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The theory of generalized thermoelasticity, based on the theory of Lord and Shulman with one relaxation time, is used to study the electromagneto-thermoelastic interactions in a semi-infinite perfectly conducting solid subjected to a thermal shock on its surface when the solid and its adjoining vacuum is subjected to a uniform axial magnetic field. The solid deforms because of thermal shock, and due to the application of the magnetic field, there result an induced magnetic and an induced electric field in the solid. The Maxwell's equations are formulated and the generalized electromagneto-thermoelastic coupled governing equations are established. Based on these governing equations, the generalized electromagneto-thermoelastic coupled finite element equations are first formulated in this paper. By means of the Laplace transform and numerical Laplace inversion the problem is solved. The distributions of the considered physical variables are represented graphically. From the distributions, it can be found the electromagnetic-thermoelastic coupled effects and the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier's in essence.

The theory of generalized thermoelasticity, based on the theory of Green and Lindsay with two relaxation times, is used to deal with a thermoelastic–piezoelectric coupled two-dimensional thermal shock problem of a thick piezoelectric plate of infinite extent by means of the hybrid Laplace transform-finite element method. The generalized thermoelastic–piezoelectric coupled finite element equations are formulated. By using Laplace transform the equations are solved and the solutions of the temperature, displacement and electric potential are obtained in the Laplace transform domain. Then the numerical inversion is carried out to obtain the temperature, displacement and electric potential distributions in the physical domain. The distributions are represented graphically. From the distributions, it can be found the wave type heat propagation in the piezoelectric plate. The heat wavefront moves forward with a finite speed in the piezoelectric plate with the passage of time. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier’s in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in media.