Nonlinear Forced Vibrations of Beams

[+] Author and Article Information
M. Countryman

Department of Mathematics and Statistics, Louisiana Tech University, Ruston, La. 71272

R. Kannan

Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019

J. Appl. Mech 52(1), 163-166 (Mar 01, 1985) (4 pages) doi:10.1115/1.3168988 History: Received September 01, 1983; Revised April 01, 1984; Online July 21, 2009


An iterative procedure for computing periodic solutions of nonlinear vibrating beams is presented. The nonlinear partial differential equation is replaced by a coupled system of equations. The contraction mapping principle is then applied to generate a method of successive approximations. The coupled equations are then approximated by discrete equations that are solved by matrix-theoretic techniques and numerical quadrature procedures. Some numerical examples are provided to illustrate the method.

Copyright © 1985 by ASME
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