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

Table 6

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 only elastically restrained against translation 𝑘_𝑥0=𝑘_𝑥𝑎=𝐾×𝐷.

𝐾	Method	1	2	3	4	5	6	7
5	Present	0.3051	0.3071	0.5397	1.2922	1.8248	2.2009	2.8356
	[4]	0.3052	0.3075	0.5396	1.3117	1.8447	2.2089	2.8913
50	Present	0.6926	0.8072	1.5785	1.9220	2.1374	2.7775	3.3443
	[4]	0.6941	0.8225	1.5797	1.9268	2.1634	2.7919	3.3823
500	Present	0.8782	1.2203	2.6177	2.8662	3.1461	4.2179	5.0805
	[4]	0.8831	1.3081	2.7583	2.8767	3.2089	4.3584	5.0980
5000	Present	0.905	1.306	2.7851	3.1319	3.4845	4.7069	5.1891
	[4]	0.9105	1.4254	2.9541	3.1485	3.6157	4.9856	5.3230