Ali H. Nayfeh, Waleed Faris, "Thermally Induced Principal Parametric Resonance in Circular Plates", Shock and Vibration, vol. 9, Article ID 718921, 8 pages, 2002. https://doi.org/10.1155/2002/718921
Thermally Induced Principal Parametric Resonance in Circular Plates
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.
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