State space approach to one-dimensional thermal shock problem for a semi-infinite piezoelectric rod

The theory of generalized thermoelasticity, based on the theory of Lord and Shulman with one relaxation time, is used to solve a boundary value problem of one-dimensional semi-infinite piezoelectric rod with its left boundary subjected to a sudden heat. The governing partial differential equations are solved in the Laplace transform domain by the state space approach of the modern control theory. Approximate small-time analytical solutions to stress, displacement and temperature are obtained by means of the Laplace transform and inverse transform. It is found that there are two discontinuous points in both stress and temperature solutions. Numerical calculation for stress, displacement and temperature is carried out and displayed graphically. [Copyright &y& Elsevier]