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

Table 6

(a) Frequency parameters 𝜔_𝑖 for [0°/45°] and [0°/90°] 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. (b) Frequency parameters 𝜔_𝑖 for [0°/45°] and [0°/90°] 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=100.

(a)

𝑘𝑓	Mode	Rotational restraint parameter 𝑅𝑖
		0.1	1	10	100	1000	10000	1.00𝐸+10
𝑎/ℎ=10
	[0°/45°]
0.2	1	1.461	1.623	1.943	2.056	2.071	2.072	2.072
	2	2.709	2.903	3.268	3.390	3.406	3.407	3.407
	3	3.350	3.497	3.861	4.010	4.030	4.032	4.032
	4	4.322	4.477	4.818	4.951	4.969	4.971	4.971
0.4	1	1.837	2.029	2.371	2.483	2.497	2.498	2.498
	2	3.249	3.493	3.875	3.988	4.002	4.003	4.003
	3	4.112	4.302	4.709	4.854	4.872	4.874	4.874
	4	5.129	5.333	5.700	5.823	5.838	5.840	5.840
0.6	1	2.182	2.408	2.803	2.931	2.947	2.949	2.949
	2	3.799	4.090	4.527	4.654	4.669	4.671	4.671
	3	4.884	5.119	5.611	5.783	5.804	5.806	5.807
	4	5.987	6.239	6.672	6.812	6.830	6.832	6.832
	[0°/90°]
0.2	1	1.386	1.562	1.916	2.034	2.048	2.050	2.050
	2	2.901	3.110	3.561	3.719	3.738	3.740	3.741
	3	2.901	3.110	3.561	3.719	3.738	3.740	3.741
	4	4.052	4.287	4.764	4.970	4.994	4.996	4.996
0.4	1	1.755	1.969	2.352	2.468	2.482	2.483	2.483
	2	3.532	3.814	4.321	4.473	4.491	4.493	4.493
	3	3.532	3.814	4.321	4.473	4.491	4.493	4.493
	4	4.932	5.218	5.745	5.949	5.971	5.973	5.973
0.6	1	2.090	2.340	2.776	2.905	2.920	2.922	2.922
	2	4.167	4.511	5.102	5.272	5.292	5.294	5.295
	3	4.167	4.511	5.102	5.272	5.292	5.294	5.295
	4	5.833	6.179	6.790	7.021	7.045	7.047	7.048

(b)

𝑘𝑓	Mode	Rotational restraint parameter 𝑅𝑖
		0.1	1	10	100	1000	10000	1.00𝐸+10
𝑎/ℎ=100
	[0°/45°]
0.2	1	1.598	1.814	2.318	2.534	2.564	2.567	2.567
	2	3.108	3.410	4.115	4.415	4.457	4.461	4.462
	3	4.161	4.421	5.275	5.759	5.831	5.839	5.840
	4	5.366	5.689	6.611	7.100	7.173	7.181	7.181
0.4	1	2.044	2.316	2.901	3.135	3.166	3.169	3.170
	2	3.783	4.185	4.997	5.311	5.353	5.358	5.358
	3	5.265	5.627	6.699	7.240	7.317	7.325	7.326
	4	6.450	6.911	8.018	8.523	8.594	8.601	8.602
0.6	1	2.428	2.748	3.423	3.689	3.725	3.729	3.729
	2	4.418	4.896	5.821	6.171	6.217	6.222	6.223
	3	6.250	6.692	7.967	8.593	8.682	8.691	8.692
	4	7.498	8.058	9.337	9.897	9.974	9.983	9.983
	[0°/90°]
0.2	1	1.493	1.719	2.223	2.413	2.437	2.440	2.440
	2	3.396	3.720	4.583	4.960	5.010	5.016	5.016
	3	3.396	3.720	4.583	4.960	5.010	5.016	5.016
	4	5.036	5.390	6.396	6.966	7.039	7.047	7.048
0.4	1	1.917	2.203	2.780	2.976	3.001	3.003	3.003
	2	4.202	4.665	5.725	6.122	6.172	6.178	6.178
	3	4.202	4.665	5.725	6.122	6.172	6.178	6.178
	4	6.173	6.688	7.937	8.560	8.634	8.641	8.642
0.6	1	2.286	2.621	3.277	3.494	3.521	3.523	3.524
	2	4.952	5.515	6.745	7.185	7.241	7.247	7.247
	3	4.952	5.515	6.745	7.185	7.241	7.247	7.247
	4	7.297	7.918	9.364	10.060	10.141	10.149	10.150