Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Table 8

Frequency parameters for Al/ZrO₂ spherical shell with SSSS boundary constraints, varying geometric parameters, and gradient power-law exponent ().

		Method
10	2	Present	7.4580	6.7593	6.4304	6.1422	5.8730	5.7072	5.3457
		[57]	7.4599	6.7612	6.4322	6.1440	5.8747	5.7088	5.4370
	3	Present	6.5826	5.9454	5.6595	5.4275	5.2222	5.0792	4.7182
		[57]	6.5834	5.9462	5.6603	5.4283	5.2230	5.0798	4.7186
	5	Present	6.0765	5.4745	5.2142	5.0165	4.8500	4.7197	4.3554
		[57]	6.0767	5.4748	5.2145	5.0168	4.8503	4.7200	4.3556
	10	Present	5.8478	5.2629	5.0149	4.8335	4.6846	4.5595	4.1915
		[57]	5.8479	5.2630	5.0150	4.8336	4.6847	4.5596	4.1915
	20	Present	5.7891	5.2096	4.9651	4.7881	4.6435	4.5193	4.1494
		[57]	5.7891	5.2096	4.9651	4.7881	4.6336	4.5194	4.1494
	100	Present	5.7701	5.1935	4.9505	4.7750	4.6316	4.5073	4.1358
		[57]	5.7701	5.1935	4.9505	4.7750	4.6316	4.5073	4.1358
50	2	Present	25.3976	23.3588	22.2354	21.0343	19.7303	19.0801	18.2042
		[57]	25.3980	23.3591	22.2357	21.0345	19.7305	19.0803	18.2044
	3	Present	17.5981	16.1645	15.3894	14.5770	13.7045	13.2582	12.6137
		[57]	17.5982	16.1646	15.3895	14.5771	13.7046	13.2583	12.6138
	5	Present	11.6130	10.6300	10.1229	9.6194	9.0953	8.8085	8.3238
		[57]	11.6130	10.6300	10.1230	9.6194	9.0953	8.8086	8.3238
	10	Present	7.7757	7.0622	6.7288	6.4393	6.1635	5.9830	5.5734
		[57]	7.7758	7.0621	6.7288	6.4393	6.1635	5.9830	5.5734
	20	Present	6.4655	5.8346	5.5615	5.3531	5.1738	5.0313	4.6342
		[57]	6.4655	5.8345	5.5615	5.3531	5.1739	5.0313	4.6342
	100	Present	5.9855	5.3827	5.1321	4.9553	4.8143	4.6859	4.2902
		[57]	5.9855	5.3827	5.1321	4.9553	4.8143	4.6859	4.2902