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RESEARCH PAPERS

On Nonlinear Modes of Continuous Systems

[+] Author and Article Information
A. H. Nayfeh, S. A. Nayfeh

Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0219

J. Vib. Acoust 116(1), 129-136 (Jan 01, 1994) (8 pages) doi:10.1115/1.2930388 History: Received October 01, 1992; Online June 17, 2008

Abstract

We use several methods to study the nonlinear modes of one-dimensional continuous systems with cubic inertia and geometric nonlinearities. Invariant manifold and perturbation methods applied to the discretized system and the method of multiple scales applied to the partial-differential equation and boundary conditions are discussed and their equivalence is demonstrated. The method of multiple scales is then applied directly to the partial-differential equation and boundary conditions governing several nonlinear beam problems.

Copyright © 1994 by The American Society of Mechanical Engineers
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