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

Table 15

Effects of 𝐻_𝛼=(1+𝑧/𝑅_𝛼) terms in benchmark 5 for 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
I mode (𝐻𝛼=1)	1067.1	106.71	10.686	5.3486
II mode (𝐻𝛼=1)	1068.3	106.83	10.688	5.3684
III mode (𝐻𝛼=1)	1855.7	185.56	18.550	9.2651
	(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
I mode (𝐻𝛼=1)	2.7747	2.7473	2.7029	2.5828
II mode (𝐻𝛼=1)	2040.3	204.03	20.403	10.201
III mode (𝐻𝛼=1)	3635.3	363.52	36.303	18.076
	(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
I mode (𝐻𝛼=1)	222.73	22.535	4.0440	3.3738
II mode (𝐻𝛼=1)	2364.5	236.45	23.668	11.868
III mode (𝐻𝛼=1)	4017.4	401.73	40.115	19.965