Deformation and Thermal Stress in a Rectangular Plate Subjected to Aerodynamic Heating : For the Case of Simply Supported Edges

Large-Amplitude Plate Vibration in an Elevated Thermal Environment

“…Approved for public release; distribution is anlimited 13. ASSTRACT (Madmum,200 word a't ,-levated temperatures the dynamics of vibrating plate (or shell) must include the three thermal effects: (i) the global expansion that is due to uniform plate temperature, (ii) the local expansion by temperature variation over the plate, and (iii) the thermal moment induced by temperature gradient across the plate thickness.…”

“…(2.8) in cosines, we write in view of Eq. (2.13) Also, a similar expansion in cosines is assumed for T [13] -to + to tpcospnX cosqiy,…”

“…Sunakawa and Uemura (13] On the other hand, to the best of our knowledge no attempt has yet been made to either measure or impose certain temperature gradient distribution through the plate thickness.…”

Topology of the Four-Mode Strain Energy of Thermally Buckling Plates

“…The heated plate was originally studied to model the aerodynami c heating of aircraft skin panels in supersonic and hypersonic¯ights [1,2]. Basically, the three displacements of plate motion are governed by coupled equations with the von Karman type of geometric nonlinearity, whereby the strain-displacement relations include up to second-order displacement terms [3].…”

“…Hence, each and every one of the cubic modal amplitude terms accounts for energy conservation, although being Hamiltonian is a much stronger dynamical property than being energy-conserving . Clearly, the existence of a Hamiltonian is anticipated because plate equations, heated or not, are the embodiment of the conservation of total energy [1,2]. In this article, the aforementioned di culties of the Galerkin procedure are overcome by using the symbolic manipulation software MATHEMATICA (TM) [24] (though some other software might also have been used).…”