SV Shock and Vibration 1875-9203 1070-9622 IOS Press 718921 10.1155/2002/718921 Thermally Induced Principal Parametric Resonance in Circular Plates Nayfeh Ali H. 1 Faris Waleed 1 Department of Engineering Science and Mechanics MC 0219 Virginia Polytechnic Institute and State University Blacksburg Virginia 24061 USA vt.edu 2002 9 3 143 150 3 7 2001 29 10 2001 2002 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.

http://dx.doi.org/10.13039/100000181 Air Force Office of Scientific Research F49620-98-1-393