Mathematical Problems in Engineering

Research Article

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

Table 6

Fundamental frequencies f (Hz) for Type (1-1-1) plate, circular cylindrical spherical and hyperbolic paraboloidal shallow shell on Winkler and Pasternak foundations with various boundary restraints.


			Boundary Restraints
			SSSS	CCCC	CFCF	SCSC	CSDCSD	CE¹E¹E¹	SE²SE²	E³E³E³E³

FG sandwich plate

10	10	0.5	69.151	99.615	89.141	94.136	96.018	43.372	77.252	33.384
	10	5	58.754	78.703	68.155	72.151	74.712	39.165	62.801	30.728
	100	0.5	77.465	113.40	96.752	102.41	109.86	52.692	84.752	36.832
	100	5	62.938	92.796	78.234	81.182	88.751	45.648	71.867	31.659
100	10	0.5	78.746	115.76	99.268	105.15	110.21	53.701	84.736	36.685
	10	5	62.998	95.398	81.680	85.145	91.327	46.408	71.651	30.625
	100	0.5	93.545	131.45	113.04	121.96	128.63	58.310	101.71	38.547
	100	5	73.742	112.72	80.124	96.584	106.23	52.522	78.087	33.201

FG sandwich circular cylindrical shallow shell

10	10	0.5	63.850	87.642	78.359	85.209	83.678	40.214	71.065	29.548
	10	5	54.243	69.245	61.953	69.321	65.251	35.247	56.428	27.651
	100	0.5	70.955	102.96	90.145	94.547	98.932	46.367	75.992	31.287
	100	5	58.987	93.970	71.625	78.520	90.240	41.140	70.222	29.748
100	10	0.5	72.568	109.64	92.323	98.336	105.63	46.215	80.571	32.214
	10	5	60.962	94.353	74.254	81.351	89.321	40.162	72.678	28.967
	100	0.5	84.647	125.21	103.35	112.42	118.96	50.271	89.524	35.124
	100	5	68.166	110.79	78.547	90.244	106.71	45.214	75.215	31.258

FG sandwich spherical shallow shell

10	10	0.5	54.156	69.759	60.297	64.392	64.253	35.157	58.739	25.172
	10	5	46.394	57.443	52.061	54.163	52.360	32.658	49.154	22.698
	100	0.5	63.582	95.245	88.570	89.571	93.575	37.687	68.215	26.215
	100	5	48.151	81.524	70.657	76.408	77.074	34.186	53.216	24.154
100	10	0.5	65.696	102.75	85.041	92.019	98.709	39.398	74.155	26.687
	10	5	50.168	88.178	70.992	74.326	84.171	35.187	65.397	25.154
	100	0.5	74.963	116.32	95.891	104.45	110.38	44.163	82.357	29.696
	100	5	67.490	105.88	74.126	85.247	101.49	40.352	70.644	27.215

FG sandwich hyperbolic paraboloidal shallow shell

10	10	0.5	34.248	43.435	38.423	40.317	40.457	31.971	36.215	22.198
	10	5	30.157	38.480	34.767	36.051	36.370	28.645	32.367	20.067
	100	0.5	45.955	64.016	54.031	57.309	58.036	34.196	50.397	24.548
	100	5	39.221	52.482	45.021	46.322	49.467	30.677	42.255	22.001
100	10	0.5	48.251	69.245	60.652	63.567	63.259	35.672	53.219	25.157
	10	5	38.195	53.522	45.682	49.294	50.245	31.015	41.488	24.695
	100	0.5	50.003	82.795	62.052	68.088	78.590	32.359	58.154	28.964
	100	5	41.326	72.278	49.992	53.355	66.048	30.248	45.570	26.175