Slaving the In-Plane Motions of a Nonlinear Plate to Its Flexural Motions: An Invariant Manifold Approach

[+] Author and Article Information
I. T. Georgiou, I. B. Schwartz

Special Project for Nonlinear Science, Code 6700.3, Naval Research Laboratory, Washington, DC 20375

J. Appl. Mech 64(1), 175-182 (Mar 01, 1997) (8 pages) doi:10.1115/1.2787270 History: Received June 08, 1995; Revised June 28, 1996; Online October 25, 2007


We show that the in-plane motions of a nonlinear isotropic plate can be decoupled from its transverse motions. We demonstrate this decoupling by showing analytically and numerically the existence of a global nonlinear invariant manifold in the phase space of three nonlinearly coupled fundamental oscillators describing the amplitudes of the coupled fundamental modes. The invariant manifold carries a continuum of slow periodic motions. In particular, for any motion on the slow invariant manifold, the transverse oscillator executes a periodic motion and it slaves the in-plane oscillators into periodic motions of half its period. Furthermore, as the energy level of a motion on the slow manifold increases, the frequency of the largest harmonic of the in-plane motion approaches the in-plane natural frequencies.

Copyright © 1997 by The American Society of Mechanical Engineers
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