Thermoelastic Dissipation in Vibrating Plates

Abstract

The thermal dissipation associated with the natural modes of free vibration of a thermoelastic medium is obtained as an integral formula involving the mode of vibration and the temperature produced in the mode. The integral formula for dissipation is applied to an infinite isotropic plate, and numerical results are given for the three lowest, real, symmetric branches of the spectrum. Finally, it is shown that low-frequency extensional vibrations of plates can be adiabatic or isothermal, depending on whether adiabatic or isothermal boundary conditions are specified on the faces of the plate.