id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ajst-21812	Pei, Zhenxing	Free vibration Analysis of Beams with Functional Gradient Materials with Cracks	2024	5	.pdf	application/pdf	3484	132	54	=0.2, a length- to-width ratio of 8, and a relative crack depth of 0.2, the impact of different crack positions and different boundary conditions on the first three natural frequency ratios of the system can be observed. The first three natural frequency ratios of functionally graded material (FGM) beams with edge cracks at different positions As seen from Figure 3, when the elastic modulus ratio of the functionally graded beam with cracks is 5 and the relative crack depth is 0.2, the impact of different length-to-thickness ratios on the third mode natural frequency ratio under different boundary conditions and crack positions can be observed.	cache/ajst-21812.pdf	txt/ajst-21812.txt