Dynamical Analysis of Long Fiber-Reinforced Laminated Plates with Elastically Restrained Edges

Table 5

(a) Frequency parameters 𝜔_𝑖 for [0°/45°]and [0°/90°] carbon-epoxy AS4-3501-6 (Table 1), with different translational restraint parameter 𝑇^𝑤_𝑖, 𝑇^𝑢_𝑖=𝑇^𝑣_𝑖=𝑅_𝑖=0 (𝑖=1,…,4), and 𝑎/ℎ=10. (b) Frequency parameters 𝜔_𝑖 for [0°/45°] and [0°/90°] carbon-epoxy AS4-3501-6 (Table 1), with different translational restraint parameter 𝑇^𝑤_𝑖, 𝑇^𝑢_𝑖=𝑇^𝑣_𝑖=𝑅_𝑖=0 (𝑖=1,…,4), and 𝑎/ℎ=100.

(a)

𝑘𝑓	Mode	Translational restraint parameter 𝑇^𝑤𝑖
		0.1	1	10	100	1000	10000	1.00𝐸+10
𝑎/ℎ=10
	[0°/45°]
0.2	1	0.060	0.187	0.520	0.969	1.161	1.191	1.195
	2	0.085	0.266	0.803	1.827	2.380	2.470	2.481
	3	0.085	0.267	0.822	2.079	2.930	3.063	3.078
	4	0.754	0.810	1.224	2.609	3.776	4.004	4.032
0.4	1	0.083	0.256	0.689	1.219	1.419	1.448	1.452
	2	0.117	0.367	1.083	2.284	2.829	2.912	2.922
	3	0.117	0.368	1.125	2.723	3.638	3.767	3.782
	4	0.890	0.978	1.590	3.325	4.530	4.735	4.759
0.6	1	0.101	0.310	0.824	1.443	1.671	1.705	1.709
	2	0.142	0.445	1.303	2.685	3.290	3.382	3.393
	3	0.142	0.447	1.364	3.274	4.342	4.492	4.509
	4	1.040	1.151	1.903	3.936	5.292	5.517	5.543
	[0°/90°]
0.2	1	0.060	0.188	0.528	0.942	1.084	1.104	1.106
	2	0.085	0.267	0.814	1.970	2.657	2.756	2.768
	3	0.085	0.267	0.814	1.970	2.657	2.756	2.768
	4	0.628	0.697	1.164	2.642	3.708	3.888	3.909
0.4	1	0.083	0.258	0.705	1.181	1.321	1.340	1.342
	2	0.117	0.368	1.110	2.546	3.251	3.344	3.355
	3	0.117	0.368	1.110	2.546	3.251	3.344	3.355
	4	0.750	0.858	1.540	3.424	4.519	4.675	4.675
0.6	1	0.101	0.313	0.847	1.395	1.553	1.574	1.577
	2	0.142	0.446	1.343	3.035	3.829	3.932	3.944
	3	0.142	0.446	1.343	3.035	3.829	3.932	3.944
	4	0.910	1.040	1.864	4.089	5.329	5.514	5.536

(b)

𝑘𝑓	Mode	Translational restraint parameter 𝑇^𝑤𝑖
		0.1	1	10	100	1000	10000	1.00𝐸+10
𝑎/ℎ=100
	[0°/45°]
0.2	1	0.060	0.187	0.525	1.014	1.276	1.329	1.340
	2	0.085	0.268	0.813	1.928	2.708	2.881	2.908
	3	0.085	0.269	0.832	2.214	3.489	3.771	3.815
	4	0.804	0.858	1.266	2.774	4.519	5.027	5.098
0.4	1	0.083	0.256	0.697	1.292	1.577	1.633	1.646
	2	0.117	0.369	1.099	2.445	3.269	3.440	3.468
	3	0.117	0.370	1.142	2.952	4.444	4.746	4.794
	4	0.947	1.032	1.642	3.588	5.531	6.011	6.073
0.6	1	0.101	0.310	0.835	1.531	1.859	1.925	1.940
	2	0.142	0.447	1.324	2.880	3.804	3.995	4.028
	3	0.143	0.450	1.385	3.555	5.304	5.654	5.711
	4	1.104	1.210	1.962	4.255	6.457	6.980	7.046
	[0°/90°]
0.2	1	0.060	0.188	0.533	0.981	1.161	1.190	1.194
	2	0.085	0.268	0.823	2.086	3.043	3.212	3.233
	3	0.085	0.268	0.823	2.086	3.043	3.212	3.233
	4	0.666	0.732	1.197	2.805	4.365	4.732	4.782
0.4	1	0.083	0.258	0.714	1.239	1.422	1.449	1.453
	2	0.117	0.370	1.126	2.738	3.783	3.948	3.969
	3	0.117	0.370	1.126	2.738	3.783	3.948	3.969
	4	0.797	0.901	1.583	3.699	5.418	5.774	5.821
0.6	1	0.101	0.313	0.857	1.464	1.674	1.706	1.710
	2	0.143	0.449	1.363	3.271	4.453	4.638	4.661
	3	0.143	0.449	1.363	3.271	4.453	4.638	4.661
	4	0.967	1.093	1.917	4.427	6.392	6.797	6.851