Some theorems in temperature-rate-dependent theory of thermoelasticity. (English) Zbl 0542.73005
The paper proves three theorems: Uniqueness of solution basing on the assumption of the positive definiteness of the energy function; a variational principle of Hamilton type for the field equations; a general reciprocal theorem of Betti-Rayleigh type for linearized anisotropic thermoelastic interactions, including as special cases some known theorems of a similar type.
Reviewer: J.L.Nowinski
MSC:
74F05 | Thermal effects in solid mechanics |
74G30 | Uniqueness of solutions of equilibrium problems in solid mechanics |
74H25 | Uniqueness of solutions of dynamical problems in solid mechanics |
74B99 | Elastic materials |
74H99 | Dynamical problems in solid mechanics |
74A15 | Thermodynamics in solid mechanics |
Keywords:
temperature-rate-dependent theory of thermoelasticity; second-sound effect; positive definiteness; energy function; variational principle of Hamilton type; field equations; general reciprocal theorem; Betti- Rayleigh type; linearized anisotropic thermoelastic interactionsReferences:
[1] | Ackerman, C. C.; Bentman, B.; Fairbank, H. A.; Guyer, R. A., Phys. Rev. Lett., 16, 789-789 (1966) · doi:10.1103/PhysRevLett.16.789 |
[2] | Ackerman, C. C.; Overton, W. C., Phys. Rev. Lett., 22, 764-764 (1969) · doi:10.1103/PhysRevLett.22.764 |
[3] | Agarwal, V. K., Acta Mech., 31, 185-185 (1979) · Zbl 0393.73121 · doi:10.1007/BF01176847 |
[4] | Agarwal, V. K., Acta Mech., 34, 181-181 (1979) · Zbl 0428.73094 · doi:10.1007/BF01227983 |
[5] | Biot, M. A., J. Appl. Phys., 27, 240-240 (1956) · Zbl 0071.41204 · doi:10.1063/1.1722351 |
[6] | Chandrasekharaiah, D. S., Proc. Indian Acad. Sci. (Math. Sci.), 89, 43-43 (1980) · Zbl 0433.73014 · doi:10.1007/BF02881024 |
[7] | Chandrasekharaiah, D. S., Indian J. pure appl. Math., 12, 226-226 (1981) · Zbl 0491.73015 |
[8] | Chandrasekharaiah D SJ. Elast. (In press) |
[9] | Green, A. E.; Lindsay, K. A., J. Elast., 2, 1-1 (1972) · Zbl 0775.73063 · doi:10.1007/BF00045689 |
[10] | Green, A. E., Mathematika, 19, 69-69 (1972) · Zbl 0351.73037 · doi:10.1112/S0025579300004952 |
[11] | Ionescu-Cazimir, V., Bull. Poln. Sci. Technol., 12, 473-473 (1964) |
[12] | Ionescu-Cazimir, V., Bull. Poln. Sci. Technol., 12, 565-565 (1964) |
[13] | Nowacki, W., Dynamical problems of Thermoelasticity, 311-311 (1975), Leyden: Noordhoff Int. Publ. Co, Leyden · Zbl 0364.73001 |
[14] | Parkus, H., Variational principles in Thermo- and magneto-elasticity, 11-11 (1972), Wien: Springer-Verlag, Wien · Zbl 0272.49018 |
[15] | Suhubi, E. S.; Eringen, A. C., Continuum Physics II, 191-191 (1975), New York: Academic Press, New York |
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