A Note on a New Stability Method for the Linear Modes of Nonlinear Two-Degree-of-Freedom Systems

[+] Author and Article Information
Jack Porter

Institute of Engineering Research, University of California, Berkeley, Calif.

C. P. Atkinson

Engineering Mechanics, University of California

J. Appl. Mech 29(2), 258-262 (Jun 01, 1962) (5 pages) doi:10.1115/1.3640538 History: Received April 11, 1961; Online September 16, 2011


This paper presents a method for analyzing the stability of the linearly related modes of nonlinear two-degree-of-freedom oscillatory systems. For systems described by the coupled equations ẍ1 = f(x1 , x2 ) and ẍ2 = g(x1 , x2 ) there exist solutions related by the linear modal restraint x1 = cx2 where c is a constant. Such oscillations are not always stable. The method of this paper allows the prediction of the stability of the modes in terms of the amplitudes of the oscillations and the parameters of the equations of motion. Analog-computer results are presented which confirm the theoretical predictions.

Copyright © 1962 by ASME
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