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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2011, Volume 52, Issue 4, Pages 169–182
(Mi pmtf1514)
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This article is cited in 24 scientific papers (total in 24 papers)
State space approach to the generalized thermoelastic problem with temperature-dependent elastic moduli and internal heat sources
M. I. A. Othman Zagazig University, Zagazig, 44519, Egypt
Abstract:
A two-dimensional equation of generalized thermoelasticity with one relaxation time in an isotropic elastic medium with the elastic modulus dependent on temperature and with an internal heat source is established using a Laplace transform in time and a Fourier transform in the space variable. The problem for the transforms is solved in the space of states. The problem of heating of the upper and the lower surface of a plate of great thickness by an exponential time law is considered. Expressions for displacements, temperature, and stresses are obtained in the transform domain. The inverse transform is obtained using a numerical method. Results of solving the problem are presented in graphical form. Comparisons are made with the results predicted by the coupled theory and with the case of temperature independence of the elastic modulus.
Keywords:
thermoelasticity, space of states, relaxation time, Laplace and Fourier transforms.
Received: 24.05.2010
Citation:
M. I. A. Othman, “State space approach to the generalized thermoelastic problem with temperature-dependent elastic moduli and internal heat sources”, Prikl. Mekh. Tekh. Fiz., 52:4 (2011), 169–182; J. Appl. Mech. Tech. Phys., 52:4 (2011), 644–656
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https://www.mathnet.ru/eng/pmtf1514 https://www.mathnet.ru/eng/pmtf/v52/i4/p169
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