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RESEARCH PAPERS

A Study of the Nonlinearly Related Modal Solutions of Coupled Nonlinear Systems by Superposition Techniques

[+] Author and Article Information
C. P. Atkinson, Beverly Taskett

University of California, Berkeley, Calif.

J. Appl. Mech 32(2), 359-364 (Jun 01, 1965) (6 pages) doi:10.1115/1.3625807 History: Received April 14, 1964; Online September 15, 2011

Abstract

The coupled nonlinear oscillating systems studied do not possess linear normal modes. The nonlinearly related modes of

m11 + k = 1n akx1k +    k = 1n Ak(x1 − x2)k = 0m22 + k = 1n bkx2k −    k = 1n Ak(x1 − x2)k = 0  (1)
with k = 1, 3, 5, . . . . . .
are expressed as superpositions of the linear normal modes of each of the homogeneous systems of the form
m11 + akx1k +    Ak(x1 − x2)k = 0m22 + bkx2k −    Ak(x1 − x2)k = 0  (2)
whose force fields are superimposed to yield the force field of equations (1).

Copyright © 1965 by ASME
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