Axisymmetric Free Vibration of Shallow Spherical Shells With a Circular Rigid Insert

[+] Author and Article Information
D. Y. Hwang

Department of Civil Engineering, Auburn University, AL 36849

W. A. Foster

Department of Aerospace Engineering, Auburn University, AL 36849

J. Pressure Vessel Technol 115(2), 207-209 (May 01, 1993) (3 pages) doi:10.1115/1.2929517 History: Received March 31, 1992; Revised December 18, 1992; Online June 17, 2008


A general solution for the third-order partial differential equations for the axisymmetric free vibration of thin isotropic shallow spherical shells with a rigid insert is presented in this paper. The frequency equation in terms of Bessel functions as well as modified Bessel functions is solved for the fundamental vibrational frequency and mode shape. Both linear and non-linear boundary conditions are applied and the results are compared. The relationship between the vibrational frequency, mode shape and the size of the rigid insert is discussed.

Copyright © 1993 by The American Society of Mechanical Engineers
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