Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels

Table 7

Benchmark 3. Simply supported isotropic rectangular plate. First three vibration modes in terms of no-dimensional circular frequency 𝜔=𝜔(𝑎²/ℎ)𝜌/𝐸 for several combinations of half-wave numbers 𝑚 and 𝑛. 𝑀=1 fictitious layers and 𝑁=18 order of expansion for the exponential matrix.

𝑎/ℎ	100	50	10	5
	(𝑚=0, 𝑛=1)
I mode	0.3318	0.3318	0.3312	0.3293
II mode	64.944	32.472	6.4944	3.2472
III mode	109.78	54.888	10.977	5.4870
	(𝑚=1, 𝑛=0)
I mode	2.9861	2.9846	2.9360	2.8012
II mode	194.83	97.417	19.483	9.7417
III mode	329.33	164.66	32.908	16.415
	(𝑚=1, 𝑛=1)
I mode	3.3179	3.3159	3.2562	3.0923
II mode	205.37	102.69	20.537	10.269
III mode	347.14	173.56	34.685	17.297
	(𝑚=1,  𝑛=2)
I mode	4.3130	4.3097	4.2099	3.9450
II mode	234.16	117.08	23.416	11.708
III mode	395.80	197.89	39.537	19.699
	(𝑚=2, 𝑛=1)
I mode	12.270	12.243	11.497	9.9094
II mode	395.04	197.52	39.504	19.752
III mode	667.72	333.83	66.559	32.908
	(𝑚=2, 𝑛=2)
I mode	13.264	13.233	12.369	10.572
II mode	410.74	205.37	41.074	20.537
III mode	694.26	347.10	69.186	34.170