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

Table 4

Assessment 3. Simply supported orthotropic cylinder with thickness ratio ℎ/𝑅_𝛼=0.3 and orthotropic angle 𝜃 equal to 0° or 90°. First three exact natural circular frequencies in no-dimensional form 𝜔=𝜔(𝑅/𝜋)𝜌/𝐺₁₂ for imposed half-wave numbers 𝑚=0 and 𝑛=1. Comparison between present three-dimensional analysis and three-dimensional analysis by Soldatos and Ye [7]. 𝑀 is the number of fictitious layers and 𝑁 is the order of expansion for the exponential matrix.

	Mode
	I	II	III	I	II	III
	(𝑚=0,  𝑛=1), 𝜃=0^∘			(𝑚=0, 𝑛=1), 𝜃=90^∘
Present 3D (𝑀=50, 𝑁=3)	1.02407	2.55671	4.66395	0.20406	0.49393	0.91564
Present 3D (𝑀=60, 𝑁=3)	0.32274	0.41827	3.29830	0.30493	0.81346	7.51166
Present 3D (𝑀=80, 𝑁=3)	0.99999	1.29840	1.85418	0.95308	1.00000	3.04558
Present 3D (𝑀=90, 𝑁=3)	1.00000	1.29714	2.48260	0.95308	1.00000	3.25249
Present 3D (𝑀=100, 𝑁=3)	1.00000	1.29714	2.48260	0.95308	1.00000	3.25249
3D [7]	1.00000	1.29730	2.48260	0.95307	1.00000	3.25250