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

Table 4

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

BC			Method
SSSS	1	0.1	Present	5.7693	5.1932	4.9504	4.7750	4.6315	4.5071	4.1352
			[57]	5.7693	5.1932	4.9504	4.7750	4.6315	4.5071	4.1353
		0.02	Present	5.9647	5.3631	5.1135	4.9382	4.7988	4.6710	4.2753
			[57]	5.9647	5.3631	5.1135	4.9382	4.7988	4.6710	4.2753
	2	0.1	Present	14.6070	13.1429	12.5296	12.0910	11.7358	11.4215	10.4698
		0.02	Present	14.9198	13.4149	12.7906	12.3523	12.0040	11.6844	10.6940
CCCC	1	0.1	Present	9.8425	8.8831	8.4665	8.1474	7.8691	7.6511	7.0548
		0.02	Present	10.8410	9.7492	9.2954	8.9754	8.7198	8.4872	7.7705
	2	0.1	Present	27.5886	24.8797	23.7153	22.8390	22.0870	21.4798	19.7746
		0.02	Present	29.6598	26.6713	25.4299	24.5558	23.8588	23.2228	21.2592
CSCS	1	0.1	Present	8.0703	7.2786	6.9375	6.6802	6.4591	6.2816	5.7845
		0.02	Present	8.7301	7.8505	7.4851	7.2277	7.0225	6.8352	6.2574
	2	0.1	Present	16.0659	14.4609	13.7857	13.2987	12.9004	12.5534	11.5155
		0.02	Present	16.5502	14.8811	14.1886	13.7021	13.3152	12.9606	11.8626
E^1E^2E^1E^2	1	0.1	Present	1.6260	1.6528	1.6666	1.6807	1.6951	1.7018	1.7098
		0.02	Present	10.8410	9.7492	9.2954	8.9754	8.7198	8.4872	7.7705
	2	0.1	Present	5.6307	5.7230	5.7706	5.8192	5.8686	5.8913	5.9186
		0.02	Present	29.6598	26.6713	25.4299	24.5559	23.8588	23.2228	21.2592
E^2E^3E^2E^3	1	0.1	Present	1.6249	1.6514	1.6651	1.6790	1.6931	1.6995	1.7073
		0.02	Present	10.4114	9.4120	8.9917	8.6918	8.4499	8.2330	7.5680
	2	0.1	Present	5.6174	5.7067	5.7522	5.7982	5.8442	5.8650	5.8896
		0.02	Present	27.4294	25.0188	23.9872	23.2505	22.6568	22.1105	20.3974