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Shock and Vibration
Volume 9, Issue 3, Pages 143-150

Thermally Induced Principal Parametric Resonance in Circular Plates

Ali H. Nayfeh and Waleed Faris

Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA

Received 3 July 2001; Revised 29 October 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the problem of large-amplitude vibrations of a simply supported circular flat plate subjected to harmonically varying temperature fields arising from an external heat flux (aeroheating for example). The plate is modeled using the von Karman equations. We used the method of multiple scales to determine an approximate solution for the case in which the frequency of the thermal variations is approximately twice the fundamental natural frequency of the plate; that is, the case of principal parametric resonance. The results show that such thermal loads produce large-amplitude vibrations, with associated multi-valued responses and subcritical instabilities.