On Normal Vibrations of a General Class of Nonlinear Dual-Mode Systems

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

Department of Mechanical Engineering, University of California, Berkeley, Calif.

J. Appl. Mech 28(2), 275-283 (Jun 01, 1961) (9 pages) doi:10.1115/1.3641668 History: Received May 31, 1960; Online September 16, 2011


Free vibrations in normal modes are examined for a system consisting of two unequal (or equal) masses, interconnected by a nonlinear coupling spring, and each mass connected by nonlinear unequal (or equal) anchor springs to fixed points. All spring forces are odd functions, and proportional to the k’th power, of the spring deflections, where k is a real, positive number. The frequency-amplitude relations for the in and out-of-phase modes are derived without approximation, the stability of these modes is analyzed, and several numerical examples are worked out. A surprising feature of these systems is that they may have a greater number of normal modes than they have degrees of freedom.

Copyright © 1961 by ASME
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