Complete solutions of a coupled system of partial differential equations arising in thermoelasticity
Author:
D. S. Chandrasekharaiah
Journal:
Quart. Appl. Math. 45 (1987), 471-480
MSC:
Primary 73C25; Secondary 73U05
DOI:
https://doi.org/10.1090/qam/910454
MathSciNet review:
910454
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Abstract: Three general, complete solutions of a coupled hyperbolic or hyperbolic-parabolic system of two second-order linear partial differential equations are presented. The system includes among its particular cases the governing field equations of the conventional as well as generalized thermoelasticity theories. The solutions obtained are analogous to the Lamé, Papkovitch, and Galerkin solutions in classical elasticity. The interrelationships among the solutions are also exhibited. Some solutions obtained in earlier works are deduced as special cases of the unified solutions obtained here.
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W. Nowacki, Dynamic problems of Thermoelasticity, Noordhoff, Leyden, pp. 26–29, 1975
A. E. Green and K. A. Lindsay, Thermoelasticity, J. Elasticity 2, 1–7 (1972)
A. E. Green, A note on linear thermoelasticity, Mathematika 19, 69–75 (1972)
D. S. Chandrasekharaiah, Wave propagation in a thermoelastic half-space, Indian J. Pure. Appl. Math. 12, 226–241 (1981)
H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids 15, 299–309 (1967)
D. S. Chandrasekharaiah, On generalized thermoelastic wave propagation, Proc. Indian Acad. Sci. (Math. Sci). 89, 43–52 (1980)
M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys. 27, 240–253 (1956)
P. Chadwick, Thermoelasticity. The dynamic theory, Progress in Solid Mechanics (Ed. R. Hill and I. N. Sneddon) Vol. 1, North Holland, Amsterdam, 1960
D. E. Carlson, Linear Thermoelasticity, Encyclopedia of Physics, Vol. VI a/2, Springer-Verlag, New York, 1972
D. S. Chandrasekharaiah, Thermoelasticity with second sound—A review, Appl. Mech. Rev. 39, 355–376 (1986)
I. S. Sokolnikoff, Mathematical theory of elasticity, 2nd Ed., McGraw-Hill, New York, 1956
M. E. Gurtin, The linear theory of elasticity, Encyclopedia of Physics, Vol VI a/2, Springer-Verlag, New York, 1972
H. Deresiewicz, Solution of the equations of thermoelasticity, Proc. 3rd U.S. National Congr. Appl. Mech., Brown University, 287–291 (1958)
H. Zorski, Singular solutions for thermoelastic media, Bull. Acad. Poln. Sci. Techn. 6, 331–339 (1958)
H. B. Phillips, Vector Analysis, John Wiley, New York, 1933
E. Sternberg and E. L. McDowell, On the steady state thermoelastic problem for the half-space, Quart. Appl. Math. 14, 381–398 (1957)
J. L. Nowinski, Theory of thermoelasticity with applications, p. 363, Sijthoff-Noordhoff, Alphen Aan Den Rijn, 1978
A. Verruijt, The completeness of Biot’s solution of the coupled thermoelastic problem, Quart. Appl. Math. 26, 485–490 (1969)
W. Nowacki, Dynamic problems of Thermoelasticity, Noordhoff, Leyden, pp. 26–29, 1975
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© Copyright 1987
American Mathematical Society