Boundary-initiated wave phenomena in thermoelastic materials
Authors:
T. S. Öncü and T. B. Moodie
Journal:
Quart. Appl. Math. 48 (1990), 295-320
MSC:
Primary 73B30; Secondary 73D99
DOI:
https://doi.org/10.1090/qam/1052138
MathSciNet review:
MR1052138
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Abstract: The linear theory of Gurtin and Pipkin, and Chen and Gurtin is adopted to study one-dimensional progressive waves generated by thermal and mechanical disturbances applied at the boundary of a circular hole in an unbounded homogeneous thermoelastic medium. A ray-series approach is employed to generate asymptotic wavefront expansions for the field variables. The characteristics of the propagation process are obtained simply and directly. The solution is then specialized to the case where this theory reduces to the linearized theory of Lord and Shulman, and numerical results for various values of material parameters obtained from the ray-series solution in conjunction with the use of Padé approximants are displayed graphically.
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C. Cattaneo, Sulla conduzione del colore, Atti Sem. Mai. Fis. Univ. Modena 3, 83–101 (1948)
M. P. Vernotte, Les paradoxes de la théorie continue de l’equation de la chaleur, C.R. Acad. Sci. Paris 246, 3154–3155 (1958)
C. Cattaneo, Sur une forme de l’equation de la chaleur éliminant le paradox d’une propagation instantanée, C.R. Acad. Sci. Paris 247, 431–433 (1958)
M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rat. Mech. Anal. 31, 113–126 (1968)
J. W. Nunziato, On heat conduction in materials with memory, Quart. Appl. Math. 29, 187–204 (1971)
A. E. Green and N. Laws, On the entropy production inequality, Arch. Rational Mech. Anal. 45, 47–53 (1972)
H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids 15, 299–209 (1967)
N. Fox, Generalized thermoelasticity, Internat. J. Engrg. Sci. 7, 437–445 (1969)
P. J. Chen and M. E. Gurtin, On second sound in materials with memory, Z. Angew. Math. Phys. 21, 232–242 (1970)
I. Müller, Die Kältefunktion, eine universelle Funktion der Thermodynamik viskoser wärmeleitender Flüssigkeiten, Arch. Rational Mech. Anal. 40, 1–36 (1971)
I. Müller, The coldness, a universal function in thermoelastic bodies, Arch. Rational Mech. Anal. 41, 319–322 (1971)
A. E. Green and K. A. Lindsay, Thermoelasticity, J. Elasticity 2, 1–7 (1972)
E. S. §uhubi, Thermoelastic solids, Continuum Physics, Vol II (A. C. Eringen, ed.), Academic Press, New York, 1975, p. 174
R. P. Sawatzky and T. B. Moodie, On thermoelastic transients in a general theory of heat conduction with finite wave speeds, Acta Mech. 56, 165–187 (1985)
B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178 (1963)
B. D. Coleman, Thermodynamics of materials with memory, Arch. Rational Mech. Anal. 17, 1–45 (1964)
T. B. Moodie and R. J. Tait, On thermal transients with finite wave speeds, Acta Mech. 50, 97–109 (1983)
M. F. McCarthy, T. B. Moodie, and R. P. Sawatzky, On the propagation of transients through thermoviscoelastic media, Quart. Appl. Math. 46, 539–557 (1988)
J. D. Achenbach, The influence of heat conduction on propagating stress jumps, J. Mech. Phys. Solids 16, 273–282 (1968)
P. Chadwick, Thermoelasticity, the dynamical theory, Progress in Solid Mechanics, Vol. I (J. N. Sneddon and R. Hill, eds.), North-Holland Publishing Company, 1960, p. 265
P. J. Chen and J. W. Nunziato, Thermodynamic restrictions on the relaxation functions of the theory of heat conduction with finite wave speeds, Z. Agnew. Math. Phys. 25, 791–797 (1974)
H. W. Lord and A. A. Lopez, Wave propagation in thermoelastic solids at very low temperature, Acta Mech. 10, 85–98 (1970)
Y. H. Pao and D. K. Banerjee, Thermal pulses in dielectric crystals, Let. Appl. Engrg. Sci. 1, 33–41 (1973)
A. H. Nayfeh, Propagation of thermoelastic disturbances in non-Fourier solids, AIAA J. 15, 957–960 (1977)
T. S. Öncü and T. B. Moodie, Finite speed thermal transients generated by nonuniform sources applied to circular boundaries in inhomogeneous conductors, Internat. J. Engrg. Sci. 27, 611–621 (1989)
R. J. Atkin and N. Fox, An Introduction to the theory of elasticity, Longman, London and New York, 1980
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© Copyright 1990
American Mathematical Society