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

Table 7

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

(a)

𝑘𝑓	Mode	Translational restraint parameter 𝑇^𝑤𝑖
		0.1	1	10	100	1000	10000	1.00𝐸+10
𝑎/𝑏=2
	1	0.158	0.464	1.043	2.045	2.778	2.903	2.917
0.2	2	0.184	0.574	1.625	3.592	4.520	4.704	4.726
	3	0.255	0.793	2.167	3.948	6.915	7.139	7.149
	4	1.652	1.823	2.838	5.127	7.177	7.419	7.449
	1	0.199	0.578	1.268	2.392	3.046	3.144	3.156
0.4	2	0.233	0.723	1.999	4.175	5.024	5.169	5.186
	3	0.322	0.999	2.649	4.774	7.759	8.125	8.148
	4	1.832	2.071	3.374	6.021	7.973	8.173	8.196
	1	0.235	0.681	1.487	2.757	3.455	3.557	3.569
0.6	2	0.275	0.853	2.347	4.837	5.763	5.915	5.933
	3	0.380	1.179	3.115	5.589	8.864	9.309	9.342
	4	2.104	2.394	3.945	6.992	9.186	9.408	9.434
𝑎/𝑏=1.5
	1	0.111	0.341	0.904	1.724	2.239	2.345	2.364
0.2	2	0.141	0.443	1.335	3.326	4.739	5.023	5.067
	3	0.171	0.539	1.627	3.705	5.946	6.580	6.673
	4	1.423	1.542	2.285	4.768	7.832	8.845	8.980
	1	0.140	0.429	1.108	2.012	2.501	2.598	2.617
0.4	2	0.178	0.559	1.664	3.964	5.396	5.649	5.686
	3	0.216	0.681	2.037	4.480	6.688	7.229	7.313
	4	1.587	1.731	2.729	5.680	8.857	9.749	9.869
	1	0.165	0.506	1.296	2.316	2.847	2.954	2.976
0.6	2	0.210	0.660	1.957	4.587	6.194	6.469	6.509
	3	0.256	0.804	2.400	5.243	7.625	8.198	8.292
	4	1.815	1.989	3.182	6.582	10.085	11.034	11.163

(b)

𝑘𝑓	Mode	Rotational restraint parameter 𝑅^𝜙𝑥,𝜙𝑦𝑖
		0.1	1	10	100	1000	10000	1.00𝐸+10
𝑎/𝑏=2
0.2	1	3.444	3.858	4.588	4.806	4.833	4.835	4.836
	2	5.467	5.742	6.278	6.450	6.472	6.474	6.474
	3	8.161	8.349	8.750	8.890	8.908	8.909	8.910
	4	8.357	8.741	9.485	9.722	9.751	9.754	9.754
0.4	1	3.854	4.314	4.989	5.183	5.183	5.185	5.186
	2	6.061	6.362	6.855	7.009	7.009	7.011	7.011
	3	8.971	9.187	9.552	9.678	9.678	9.680	9.680
	4	8.987	9.437	10.142	10.37	10.347	10.349	10.349
0.6	1	4.421	4.946	5.682	5.866	5.887	5.889	5.889
	2	6.961	7.309	7.858	8.006	8.024	8.026	8.026
	3	10.160	10.584	10.999	11.124	11.139	11.140	11.141
	4	10.352	10.720	11.512	11.709	11.732	11.734	11.735
𝑎/𝑏=1.5
0.2	1	2.764	3.203	4.114	4.438	4.479	4.483	4.484
	2	5.686	6.122	7.270	7.771	7.839	7.846	7.847
	3	7.047	7.669	9.272	9.946	10.035	10.045	10.046
	4	9.588	10.107	11.673	12.471	12.586	12.598	12.599
0.4	1	3.188	3.703	4.631	4.925	4.961	4.965	4.966
	2	6.470	7.016	8.260	8.739	8.801	8.807	8.808
	3	7.847	8.632	10.324	10.927	11.003	11.011	11.012
	4	10.679	11.329	13.007	13.742	13.843	13.853	13.854
0.6	1	3.663	4.252	5.272	5.585	5.624	5.628	5.628
	2	7.394	8.040	9.448	9.973	10.040	10.047	10.048
	3	8.920	9.842	11.721	12.360	12.440	12.448	12.449
	4	12.113	12.873	14.748	15.537	15.643	15.654	15.655