Free Vibration of Functionally Graded Sandwich Shallow Shells on Winkler and Pasternak Foundations with General Boundary Restraints

Table 5

The first four frequencies f (Hz) for Type (1-1-1) FGSSS with various boundary restraints and radius-length ratios (p=5, a/b=1, and h/a=0.1).

/	/a	Mode	Boundary restraints
			SSSS	CCCC	CFCF	SCSC	CSDCSD	CE^1E^1E^1	SE^2SE^2	E^3E^3E^3E^3
Plate		1	66.545	79.857	72.148	58.102	75.279	39.310	74.196	21.214
		2	93.851	105.51	96.792	73.858	99.082	51.903	98.154	35.150
		3	138.47	140.48	123.95	97.593	123.27	71.192	102.21	45.211
		4	159.68	173.65	143.54	120.97	135.36	98.115	125.34	59.633
+1	5	1	68.563	80.374	75.156	60.154	78.364	40.151	77.458	23.157
		2	97.471	106.35	85.215	79.585	95.544	53.31	90.17	41.405
		3	135.54	133.37	98.410	89.361	126.55	79.87	107.01	58.649
		4	152.12	159.51	112.12	103.52	135.10	108.81	130.97	61.056
	2	1	76.167	87.355	78.124	72.195	83.954	43.486	80.853	25.699
		2	90.544	106.05	95.439	80.398	97.610	55.439	98.398	46.378
		3	99.202	117.08	106.25	97.403	116.21	86.925	107.403	71.642
		4	119.14	139.52	115.58	115.46	130.47	100.54	125.468	76.557
0	5	1	64.479	78.545	67.191	58.235	74.407	36.419	70.435	21.244
		2	89.655	96.405	85.366	78.981	89.541	55.661	98.918	45.112
		3	105.24	120.94	109.01	99.210	111.24	79.015	119.21	55.880
		4	126.50	135.79	122.47	119.58	125.19	95.471	139.58	73.385
	2	1	70.571	82.998	73.164	64.771	79.547	39.486	75.761	23.446
		2	86.454	89.699	89.101	82.913	85.254	58.212	93.157	47.254
		3	102.15	117.20	117.80	100.24	100.30	82.172	109.97	60.351
		4	105.85	126.79	128.58	115.38	123.21	90.309	110.58	76.245
-1	5	1	56.152	69.385	59.526	51.402	65.265	32.863	61.626	20.137
		2	79.544	89.510	69.624	77.273	84.541	59.784	76.587	37.560
		3	100.58	111.34	85.060	94.783	100.24	80.479	92.129	54.783
		4	126.24	130.75	115.11	109.23	135.97	92.442	127.66	57.311
	2	1	65.931	79.312	68.214	60.109	75.542	38.651	70.721	22.192
		2	79.654	95.702	85.824	82.562	89.032	60.082	95.104	45.595
		3	98.312	123.54	103.96	95.351	112.33	79.364	107.31	53.102
		4	105.29	126.50	120.54	100.33	135.61	87.115	120.25	69.548