Coupled thermomechanical waves in hyperbolic thermoelasticity

Abstract

Using models incorporating a thermal relaxation time (hyperbolic models), we study the properties of spatially periodic thermoelastic waves propagating in an infinite rod. Analyzing the Lord-Schulman and Green-Lindsay linear models, we reveal dependencies of decay rates and frequency shifts of temperature and displacement upon the wave number for the case of weak thermoelastic coupling. We explore numerically a general nonlinear hyperbolic model, describing the time evolution of initially sinusoidal distributions of displacement and temperature. Mechanisms of nonlinear interaction between thermal and mechanical fields are qualitatively analyzed. It is demonstrated that larger relaxation times may provide smoother temperature profiles at an intermediate stage of the dynamics.