Nonlinear Vibrations of Shallow Spherical Shells

[+] Author and Article Information
P. L. Grossman

Department of Mechanical Engineering, The Cooper Union, New York, N. Y.

B. Koplik

Department of Mechanical Engineering, Polytechnic Institute of Brooklyn, Brooklyn, N. Y.

Yi-Yuan Yu

General Electric Missile and Space Division, Valley Forge, Pa.

J. Appl. Mech 36(3), 451-458 (Sep 01, 1969) (8 pages) doi:10.1115/1.3564701 History: Revised March 25, 1969; Received July 05, 1969; Online September 14, 2011


Based on a system of nonlinear dynamic equations and the associated variational equation of motion derived for elastic spherical shells (deep or shallow), an investigation of the axisymmetric vibrations of spherical caps with various edge conditions is made by carrying out a consistent sequence of approximations with respect to space and time. Numerical results are obtained for both free and forced oscillations involving finite deflection. The effect of curvature is examined, with particular emphasis on the transition from a flat plate to a curved shell. In fact, in such a transition, the nonlinearity of the hardening type gradually reverses into one of softening.

Copyright © 1969 by ASME
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