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.
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March 1997
Technical Papers
Slaving the In-Plane Motions of a Nonlinear Plate to Its Flexural Motions: An Invariant Manifold Approach
I. T. Georgiou,
I. T. Georgiou
Special Project for Nonlinear Science, Code 6700.3, Naval Research Laboratory, Washington, DC 20375
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I. B. Schwartz
I. B. Schwartz
Special Project for Nonlinear Science, Code 6700.3, Naval Research Laboratory, Washington, DC 20375
Search for other works by this author on:
I. T. Georgiou
Special Project for Nonlinear Science, Code 6700.3, Naval Research Laboratory, Washington, DC 20375
I. B. Schwartz
Special Project for Nonlinear Science, Code 6700.3, Naval Research Laboratory, Washington, DC 20375
J. Appl. Mech. Mar 1997, 64(1): 175-182 (8 pages)
Published Online: March 1, 1997
Article history
Received:
June 8, 1995
Revised:
June 28, 1996
Online:
October 25, 2007
Citation
Georgiou, I. T., and Schwartz, I. B. (March 1, 1997). "Slaving the In-Plane Motions of a Nonlinear Plate to Its Flexural Motions: An Invariant Manifold Approach." ASME. J. Appl. Mech. March 1997; 64(1): 175–182. https://doi.org/10.1115/1.2787270
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