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

Table 12

The lowest six parameterized natural frequencies of triangular plates with .

Skew angle	Method	Mode sequence number
		1	2	3	4	5	6
0°	DSG3	0.6288	2.4399	3.4796	5.9913	8.3737	11.2081
	MIN3	0.6272	2.4242	3.4344	5.9458	8.2460	11.0178
	ES-FEM+DSG3	0.6241	2.3970	3.3631	5.7976	7.9696	10.5356
	NS+ES-FEM	0.6253	2.3335	3.1888	5.4772	7.4350	9.2790
	Rayleigh-Ritz	0.6240	2.3770	3.3080	5.6890	7.7430	—
	ASN4	0.6240	2.3790	3.3170	5.7240	7.7940	10.2000
	QH8-RCV	0.6232	2.3709	3.2980	5.6766	7.7627	10.0574
	QH8-LV	0.6165	2.3143	3.1843	5.4810	7.5749	9.6271
15°	DSG3	0.5915	2.2360	3.6467	5.5686	7.8875	11.1572
	MIN3	0.5886	2.2229	3.5717	5.5286	7.7447	10.9544
	ES-FEM+DSG3	0.5843	2.1979	3.4937	5.3893	7.4745	10.4532
	NS+ES-FEM	0.5854	2.1449	3.2938	5.0391	7.0313	9.1652
	Rayleigh-Ritz	0.5840	2.1810	3.4090	5.2800	7.2640	—
	ASN4	0.5830	2.1810	3.4130	5.3030	7.2890	10.0950
	QH8-RCV	0.5829	2.1759	3.3995	5.2687	7.2983	9.9691
	QH8-LV	0.5750	2.1291	3.2332	5.0577	7.0972	9.4300
30°	DSG3	0.5928	2.2293	3.9729	5.8523	7.8772	11.9930
	MIN3	0.5866	2.2164	3.8656	5.8059	7.6697	11.5791
	ES-FEM+DSG3	0.5795	2.1881	3.7620	5.6464	7.3608	10.9609
	NS+ES-FEM	0.5801	2.1433	3.5402	5.2019	6.8932	9.6373
	Rayleigh-Ritz	0.5760	2.1740	3.6390	5.5110	7.1080	—
	ASN4	0.5750	2.1740	3.6380	5.5340	7.1390	10.4770
	QH8-RCV	0.5763	2.1685	3.6379	5.4957	7.1296	10.3946
	QH8-LV	0.5714	2.1368	3.5544	5.3345	6.9689	9.9234
45°	DSG3	0.6265	2.4298	4.5709	6.9888	8.7055	13.4984
	MIN3	0.6125	2.4038	4.4237	6.9194	8.3447	12.7848
	ES-FEM+DSG3	0.6001	2.3557	4.2652	6.6442	7.9210	11.8923
	NS+ES-FEM	0.6020	2.3189	4.0352	6.0299	7.3322	10.5988
	Rayleigh-Ritz	0.5900	2.3290	4.1370	6.3810	7.6020	—
	ASN4	0.5880	2.3240	4.1260	6.3810	7.6140	11.2240
	QH8-RCV	0.5925	2.3290	4.1374	6.4133	7.6019	11.2205
	QH8-LV	0.5858	2.3042	3.9784	6.1554	7.4240	10.8429
60°	DSG3	0.6969	2.9282	6.0785	9.3379	11.8340	17.8590
	MIN3	0.6631	2.8106	5.8343	8.9727	11.3197	16.3597
	ES-FEM+DSG3	0.6371	2.6804	5.4909	8.1353	10.6516	14.5225
	NS+ES-FEM	0.6546	2.6792	5.3330	7.3384	9.6825	12.9900
	Rayleigh-Ritz	0.6170	2.5760	5.3760	7.5240	10.2850	—
	ASN4	0.6130	2.5640	5.3530	7.4600	10.3060	12.9420
	QH8-RCV	0.6234	2.5978	5.3502	7.5829	10.2623	13.0926
	QH8-LV	0.6164	2.5712	5.1891	7.3141	9.8462	12.8085