At elevated temperatures the dynamics of vibrating plate (or shell) must include the three thermal effects: (i) the global expansion by 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. For the single-mode prototype model of Galerkin representation, (i) and (ii) give rise to the combined stiffness that is responsible for thermal buckling, whereas (iii) contributes to the combined forcing of acoustic and thermal excitations. For the high-temperature sonic fatigue test facility at the Wright Lab, the present study is devoted to the mean square estimates on transverse displacement and normal stress/strain by the equivalent linearization technique.

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