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

Table 13

The lowest six parameterized natural frequencies of triangular plates with .

Skew angle	Method	Mode sequence number
		1	2	3	4	5	6
0°	DSG3	0.5872	1.9529	2.4678	4.1305	5.2243	6.2886
	MIN3	0.6042	2.1109	2.7737	4.6581	6.1311	7.3208
	ES-FEM+DSG3	0.5856	1.9376	2.4411	4.0678	5.1289	6.1359
	Rayleigh-Ritz	0.5820	1.9000	2.4080	3.9360	—	—
	ASN4	0.5820	1.9150	2.4280	3.9840	5.0180	5.9440
	NS+ES-FEM	0.5821	1.8710	2.3600	3.8330	4.8217	5.5683
	QH8-RCV	0.5821	1.8907	2.3931	3.8677	4.8701	5.6897
	QH8-LV	0.5826	1.9628	2.5320	4.1115	5.2710	6.4029
15°	DSG3	0.5478	1.8160	2.4429	3.8111	5.0253	6.0033
	MIN3	0.5656	1.9555	2.7772	4.2851	5.8857	6.9977
	ES-FEM+DSG3	0.5457	1.8018	2.4121	3.7529	4.9317	5.8327
	Rayleigh-Ritz	0.5440	1.7710	2.3860	3.6280	—	—
	ASN4	0.5450	1.7640	2.4200	3.6080	4.8200	5.4310
	NS+ES-FEM	0.5442	1.7466	2.3391	3.5289	4.6721	5.1901
	QH8-RCV	0.5441	1.7644	2.3687	3.5813	4.7024	5.3504
	QH8-LV	0.5427	1.8251	2.5244	3.8353	5.0144	6.1823
30°	DSG3	0.5365	1.8126	2.4954	3.7549	4.9796	5.9219
	MIN3	0.5582	1.9551	2.8595	4.2605	5.8273	6.9945
	ES-FEM+DSG3	0.5329	1.7963	2.4552	3.6902	4.8717	5.6942
	Rayleigh-Ritz	0.5330	1.7720	2.4190	3.5650	—	—
	ASN4	0.5320	1.7730	2.4370	3.5910	4.7650	5.3230
	NS+ES-FEM	0.5336	1.7485	2.3730	3.4615	4.5927	4.9630
	QH8-RCV	0.5331	1.7663	2.4045	3.5167	4.6384	5.1512
	QH8-LV	0.5342	1.8391	2.7165	3.9146	4.9778	6.4454
45°	DSG3	0.5448	1.9269	2.6246	3.9196	5.1474	5.9838
	MIN3	0.5724	2.1044	3.0165	4.5535	6.0525	7.2736
	ES-FEM+DSG3	0.5380	1.9002	2.5682	3.8239	4.9806	5.6000
	Rayleigh-Ritz	0.5400	1.8850	2.4890	3.6740	—	—
	ASN4	0.5410	1.8840	2.5180	3.7480	4.7400	5.2920
	NS+ES-FEM	0.5408	1.8634	2.4323	3.5593	4.4299	4.9328
	QH8-RCV	0.5391	1.8765	2.4729	3.6337	4.5699	5.0583
	QH8-LV	0.5389	1.9562	2.9904	4.2186	5.2159	6.9240
60°	DSG3	0.5691	2.1281	2.7093	4.3427	5.3437	6.5278
	MIN3	0.6017	2.3742	3.2377	5.1762	6.5578	8.1003
	ES-FEM+DSG3	0.5569	2.0692	2.5955	4.1109	4.7967	6.0192
	Rayleigh-Ritz	0.5590	2.0590	2.3960	3.5900	—	—
	ASN4	0.5590	2.0950	2.4830	3.9100	4.5170	5.7630
	NS+ES-FEM	0.5611	2.0446	2.3276	3.5969	4.2312	5.3615
	QH8-RCV	0.5574	2.0455	2.3807	3.6046	4.2131	5.2640
	QH8-LV	0.5573	2.1170	3.8244	4.6656	6.2099	7.7794