A Refined Higher-Order Hybrid Stress Quadrilateral Element for Free Vibration and Buckling Analyses of Reissner-Mindlin Plates

Table 9

Frequency parameters for square Mindlin plates with different boundary conditions.

Boundary		Element	Mode sequence number
			1	2	3	4	5	6
SSFF	0.001	QH8-RCV	0.3407	1.7530	1.9541	3.8675	5.1729	5.4231
		QH8-LV	0.3405	1.7485	1.9504	3.8550	5.1471	5.4000
		Ref. sol	0.341	1.754	1.955	3.872	5.171	5.419
	0.1	QH8-RCV	0.3329	1.6780	1.8751	3.5579	4.7179	4.9445
		QH8-LV	0.3335	1.6944	1.8922	3.6122	4.8227	5.0496
		Ref. sol	0.333	1.677	1.874	3.557	4.718	4.945
SFSF	0.001	QH8-RCV	0.9759	1.6329	3.7170	3.9486	4.7357	7.1656
		QH8-LV	0.9755	1.6303	3.7009	3.9431	4.7240	7.1313
		Ref. sol	0.976	1.635	3.721	3.946	4.735	7.167
	0.1	QH8-RCV	0.9567	1.5594	3.4297	3.6829	4.3331	6.2859
		QH8-LV	0.9601	1.5703	3.4900	3.7305	4.4011	6.4372
		Ref. sol	0.956	1.559	3.429	3.681	4.332	6.290
SCSC	0.001	QH8-RCV	2.9350	5.5542	7.0348	9.6060	10.3849	13.1192
		QH8-LV	2.9333	5.5466	7.0242	9.5833	10.3566	13.0799
		Ref. sol	2.933	5.547	7.024	9.583	10.356	13.080
	0.1	QH8-RCV	2.7019	4.9725	5.9898	7.9621	8.7685	10.2141
		QH8-LV	2.7212	5.0501	6.0804	8.1367	8.9997	10.4651
		Ref. sol	2.700	4.971	5.990	7.972	8.787	10.249
CFFF	0.001	QH8-RCV	0.3516	0.8603	2.1563	2.7540	3.1315	5.4804
		QH8-LV	0.3514	0.8590	2.1499	2.7427	3.1211	5.4505
		Ref. sol	0.352	0.862	2.157	2.756	3.136	5.490
	0.1	QH8-RCV	0.3476	0.8167	2.0353	2.5832	2.8610	4.8108
		QH8-LV	0.3481	0.8205	2.0567	2.6220	2.8963	4.9106
		Ref. sol	0.348	0.816	2.034	2.582	2.860	4.811
CCFF	0.001	QH8-RCV	0.7003	2.4197	2.6929	4.8226	6.3563	6.6444
		QH8-LV	0.6997	2.4117	2.6870	4.8039	6.3216	6.6129
		Ref. sol	0.701	2.422	2.694	4.828	6.353	6.640
	0.1	QH8-RCV	0.6761	2.2434	2.5046	4.2523	5.5551	5.8093
		QH8-LV	0.6777	2.2687	2.5294	4.3213	5.6786	5.9314
		Ref. sol	0.676	2.242	2.503	4.251	5.557	5.812
CFCF	0.001	QH8-RCV	2.2459	2.6732	4.4127	6.2028	6.8074	8.0892
		QH8-LV	2.2448	2.6689	4.3935	6.1928	6.7890	8.0240
		Ref. sol	2.246	2.675	4.417	6.198	6.806	8.087
	0.1	QH8-RCV	2.0899	2.4334	3.9032	5.3315	5.7707	6.9214
		QH8-LV	2.0979	2.4508	3.9716	5.3982	5.8585	7.1420
		Ref. sol	2.088	2.431	3.901	5.331	5.771	6.929