The dynamic behavior of a rectangular thin plate under parametric and external excitations is investigated. The motion of the thin plate is modeled by coupled second-order nonlinear ordinary differential equations. Their approximate solutions are sought by applying the method of multiple scales. A reduced system of four first-order ordinary differential equations is determined to describe the time variation of the amplitudes and phases of the vibration in the horizontal and vertical directions. The steady-state response and the stability of the solutions for various parameters are studied numerically, using the frequency-response function and the phase-plane methods. It is also shown that the system parameters have different effects on the nonlinear response of the thin plate. Moreover, the chaotic motion of the thin plate is found by numerical simulation.
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October 2010
Research Papers
Nonlinear Vibrations of a Thin Plate Under Simultaneous Internal and External Resonances
Usama H. Hegazy
Usama H. Hegazy
Department of Mathematics, Faculty of Science,
e-mail: u.hejazy@alazhar.edu.ps, uhijazy@yahoo.com
Al-Azhar University
, P.O. Box 1277, Gaza, Palestine
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Usama H. Hegazy
Department of Mathematics, Faculty of Science,
Al-Azhar University
, P.O. Box 1277, Gaza, Palestinee-mail: u.hejazy@alazhar.edu.ps, uhijazy@yahoo.com
J. Vib. Acoust. Oct 2010, 132(5): 051004 (9 pages)
Published Online: August 19, 2010
Article history
Received:
April 11, 2009
Revised:
January 25, 2010
Online:
August 19, 2010
Published:
August 19, 2010
Citation
Hegazy, U. H. (August 19, 2010). "Nonlinear Vibrations of a Thin Plate Under Simultaneous Internal and External Resonances." ASME. J. Vib. Acoust. October 2010; 132(5): 051004. https://doi.org/10.1115/1.4001502
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