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

Table 14

Fundamental frequency parameter Ω for annular sector plate with various boundary conditions and material types ( = 0.5, = 120°, = 0.2, and ).

(KW, KG)		Boundary conditions
		CCCC	CSDCSD	CFCF	CSCS	CE^1CE^1	E^2SE^2S	E^1E^1E^1E^1	E^2E^2E^2E^2	E^3E^3E^3E^3
		Type 1-1 (2-2-1)
(10, 10)	0.5	90.522	89.567	87.632	89.674	89.042	83.012	19.380	83.713	19.380
	5	73.835	73.120	71.544	73.192	72.946	69.642	20.166	70.235	20.090
	20	70.370	69.699	68.191	69.764	69.563	66.756	20.320	67.323	20.234
(10, 100)	0.5	105.518	104.589	101.772	104.683	103.066	98.766	19.380	99.425	19.380
	5	93.191	92.491	89.841	92.546	91.158	89.502	20.173	90.074	20.173
	20	90.876	90.217	87.584	90.265	88.880	87.711	20.366	88.263	20.365
(100, 100)	0.5	105.831	104.904	102.099	104.997	103.389	99.097	19.380	99.755	19.380
	5	93.576	92.878	90.243	92.933	91.555	89.899	20.173	90.471	20.173
	20	91.280	90.622	88.005	90.669	89.296	88.125	20.366	88.677	20.365
		Type 1-2 (2-2-1)
(10, 10)	0.5	83.227	82.291	80.354	82.397	81.477	78.022	20.444	78.694	20.444
	5	65.098	64.393	62.809	64.472	63.873	62.579	21.186	63.134	21.186
	20	57.950	57.345	55.941	57.413	57.003	56.131	21.266	56.626	21.193
(10, 100)	0.5	101.277	100.373	97.371	100.460	98.366	96.747	20.444	97.387	20.444
	5	85.865	85.396	74.553	85.411	75.644	85.318	21.187	85.839	21.187
	20	77.059	76.696	66.901	76.701	68.098	76.697	21.305	77.056	21.305
(100, 100)	0.5	101.652	100.749	97.521	100.835	98.441	97.135	20.444	97.775	20.444
	5	85.865	85.404	74.554	85.420	75.644	85.348	21.187	85.839	21.187
	20	77.059	76.697	66.901	76.701	68.098	76.697	21.305	77.056	21.305
		Type 2-1 (2-2-1)
(10, 10)	0.5	84.174	83.314	81.544	83.387	82.961	78.145	19.719	78.850	19.717
	5	76.294	75.520	73.953	75.564	75.310	71.886	20.230	72.581	20.219
	20	74.898	74.130	72.599	74.169	73.931	70.757	20.352	71.454	20.340
(10, 100)	0.5	100.681	99.821	97.138	99.874	98.445	95.280	19.722	95.986	19.721
	5	95.109	94.256	91.774	94.272	93.031	91.124	20.247	91.929	20.243
	20	94.226	93.337	90.916	93.346	92.149	90.445	20.372	91.302	20.368
(100, 100)	0.5	101.020	100.161	97.492	100.214	98.795	95.633	19.722	96.339	19.721
	5	95.488	94.632	92.171	94.647	93.424	91.510	20.247	92.319	20.244
	20	94.614	93.720	91.322	93.728	92.551	90.838	20.372	91.701	20.369
		Type 2-2 (2-2-1)
(10, 10)	0.5	76.761	75.979	74.394	76.026	75.745	72.279	20.234	72.973	20.225
	5	71.047	70.274	68.805	70.313	70.024	67.595	20.748	68.291	20.739
	20	69.482	68.713	67.255	68.753	68.435	66.274	20.868	66.960	20.860
(10, 100)	0.5	95.506	94.654	92.140	94.673	93.389	91.466	20.248	92.258	20.246
	5	92.119	90.905	85.329	90.907	87.243	88.700	20.771	89.851	20.767
	20	91.249	89.712	82.231	89.730	83.971	87.816	20.891	89.202	20.888
(100, 100)	0.5	95.884	95.030	92.536	95.048	93.780	91.853	20.249	92.647	20.246
	5	92.538	91.287	85.389	91.291	87.279	88.822	20.771	90.280	20.768
	20	91.681	90.057	82.264	90.083	83.990	88.194	20.891	89.642	20.888