Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher-Order Hierarchical Beam Element

Table 4

Dimensionless frequency of FGM beam with different aspect ratios and temperature rises.

	(K)
10	50	4.4184	3.9576	3.5941	3.1895	2.9432
	100	4.3496	3.8889	3.5250	3.1185	2.8688
	150	4.2803	3.8193	3.4543	3.0447	2.7902
15	50	4.3864	3.9204	3.5524	3.1417	2.8891
	100	4.2408	3.7730	3.4021	2.9848	2.7230
	150	4.0904	3.6193	3.2435	2.8164	2.5413
25	50	4.1663	3.6932	3.3171	2.8928	2.6232
	100	3.7439	3.2564	2.8617	2.4014	2.0858
	150	3.2663	2.7477	2.3123	1.7661	1.3263