Normal Modes of Nonlinear Dual-Mode Systems

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

Mechanical Engineering: Mechanics and Design, University of California, Berkeley, Calif.

J. Appl. Mech 27(2), 263-268 (Jun 01, 1960) (6 pages) doi:10.1115/1.3643948 History: Received February 27, 1959; Online September 16, 2011


A system consisting of two unequal masses, interconnected by a coupling spring, and each connected to an anchor spring, is examined. The springs may all be unequal and nonlinear, but each resists being compressed to the same degree as being stretched. The concept of normal modes is rigorously defined, and methods of finding them are given. A knowledge of these modes reduces the coupled system to two uncoupled ones which can always be integrated in quadrature. There exists an infinity of systems, of which the linear is one, which can be integrated in closed form. This approach yields, even for the linear system, new results of great simplicity.

Copyright © 1960 by ASME
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