State space approach to two-dimensional electromagneto-thermoelastic problem with two relaxation times

The model of the two-dimensional equations of generalized magneto-thermoelasticity with two relaxation times in a perfectly conducting medium are established. The method of the matrix exponential, which constitutes the basis of the state space approach of modern theory, is applied to the non-dimensional equations. Laplace and Fourier integral transforms are used. The resulting formulation is applied to a problem of a thick plate subject to heating on parts of the upper and lower surfaces of the plate that varies exponentially with time. Numerical results are given and illustrated graphically for the problem considered. A comparison was made with the results obtained in the absence of a magnetic field. (C) 2001 Elsevier Science Ltd. All rights reserved.