Thermally Induced Principal Parametric Resonance in Circular Plates

Abstract

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.

Dynamic stability of laminated FGM plates based on higher-order shear deformation theory

“…Marcus et al (1995) examined the dynamic stability of symmetrically laminated orthotropic rectangular plates due to a thermally oscillating load by using an extension of Bolotin's theory. Nayfeh and Faris (2002) discussed the principal parametric resonance of a simply supported circular plate subjected to harmonically varying temperature fields arising from an external heat flux. Takahashi and Furutani (1995) dealt with the dynamic stability of a non-uniform rectangular cantilever plate on a Pasternak foundation under the action of a pulsating in-plane load and a thermal gradient.…”

Modal interactions in the vibrations of a heated annular plate

“…They applied the Kantorovich averaging method and examined the non-linear natural frequencies and thermal buckling loads. Nayfeh and Faris [25] investigated the non-linear vibrations of a simply supported circular plate under a thermally induced principal parametric excitation of an axisymmetric mode (i.e., ≈2! 0k ).…”