeling of the crack, a taper ratio b 2 /b 1 =1 and a geometric index β=0 is assumed, which will result in the non-uniform cracked FG beam, becoming a cracked uniform FG beam. Numerical results are then compared with existing results in the literature [10] and are also cross checked with ANSYS software. The results are presented in table 2 proving that the model for the crack is also correct.…”

“…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].…”

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

“…The eigenvalue problem of free vibration of an intact beam given by Cunedioglu (2015) and cracked beam given by Akbaş (2013) is as follows…”

“…There are plenty of studies on free vibration behaviour and characteristics of uniform cross-section homogeneous and composite intact structures (Erdurcan and Cunedioğlu, 2020; Jiang et al, 2018; Kim and Shin, 2008; Mohanty et al, 2013; Zahedinejad, 2016; Zhang et al, 2020) and cracked structures (Cunedioglu, 2015; Ferezqi et al, 2010; Gayen and Chakraborty, 2016; Gayen et al, 2017a, 2017b, 2018; Han et al, 2020; Kisa and Brandon, 2000; Kisa et al, 1998; Liu et al, 2017; Papadopoulos, 2004; Papadopoulos and Dimarogonas, 1987; Shabani and Cunedioglu, 2019).…”