Thermoelastic Waves in a Constrained Isotropic Plate: Incompressibility at Uniform Entropy

Abstract

Thermoelastic waves are investigated which propagate through an isotropic plate which is constrained to be incompressible at uniform entropy. This is an example of a deformation-entropy constraint, also known as a strain-entropy constraint. The boundaries of the plate are taken to be traction-free and either isothermal or insulated. Dispersion relations are derived and expanded asymptotically in the long-wave low-frequency limit. The short-wave limit is discussed. Thermal dissipation is also discussed. The higher modes are investigated numerically. Graphical comparison with a material incompressible at uniform temperature is also presented.