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STATE SPACE APPROACH TO THE GENERALIZED THERMOELASTIC PROBLEM WITH TEMPERATURE-DEPENDENT ELASTIC MODULI AND INTERNAL HEAT SOURCES
Faculty
Not Specified
Year:
2011
Type of Publication:
Article
Pages:
644-656
Authors:
Othman, M. I. A
DOI:
10.1134/S0021894411040183
Journal:
JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS SPRINGER
Volume:
52
Research Area:
Mechanics; Physics
ISSN
ISI:000297623000018
Keywords :
thermoelasticity, space of states, relaxation time, Laplace and Fourier transforms
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.
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