The Normal Modes of Nonlinear n-Degree-of-Freedom Systems

[+] Author and Article Information
R. M. Rosenberg

University of California, Berkeley, Calif.

J. Appl. Mech 29(1), 7-14 (Mar 01, 1962) (8 pages) doi:10.1115/1.3636501 History: Received November 01, 1960; Online September 16, 2011


A system of n masses, equal or not, interconnected by nonlinear “symmetric” springs, and having n degrees of freedom is examined. The concept of normal modes is rigorously defined and the problem of finding them is reduced to a geometrical maximum-minimum problem in an n-space of known metric. The solution of the geometrical problem reduces the coupled equations of motion to n uncoupled equations whose natural frequencies can always be found by a single quadrature. An infinite class of systems, of which the linear system is a member, has been isolated for which the frequency amplitude can be found in closed form.

Copyright © 1962 by ASME
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