Application of Variational Equation of Motion to the Nonlinear Vibration Analysis of Homogeneous and Layered Plates and Shells

[+] Author and Article Information
Yi-Yuan Yu

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

J. Appl. Mech 30(1), 79-86 (Mar 01, 1963) (8 pages) doi:10.1115/1.3630109 History: Received February 09, 1962; Online September 16, 2011


An integrated procedure is presented for applying the variational equation of motion to the approximate analysis of nonlinear vibrations of homogeneous and layered plates and shells involving large deflections. The procedure consists of a sequence of variational approximations. The first of these involves an approximation in the thickness direction and yields a system of equations of motion and boundary conditions for the plate or shell. Subsequent variational approximations with respect to the remaining space coordinates and time, wherever needed, lead to a solution to the nonlinear vibration problem. The procedure is illustrated by a study of the nonlinear free vibrations of homogeneous and sandwich cylindrical shells, and it appears to be applicable to still many other homogeneous and composite elastic systems.

Copyright © 1963 by ASME
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