Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

Table 15

Fundamental frequency parameter for circular sector plate with various boundary conditions and material types ( = 120°, = 0.2, and ).

(KW, KG)		Boundary conditions
		CCC	CSDSD	CFC	CSC	CE^1E^1	E^2CE^2	E^1E^1E^1	E^2E^2E^2	E^3E^3E^3
		Type 1-1 (2-2-1)
(10, 10)	0.5	49.067	35.093	15.397	39.729	21.501	47.290	16.598	45.630	16.459
	5	38.629	27.661	12.888	31.189	20.261	37.845	16.857	37.116	16.730
	20	36.774	26.473	12.541	29.772	20.058	36.126	16.902	35.522	16.779
(10, 100)	0.5	61.880	50.832	27.164	54.445	25.231	60.311	16.695	58.832	16.695
	5	55.308	47.427	26.216	49.943	24.801	54.623	17.346	53.978	17.345
	20	54.348	47.099	26.161	49.404	24.815	53.783	17.497	53.251	17.497
(100, 100)	0.5	62.411	51.467	28.366	55.040	26.536	60.855	16.695	59.388	16.695
	5	55.956	48.171	27.583	50.652	26.194	55.279	17.346	54.642	17.345
	20	55.023	47.866	27.563	50.135	25.911	54.465	17.497	53.939	17.497
		Type 1-2 (2-2-1)
(10, 10)	0.5	48.273	36.215	16.399	40.329	22.268	46.823	17.555	45.444	17.418
	5	38.187	28.868	14.075	32.353	21.065	37.571	17.809	36.981	17.690
	20	33.685	25.898	12.888	28.601	20.241	33.299	17.566	32.930	17.463
(10, 100)	0.5	62.582	53.284	28.603	55.930	25.792	61.359	17.557	60.189	17.557
	5	56.710	50.599	27.835	42.896	23.948	56.230	18.029	55.767	18.029
	20	54.211	49.201	27.309	38.461	23.213	53.919	18.035	53.637	18.035
(100, 100)	0.5	63.184	53.975	29.902	56.093	25.792	61.972	17.557	60.813	17.557
	5	57.452	51.410	29.325	42.897	23.948	56.978	18.029	56.520	18.029
	20	55.007	50.058	28.869	38.461	23.213	54.719	18.035	54.440	18.035
		Type 2-1 (2-2-1)
(10, 10)	0.5	45.085	32.207	14.401	36.416	21.073	43.762	16.779	42.542	16.642
	5	40.914	29.476	13.586	33.169	20.750	40.008	17.073	39.180	16.942
	20	40.378	29.203	13.540	32.813	20.753	39.528	17.161	38.750	17.031
(10, 100)	0.5	59.248	49.411	26.795	52.533	25.079	58.090	16.980	57.014	16.978
	5	56.875	48.481	26.700	50.992	25.156	56.102	17.404	55.392	17.400
	20	56.666	48.513	26.774	50.873	25.238	55.946	17.501	55.286	17.497
(100, 100)	0.5	59.822	50.085	28.061	53.168	26.444	58.675	16.980	57.610	16.978
	5	57.508	49.246	28.050	51.662	26.029	56.744	17.404	56.042	17.400
	20	57.311	49.205	28.141	51.536	25.828	56.599	17.501	55.947	17.497
		Type 2-2 (2-2-1)
(10, 10)	0.5	41.276	29.759	13.690	33.489	20.813	40.343	17.091	39.489	16.959
	5	39.492	29.102	13.702	32.507	20.919	38.751	17.486	38.066	17.359
	20	39.075	29.014	13.745	32.337	20.949	38.375	17.578	37.723	17.454
(10, 100)	0.5	57.144	48.672	26.770	51.223	25.198	56.347	17.405	55.613	17.402
	5	56.671	49.199	27.215	49.839	25.074	56.066	17.792	55.505	17.788
	20	56.603	49.076	27.346	48.227	24.789	56.038	17.870	55.513	17.867
(100, 100)	0.5	57.775	49.395	28.117	51.893	26.033	56.987	17.405	56.262	17.402
	5	57.354	49.956	28.631	50.040	25.076	56.756	17.793	56.202	17.789
	20	57.300	49.096	28.780	48.295	24.791	56.742	17.871	56.224	17.867