An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges

Table 8

The first seven frequency parameters Ω=(𝜔𝑏²/𝜋²)(𝜌ℎ/𝐷)^1/2 for C-C-F-C Mindlin rectangular plates with translational, rotational, and torsional restraints at 𝑥=𝑎, 𝑘_𝑥𝑎=𝐾_𝑥𝑎=𝐾_𝑦𝑥𝑎=𝐾×𝐷.

𝐾	1	2	3	4	5	6	7
0	2.2388	3.6105	5.4944	6.6135	6.8022	9.4188	9.7667
0.1	2.2476	3.6233	5.5034	6.6282	6.811	9.4295	9.775
1	2.3132	3.7213	5.5721	6.7447	6.8826	9.5158	9.8391
10^2	2.878	4.562	6.0184	7.641	7.6707	10.2284	10.3535
10^4	3.2854	6.2286	6.2735	8.7475	10.2438	10.4305	12.3813
10^6	3.2954	6.2857	6.2861	8.8102	10.3788	10.4778	12.5528
10^7	3.2955	6.2863	6.2863	8.8109	10.3797	10.4786	12.5545
10^9	3.2955	6.2863	6.2863	8.8109	10.3797	10.4786	12.5546
∞	3.2955	6.2863	6.2863	8.8109	10.3797	10.4786	12.5546