State-space approach to two-dimensional generalized thermoelasticity problems

In this work the state-space formulation for two-dimensional problems of generalized thermoelasticity with one relaxation time is introduced. Laplace and Fourier integral transforms are used The resulting formulation is applied to a problem of a thick plate subject to heating that varies exponentially with time on parts of its upper and lower surfaces. The Fourier transforms are inverted analytically. A numerical method is employed for the inversion of the Laplace transforms. Numerical results are given and illustrated graphically for the problem considered.