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

Table 7

The first seven frequency parameters Ω=(𝜔𝑏²/𝜋²)(𝜌ℎ/𝐷)^1/2 for Mindlin rectangular plates with two opposite free edges, the other two edges symmetrically elastically restrained 𝑘_𝑥0=𝑘_𝑥𝑎=𝐾₁×𝐷 and 𝐾_𝑥0=𝐾_𝑥𝑎=𝐾₂×𝐷.

𝐾1	𝐾2	Method	1	2	3	4	5	6	7
5	10	Present	0.3105	0.3148	0.9155	1.4411	2.006	2.8874	2.9385
		[4]	0.3104	0.3148	0.9208	1.4505	2.0122	2.8989	2.9659
50	50	Present	0.8936	0.901	1.6281	1.9545	2.1865	3.2206	3.412
		[4]	0.8944	0.9032	1.6305	1.9599	2.1912	3.2374	3.4255
5000	5000	Present	1.7537	1.958	3.0634	3.9445	4.1976	5.1453	5.2879
		[4]	1.7607	1.9901	3.1318	3.9578	4.2553	5.2883	5.3548