Propagation of discontinuities in thermopiezoelectric rod

A model of the equations of generalized linear thermoelasticity theory for piezoelectric media is given. The formulation is applied to the generalized thermoelasticity theories-Lord-Shulman, Green-Lindsay, and Chandrasekharaiah and Tzou-as well as to the dynamic coupled theory. The state space approach is adopted for the solution of the one-dimensional problem of a semi-infinite piezoelectric rod. The Laplace transform technique is used. The expansions of the stress component, the temperature increment, the electric field, and the displacement, in Laplace transform domain, in power series, and the exact inversions for arbitrary time are given. The jump discontinuities are calculated for the four theories and the kinematical conditions of compatibility are verified. Numerical results are given and illustrated graphically by employing the numerical method for the inversion of the Laplace transforms. Comparisons are made with the results predicted by the four theories.