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

Table 3

Assessment 2 (part II). Simply supported aluminum cylinder with Poisson ratio 𝜈=0.3 and thickness ratio ℎ/𝑅_𝛼=0.18. Lowest exact natural circular frequencies in no-dimensional form 𝜔=𝜔(ℎ/𝜋)𝜌/𝐺 for imposed axial half-wave number 𝑛=1 and several half-wave numbers 𝑚 in circumferential direction. Comparison between present three-dimensional analysis and three-dimensional analysis by Armenakas et al. [8] as adapted in Bhimaraddi [9]. 𝑀 is the number of fictitious layers and 𝑁 is the order of expansion for the exponential matrix.

	ℎ/𝑅𝛼=0.18
	𝑚=2	𝑚=4	𝑚=6	𝑚=8
	𝑏/𝑅𝛼=2
Present 3D (𝑀=1, 𝑁=3)	0.05613	0.03607	0.03241	0.02570
Present 3D (𝑀=10, 𝑁=3)	0.05652	0.03930	0.04998	0.07822
Present 3D (𝑀=50, 𝑁=3)	0.05652	0.03929	0.04996	0.07821
Present 3D (𝑀=100, 𝑁=3)	0.05652	0.03929	0.04996	0.07821
3D [8, 9]	0.05652	0.03929	0.04996	0.07821
	𝑏/𝑅𝛼=1
Present 3D (𝑀=1, 𝑁=3)	0.08833	0.07237	0.05717	0.01965
Present 3D (𝑀=10, 𝑁=3)	0.09403	0.08546	0.09094	0.11205
Present 3D (𝑀=50, 𝑁=3)	0.09402	0.08545	0.09093	0.11205
Present 3D (𝑀=100, 𝑁=3)	0.09402	0.08545	0.09093	0.11205
3D [8, 9]	0.09402	0.08545	0.09093	0.11205
	𝑏/𝑅𝛼=0.5
Present 3D (𝑀=1, 𝑁=3)	0.36506	0.37946	0.40165	0.43001
Present 3D (𝑀=10, 𝑁=3)	0.18895	0.19467	0.20616	0.22449
Present 3D (𝑀=50, 𝑁=3)	0.18894	0.19467	0.20616	0.22450
Present 3D (𝑀=100, 𝑁=3)	0.18894	0.19467	0.20616	0.22450
3D [8, 9]	0.18894	0.19467	0.20616	0.22450
	𝑏/𝑅𝛼=0.25
Present 3D (𝑀=1, 𝑁=3)	0.72230	0.72911	0.74032	0.75570
Present 3D (𝑀=10, 𝑁=3)	0.50335	0.50934	0.51931	0.53321
Present 3D (𝑀=50, 𝑁=3)	0.50338	0.50937	0.51934	0.53325
Present 3D (𝑀=100, 𝑁=3)	0.50338	0.50937	0.51934	0.53325
3D [8, 9]	0.50338	0.50937	0.51934	0.53325