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.
Highlights
The static and dynamic behavior of flat and curved plates, including isotropic and composite plates, subjected to thermal loads is a problem of considerable relevance in the design and development of supersonic/hypersonic vehicles, reusable space transportation, and launch vehicles [11]
Other applications could be found in thermally actuated composite diaphragms [19], pressure sensors that are used in automotive engines, compensation of thermally induced effects in force resonant sensors [6], and brake discs and rotors
Most of the previous research on thermally induced vibrations in circular plates has been limited to solving for small deflections
Summary
The static and dynamic behavior of flat and curved plates, including isotropic and composite plates, subjected to thermal loads is a problem of considerable relevance in the design and development of supersonic/hypersonic vehicles, reusable space transportation, and launch vehicles [11]. The first category includes the studies of Heldenfels and Roberts [7] and Gatewood [5] who solved the thermal flat plate problem for small deflections and constant temperature distributions. Sokolnikoff and Sokolnikoff [20] studied the linear thermal stresses in clamped elastic plates under constant linear temperature distributions and showed that the solution is similar to the solution of equivalent transverse loaded elastic plates. This point was later elaborated by Boley and Weiner [3]. Faris / Thermally induced principal parametric resonance in circular plates. We consider the case of principal parametric resonance
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