Transverse Vibration Analysis of Composite Plates with Multiple Distributed Composite Patches

Table 1

Nondimensional frequencies of the cross-ply laminate ([0/90]s) with CCCC boundary condition, E1/E2 = 10, and a = b = 10 h and for different patch sizes and numbers.

Modes			1st	2nd	3rd	4th	5th	6th	7th	8th	9th
CASE I	0 × 0	Present	5.288	8.178	13.220	13.618	15.079	19.171	21.347	25.409	25.831
		FEM	5.337	8.013	12.693	13.171	14.390	/	/	/	/
	0.1 × 0.1	Present	5.226	8.173	13.214	13.504	15.097	19.164	21.318	25.199	25.861
		FEM	5.205	8.064	12.416	13.119	14.506	/	/	/	/
	0.2 × 0.2	Present	5.067	8.121	13.131	13.322	15.124	19.096	21.018	24.865	25.851
		FEM	4.942	8.284	12.243	13.102	14.708	/	/	/	/
	0.3 × 0.3	Present	4.878	7.951	12.860	13.301	15.046	18.997	20.504	24.853	25.556
		FEM	4.650	8.476	12.299	13.021	14.242	/	/	/	/
CASE II	0.1 × 0.1	Present	5.180	8.170	13.209	13.423	15.110	19.158	21.296	25.039	25.883
		FEM	5.085	7.788	11.798	12.895	15.463	/	/	/	/
	0.2 × 0.2	Present	4.916	8.079	13.063	13.137	15.157	19.041	20.772	24.518	25.865
		FEM	4.928	7.174	11.992	12.559	15.160	/	/	/	/
	0.3 × 0.3	Present	4.624	7.790	12.599	13.131	15.022	18.886	19.958	24.565	25.355
		FEM	4.858	6.849	11.895	12.117	13.678	/	/	/	/
CASE III	0.1 × 0.1	Present	5.106	8.165	13.201	13.294	15.131	19.150	21.260	24.772	25.918
		FEM	4.998	7.767	11.749	12.708	15.103	/	/	/	/
	0.2 × 0.2	Present	4.690	8.009	12.883	12.951	15.208	18.954	20.370	24.051	25.889
		FEM	4.801	7.087	11.955	12.221	14.971	/	/	/	/
	0.3 × 0.3	Present	4.274	7.536	12.185	12.925	14.982	18.730	19.201	24.230	25.030
		FEM	4.650	6.799	11.956	12.409	14.217	/	/	/	/