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

Table 9

Benchmark 5. Simply supported isotropic cylindrical shell panel. 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=100 fictitious layers and 𝑁=3 order of expansion for the exponential matrix.

𝑅𝛼/ℎ	1000	100	10	5
	(𝑚=0,𝑛=1)
I mode	1067.1	106.71	10.683	5.3415
II mode	1068.3	106.83	10.690	5.3727
III mode	1855.7	185.57	18.557	9.2797
	(𝑚=1,𝑛=0)
I mode	2.5478	2.5184	2.4853	2.3948
II mode	2040.3	204.03	20.411	10.216
III mode	3635.3	363.51	36.229	17.917
	(𝑚=1,𝑛=1)
I mode	222.72	22.503	3.8758	3.2156
II mode	2364.5	236.45	23.656	11.842
III mode	4017.4	401.73	40.060	19.846
	(𝑚=1,𝑛=2)
I mode	552.89	55.574	7.7851	5.7590
II mode	3031.5	303.16	30.328	15.181
III mode	5048.7	504.86	50.367	24.983
	(𝑚=2,𝑛=1)
I mode	70.382	14.052	11.533	10.021
II mode	4230.8	423.08	42.325	21.174
III mode	7214.2	721.38	71.724	35.120
	(𝑚=2,𝑛=2)
I mode	232.90	27.451	13.793	11.643
II mode	4639.2	463.92	46.414	23.226
III mode	7847.2	784.68	78.020	38.182