Transients in Certain Autonomous Multiple-Degree-of-Freedom Nonlinear Vibrating Systems

[+] Author and Article Information
P. R. Sethna

Department of Aeronautics and Engineering Mechanics, University of Minnesota, Minneapolis, Minn.

J. Appl. Mech 30(1), 44-50 (Mar 01, 1963) (7 pages) doi:10.1115/1.3630104 History: Received June 30, 1961; Online September 16, 2011


Oscillations of weakly nonlinear autonomous multiple-degree-of-freedom dynamical systems are studied. The analysis includes nonlinear effects arising from the potential as well as the kinetic energies of the systems and the systems include elements that produce nonlinear dissipative forces. The method of averaging is applied to a suitably transformed set of equations. In several important cases nonperiodic solutions for arbitrary initial conditions are obtained by quadratures.

Copyright © 1963 by ASME
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