A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

Table 4

Temperature and material graduation effect on first dimensionless natural frequency of S-S FG porous beam with different temperature changes and porosity parameter under uniform temperature rise .

FGM type
FGM-I	0	6.55957	6.30389	6.03310	5.43496	5.09981	4.73303	4.32582
	0.1	7.12576	6.88939	6.64113	6.10107	5.80417	5.48474	5.13790
	0.2	8.04528	7.82479	7.59524	7.10358	6.83815	6.55684	6.25690
FGM-II	0	6.55957	6.30389	6.03310	5.43496	5.09981	4.73303	4.32582
	0.1	6.88457	6.64111	6.38455	5.82315	5.51229	5.17575	4.80744
	0.2	7.28099	7.04845	6.80459	6.27567	5.98594	5.67521	5.39915
FGM-I	0	4.51585	4.27875	4.02257	3.43413	3.08651	2.68466	2.19832
	0.1	4.58213	4.36908	4.14065	3.62453	3.32690	2.99204	2.60510
	0.2	4.66783	4.47876	4.27759	3.83009	3.57746	3.29930	2.98806
FGM-II	0	4.51585	4.27875	4.02257	3.43413	3.08651	2.68466	2.19832
	0.1	4.60304	4.38047	4.14128	3.59813	3.28268	2.92503	2.50660
	0.2	4.70024	4.49154	4.26838	3.76693	3.47998	3.15974	2.79427
FGM-I	0	3.95829	3.72764	3.47629	2.88836	2.53136	2.10424	1.54940
	0.1	3.95091	3.74463	3.52152	3.00865	2.70569	2.35577	1.93306
	0.2	3.94056	3.75865	3.56334	3.12151	2.86664	2.58004	2.24928
FGM-II	0	3.95829	3.72764	3.47629	2.88836	2.53136	2.10424	1.54940
	0.1	4.00686	3.79112	3.55732	3.01746	2.69634	2.32229	1.86318
	0.2	4.05989	3.85843	3.64126	3.14561	2.85597	2.52554	2.13508
FGM-I	0	3.55529	3.33104	3.08492	2.49999	2.13545	1.68262	1.03051
	0.1	3.50825	3.30844	3.09073	2.58294	2.27626	1.91230	1.44817
	0.2	3.44947	3.27411	3.08445	2.64928	2.39337	2.09961	1.74880
FGM-II	0	3.55529	3.33104	3.08492	2.49999	2.13545	1.68262	1.03051
	0.1	3.58170	3.37261	3.14447	2.61003	2.28511	1.89595	1.38920
	0.2	3.61002	3.41549	3.20441	2.71632	2.42572	2.08703	1.67099
FGM-I	0	3.23323	3.01417	2.77209	2.18730	1.81215	1.32261	0.42425
	0.1	3.16336	2.96886	2.75553	2.25038	1.93806	1.55511	1.02507
	0.2	3.07867	2.90872	2.72367	2.29333	2.03530	1.73218	1.35400
FGM-II	0	3.23323	3.01417	2.77209	2.18730	1.81215	1.32261	0.42425
	0.1	3.24609	3.04242	2.81874	2.28715	1.95630	1.54641	0.96094
	0.2	3.25967	3.07080	2.86460	2.38167	2.08853	1.73843	1.28550