Kármán-Mindlin plate equations for thermoelastic vibrations of temperature-dependent materials

Abstract

In relation to temperature-dependent anisotropic materials, this paper develops the two-dimensional dynamic equations of an elastic plate with large deflections under the thermomechanical loading. The nonisothermal plate equations, formulated in invariant differential and invariant variational forms, are deduced from the three-dimensional equations of coupled thermoelasticity with second sound by means of a recent variational principle together with Mindlin’s kinematic hypothesis of elastic plates. Some cases involving special material, motion, and geometry are indicated, and a theorem of uniqueness is derived so as to ensure unique solutions of the fully linearized thermoelastic plate equations.