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State space approach to two-dimensional generalized thermo-viscoelasticity with two relaxation times. (English) Zbl 1211.74068
Summary: The model of the two-dimensional equations of generalized thermo-viscoelasticity with two relaxation times is established. The state space formulation for two-dimensional problems is introduced. 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. 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. Comparisons are made with the results predicted by the coupled theory.

MSC:
74F05Thermal effects in solid mechanics
74D05Linear constitutive equations (materials with memory)
74H15Numerical approximation of solutions for dynamical problems in solid mechanics
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References:
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