Free Vibration Analysis for Cracked FGM Beams by Means of a Continuous Beam Model

Table 2

The first three nondimensional natural frequencies of intact FGM beams.

Clamped-free
0.2	Yang and Chen [27]	0.83	5.18	14.49
	Present	0.8258	5.1752	14.4910
	3D FEM	0.8269	5.1270	14.1144
1.0	Yang and Chen [27]	0.88	5.51	15.42
	Present	0.8790	5.5086	15.4243
	3D FEM	0.8799	5.4501	15.0078
5.0	Yang and Chen [27]	0.83	5.18	14.49
	Present	0.8258	5.1752	14.4910
	3D FEM	0.8268	5.1270	14.1144
Clamped-clamped
0.2	Yang and Chen [27]	2.51	9.27	21.07
	Present	2.3181	9.2724	20.8628
	3D FEM	2.3085	9.1219	20.0568
1.0	Yang and Chen [27]	2.47	9.87	22.21
	Present	2.4674	9.8696	22.2066
	3D FEM	2.4579	9.7116	21.4361
5.0	Yang and Chen [27]	2.51	9.27	21.07
	Present	2.3181	9.2724	20.8628
	3D FEM	2.3085	9.1219	20.0568
Hinged-hinged
0.2	Yang and Chen [27]	5.25	14.49	28.40
	Present	5.2548	14.4852	28.3968
	3D FEM	5.2050	14.0623	26.8927
1.0	Yang and Chen [27]	5.59	15.42	30.23
	Present	5.5933	15.4182	30.2258
	3D FEM	5.5319	14.9257	28.4977
5.0	Yang and Chen [27]	5.25	14.49	28.40
	Present	5.2548	14.4852	28.3968
	3D FEM	5.2050	14.0623	26.8927