Free Vibration Investigations of Rotating FG Beams Resting on Elastic Foundation with Initial Geometrical Imperfection in Thermal Environments

Table 4

The dependence of nondimensional frequencies of clamped-clamped FGM beams in the thermal environment on the volume fraction index n, L/h = 20.

		n
		0		0.2		1		5
		Exact [48]	This work	Exact [48]	This work	Exact [48]	This work	Exact [23]	This work
0	1	22.3447	22.0003	19.6819	19.3997	16.0094	15.8072	13.7110	13.5306
	2	61.3790	59.6498	54.0567	52.6094	43.9727	42.8791	37.6706	36.6636
20	1	22.1532	21.8079	19.4789	19.1986	15.7954	15.5992	13.4954	13.3222
	2	61.1205	59.3870	53.7827	52.3393	43.6841	42.6058	37.3801	36.3926
40	1	21.9585	21.6122	19.2695	18.9915	15.5703	15.3809	13.2663	13.1010
	2	60.8590	59.1212	53.4998	52.0612	43.3779	42.3176	37.0678	36.1027