State space approach to two-dimensional generalized thermo-viscoelasticity with two relaxation times

• Published in: International journal of engineering science Vol. 40; no. 11; pp. 1251 - 1274
• Main Authors: Ezzat, Magdy A., Othman, Mohamed I., El-Karamany, Ahmed M.S.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.07.2002; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Viscoelasticity; Two dimensional equation; Heat source; Fourier transformation; Thermomechanical properties; Two dimensional model; Thick plate; Laplace transformation; State space method; Modeling; Integral transformation; Relaxation time
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/S0020-7225(02)00012-5

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.