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

Table 2

Assessment 2 (part I). Simply supported aluminum cylinder with Poisson ratio 𝜈=0.3 and thickness ratio ℎ/𝑅_𝛼=0.12. 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=0.12
	𝑚=2	𝑚=4	𝑚=6	𝑚=8
	𝑏/𝑅𝛼=2
Present 3D (𝑀=1, 𝑁=3)	0.03724	0.02323	0.02175	0.02846
Present 3D (𝑀=10, 𝑁=3)	0.03730	0.02360	0.02464	0.03687
Present 3D (𝑀=50, 𝑁=3)	0.03730	0.02359	0.02463	0.03686
Present 3D (𝑀=100, 𝑁=3)	0.03730	0.02359	0.02462	0.03686
3D [8, 9]	0.03730	0.02359	0.02462	0.03686
	𝑏/𝑅𝛼=1
Present 3D (𝑀=1, 𝑁=3)	0.05769	0.04772	0.04229	0.04272
Present 3D (𝑀=10, 𝑁=3)	0.05853	0.04979	0.04790	0.05546
Present 3D (𝑀=50, 𝑁=3)	0.05853	0.04978	0.04789	0.05545
Present 3D (𝑀=100, 𝑁=3)	0.05853	0.04978	0.04789	0.05545
3D [8, 9]	0.05853	0.04978	0.04789	0.05545
	𝑏/𝑅𝛼=0.5
Present 3D (𝑀=1, 𝑁=3)	0.08017	0.07732	0.07308	0.06667
Present 3D (𝑀=10, 𝑁=3)	0.10057	0.10234	0.10688	0.11528
Present 3D (𝑀=50, 𝑁=3)	0.10057	0.10234	0.10688	0.11528
Present 3D (𝑀=100, 𝑁=3)	0.10057	0.10234	0.10688	0.11528
3D [8, 9]	0.10057	0.10234	0.10688	0.11528
	𝑏/𝑅𝛼=0.25
Present 3D (𝑀=1, 𝑁=3)	0.48156	0.48619	0.49378	0.50419
Present 3D (𝑀=10, 𝑁=3)	0.27489	0.27848	0.28446	0.29286
Present 3D (𝑀=50, 𝑁=3)	0.27491	0.27849	0.28447	0.29287
Present 3D (𝑀=100, 𝑁=3)	0.27491	0.27849	0.28447	0.29287
3D [8, 9]	0.27491	0.27849	0.28447	0.29287