Nonlinear Normal Modes of a Cantilever Beam

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

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

J. Vib. Acoust 117(4), 477-481 (Oct 01, 1995) (5 pages) doi:10.1115/1.2874486 History: Received August 01, 1993; Online February 26, 2008


Two approaches for determination of the nonlinear planar modes of a cantilever beam are compared. In the first approach, the governing partial-differential system is discretized using the linear mode shapes and then the nonlinear mode shapes are determined from the discretized system. In the second approach, the boundary-value problem is treated directly by using the method of multiple scales. The results show that both approaches yield the same nonlinear modes because the discretization is performed using a complete set of basis functions, namely, the linear mode shapes.

Copyright © 1995 by The American Society of Mechanical Engineers
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