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

Table 11

Benchmark 7. Simply supported isotropic cylinder. First three vibration modes in term 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	7691.7	769.17	76.917	38.459
II mode	12342	1234.2	123.42	61.710
III mode	41586	4158.6	416.30	208.81
	(𝑚=2, 𝑛=1)
I mode	2445.9	244.59	24.492	12.295
II mode	27270	2727.0	272.81	136.56
III mode	59189	5918.8	591.08	294.28
	(𝑚=2,  𝑛=2)
I mode	7712.1	771.23	77.252	38.820
II mode	33375	3337.5	333.85	167.09
III mode	61353	6135.3	612.74	305.15
	(𝑚=2,  𝑛=3)
I mode	13536	1353.7	135.69	68.323
II mode	40081	4008.1	400.89	200.56
III mode	65490	6548.9	654.17	325.96