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

Table 6

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

		Method
10	2	Present	6.1667	5.5612	5.2958	5.0890	4.9112	4.7782	4.4201
		[57]	6.1552	5.5522	5.2876	5.0812	4.9032	4.7700	4.4119
	3	Present	5.9510	5.3592	5.1052	4.9150	4.7563	4.6288	4.2655
		[57]	5.9456	5.3548	5.1012	4.9111	4.7524	4.6249	4.2616
	5	Present	5.8357	5.2521	5.0046	4.8235	4.6749	4.5501	4.1829
		[57]	5.8337	5.2504	5.0031	4.8220	4.6734	4.5486	4.1814
	10	Present	5.7860	5.2069	4.9625	4.7856	4.6411	4.5170	4.1472
		[57]	5.7855	5.2065	4.9622	4.7852	4.6407	4.5166	4.1469
	20	Present	5.7735	5.1960	4.9527	4.7768	4.6333	4.5091	4.1382
		[57]	5.7734	5.1959	4.9526	4.7767	4.6332	4.5090	4.1382
	100	Present	5.7695	5.1931	4.9503	4.7748	4.6314	4.5070	4.1354
		[57]	5.7695	5.1931	4.9503	4.7748	4.6314	4.5070	4.1354
50	2	Present	13.6959	12.5601	11.9594	11.3453	10.6948	10.3516	9.8168
		[57]	13.6904	12.5575	11.9578	11.3440	10.6928	10.3488	9.8128
	3	Present	10.1888	9.3097	8.8667	8.4394	8.0024	7.7542	7.3030
		[57]	10.1854	9.3077	8.8651	8.4379	8.0006	7.7522	7.3006
	5	Present	7.7632	7.0509	6.7181	6.4289	6.1535	5.9732	5.5644
		[57]	7.7616	7.0497	6.7171	6.4280	6.1525	5.9721	5.5633
	10	Present	6.4625	5.8318	5.5589	5.3505	5.1714	5.0289	4.6321
		[57]	6.4620	5.8314	5.5586	5.3502	5.1711	5.0285	4.6317
	20	Present	6.0930	5.4840	5.2283	5.0443	4.8945	4.7630	4.3673
		[57]	6.0929	5.4839	5.2282	5.0442	4.8944	4.7629	4.3672
	100	Present	5.9699	5.3680	5.1181	4.9424	4.8026	4.6747	4.2790
		[57]	5.9699	5.3680	5.1181	4.9424	4.8026	4.6747	4.2790