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Research Papers

Free Vibration of a High-Speed Rotating Truncated Spherical Shell

[+] Author and Article Information
Hua Li

School of Mechanical and Aerospace Engineering,
Nanyang Technological University,
50 Nanyang Avenue,
Singapore 639798, Republic of Singapore
e-mail: lihua@ntu.edu.sg

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 30, 2012; final manuscript received November 26, 2012; published online March 28, 2013. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 135(3), 031006 (Mar 28, 2013) (14 pages) Paper No: VIB-12-1085; doi: 10.1115/1.4023144 History: Received March 30, 2012; Revised November 26, 2012

This paper is the first work on the vibration of a high-speed rotating spherical shell that rotates about its symmetric axis by developing a set of motion governing equations with consideration of both the Coriolis and centrifugal accelerations as well as the hoop tension arising in the rotating shell due to the angular velocity. To the author's understanding, no such work has so far been published on the rotating spherical shell with the Coriolis and centrifugal accelerations as well as the hoop tension, although there have been the works published on the rotating hemispherical shell with consideration of the Coriolis and centrifugal forces. A thin rotating isotropic truncated circular spherical shell with the simply supported boundary conditions at both the ends is taken as an example for the free vibrational analysis. In order to validate the present formulation, comparisons are made with a nonrotating isotropic spherical shell, and a good agreement is achieved since no published data results from open literature are available for comparison on the dynamics of rotating spherical shell. By the Galerkin method, several case studies are conducted for investigation of the influence of the important parameters on the frequency characteristics of the rotating spherical shell. The parameters studied include the circumferential wave number, the rotational angular velocity, Young's modulus of the shell material, and the geometric ratio of the thickness to radius of the spherical shell.

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Figures

Grahic Jump Location
Fig. 1

A rotating shell of revolution defined in the curvilinear coordinate system

Grahic Jump Location
Fig. 2

(a) A rotating spherical shell and its coordinate system. (b) A rotating spherical shell truncated at both ends (ϕ = ϕ1 and ϕ2) in the convex domains near symmetrical axis, where the simply supported boundary conditions are imposed.

Grahic Jump Location
Fig. 3

Variation of the nondimensional frequency parameter f* with the rotational speed Ω for the four circumferential wave numbers n = 1,2,3, and 4 (m = 1, ϕ1 = 60 deg, ϕ2 = 120 deg, h/R = 0.05, μ = 0.3)

Grahic Jump Location
Fig. 4

Variation of the nondimensional frequency parameter f* with the circumferential wave number n for the three rotational speeds Ω = 200,400, and 600 rps (m = 1, ϕ1 = 60 deg, ϕ2 = 120 deg, h/R = 0.05, μ = 0.3)

Grahic Jump Location
Fig. 5

Variation of the nondimensional frequency parameter f* with rotating speed Ω for various Young's moduli E (m = 1, n = 1, ϕ1 = 60 deg, ϕ2 = 120 deg, h/R = 0.05, μ = 0.3)

Grahic Jump Location
Fig. 6

Variation of the nondimensional frequency parameter f* with the circumferential wave number n for various Young's moduli E (m = 1, ϕ1 = 60 deg, ϕ2 = 120 deg, h/R = 0.05, μ = 0.3, Ω = 200 rps)

Grahic Jump Location
Fig. 7

Variation of the nondimensional frequency parameter f* with rotating speed Ω for various thickness-to-radius (h/R) ratios (m = 1, n = 1, ϕ1 = 60 deg, ϕ2 = 120 deg, μ = 0.3)

Grahic Jump Location
Fig. 8

Variation of the nondimensional frequency parameter f* with the circumferential wave number n for various thickness-to-radius (h/R) ratios (m = 1, ϕ1 = 60 deg, ϕ2 = 120 deg, μ = 0.3, Ω = 100 rps)

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