Thermoviscoelastic waves due to time harmonic loads acting on the boundary of a solid halfspace

• Autorzy: Sharma J. N. , Chand R. , Chand D.
• Języki publikacji: EN

Abstrakty

EN

This paper studies the disturbance due to time harmonic normal and thermal point loads acting on the boundary of a homogeneous isotropic thermoviscoelastic solid halfspace. The Kelvin-Voigt model is used to investigate the instant problem in the context of generalized theories of thermoelasticity. The Hankel transform technique has been employed to solve the boundary value problem in the transformed domain. The inverse transform integrals are evaluated by using Romberg integration with adaptive step-size after using the results from successive refinements of recurresive trapezoidal rule and extrapolation of the results to the limit when the step size tends to zero. The temperature and stresses so obtained in the physical domain are computed numerically and presented graphically in different situations for the polymethyl methacrylate material which has wide applications in industry and medicine. A complete and comprehensive analysis and comparison of the results in various theories of generalized thermoviscoelasticity are also presented.

Słowa kluczowe

EN

point loads; generalized thermoelasticity; mechanical relaxation; Kelvin-Voigt; polymethyl methacrylate

PL

tworzywa termoplastyczne; model Kelvina-Voigta; reologia

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2007
• Tom: Vol. 12, no 3
• Strony: 781--797
• Opis fizyczny: Bibliogr. 31 poz., wykr.

Twórcy

autor

Sharma J. N.

autor

Chand R.

autor

Chand D.

• Department of Applied Sciences National Institute of Technology Hamirpur - 177 005 INDIA,

Bibliografia

• Acharya D.P. and Mondal A. ( 2002): Propagation of Rayleigh surface waves with small wavelengths in non-local viscoelastic solids. - Sadhana, vol.27, pp.605-612.
• Ackerman C.C., Bentman B., Fairbank H.A. and Krumhansal R.A. (1966): Second sound in helium. - Phys. Rev. Lett., vol.16, pp.789-791.
• Ackerman C.C. and Overtone W.C. Jr. (1969): Second Sound in Solid Helium-3. - Phys. Rev. Lett.-vol. 22, pp.764-766.
• Cagniard L. (1962): Reflection and Refraction of Progress Seismic Waves. - New York: McGraw - Hill.
• Chandrasekharaiah D.S. ( 1986): Thermoelasticity with second sound-A Review. - Appl. Mech. Rev., vol.39, pp.355-376.
• De-Hoop A.T. (1959): A modification of Cagniard method for solving seismic pulse problems. - Appl. Sci. Res., vol.38, pp.349-356.
• Ewing M., Jardetzky W.S. and Press F. (1957): Elastic waves in layered media. - New York: McGraw Hill, pp.272-280.
• Ezzat M.A. and El-Karamany A.E. (2002): The uniqueness reciprocity theorems for generalized thermo-viscoelasticity with two relaxation times. - Int. J. Eng. Sci., vol. 40, pp.1275-1284.
• Ezzat M.A., Othman M.I.A. and El-Karamany M.S. (2002a): State space approach two-dimensional generalized thermo-viscoelasticity with two relaxation time. - Int. J. Eng. Sci., vol.40, pp.1251-1274.
• Ezzat M.A., Othman M.I.A. and El-Karamany M.S. (2002b): State space approach to generalized thermo-viscoelasticity with two relaxation times. - Int. J. Eng. Sci., vol 40, pp.283-302.
• Fredudenthal A.M. (1954): Effect of rheological behaviour on thermal stresses. - J. Appl. Phys., vol.25, pp.1-10.
• Green A.E. (1972): A note on linear thermoelasticity. - Mathematica, vol.19, pp.69-75.
• Green A.E. and Lindsay K.A. (1972): Thermoelasticity. - J. Elasticity, vol.2, pp.1-7.
• Green A .E. and Nagdhi P.M. (1991): A re-examination of the basic postulates of thermo-dynamics. - Proc. Roy. oc. London Ser. A, vol. 432, pp.171-194.
• Green A.E. and Nagadhi P.M. (1992): On undamped heat waves in an elastic solid. - J. Thermal Stresses, vol.15, pp.252-264.
• Green A.E. and Nagadhi P.M. (1993): Thermoelasticity without energy dissipation. - J. Elasticity, vol.31, pp.189-208.
• Guyer R.A. and Kurmhansal J.A. (1966): Thermal conductivity, second sound and phenon hydrodynamic phenomena in nonmetallic crystals. - Phys. Rev., vol.148, pp.778-781.
• Lord H.W. and Shulman Y. (1967): The generalized dynamical theory of thermoelasticity. - J. Mech. Phys Solids, vol.15, pp.299-309.
• Mukhopadhya B. and Bera R.K. (1989): Effect of distributed instantaneous and continuous heat sources in an infinite conducting magneto-thermo-viscoelastic solid with thermal relaxation. - Comput. Math. Appl., vol.18, pp.728.
• Mukhopadhyay S. (2000): Effects of thermal relaxations on thermoviscoelasticity interactions in an unbounded body with a spherical cavity subjected to a periodic loading on the boundary. - J. Thermal Stresses, vol.23, pp.675-684.
• Nayfeh A. and Nasser S.N. (1972): Transient thermoelastic waves in a half space with thermal relaxations. - J. App. Math. Physics, vol.23, pp.50-67.
• Othman M.I.A., Ezzat M.A., Zaki S.A. and El-Karamany A.S. (2002): Generalized thermoviscoelastic plane waves with two relaxation times. - Int. J. Eng. Sci., vol.40, pp.1329-1347.
• Press W.H., Teukolky S.K., Velleraing W.T. and Flannery B.P. (1992) Numerical Recipes in FORTRAN, 2nd. Edition, Cambridge University Press.
• Sharma J.N. (1986): Transient generalized thermoelastic waves in a transversely isotropic half-space. - Bull. Polish Acad. Sci. Tech. Sci., vol.34, pp.632-646.
• Sharma J.N., Chauhan R.S. and Kumar R. (2000): Time harmonic sources in a generalized thermoelastic continuum. - J. Thermal Stresses, vol.23, pp.657-674.
• Sharma J.N. and Chauhan R.S. (2001): Mechanical loads and heat sources in a generalized thermoelastic half space. - J. Thermal Stresses, vol.24, pp.651-675.
• Sharma J.N. and Sharma P.K. (2001): On the transient thermoelastic waves. - Int. J. Mech. Eng., vol.6, pp.923-946.
• Sharma J.N. and Chand R. (2005): Transient thermoviscoelastic waves in a half space due to thermal loads. - Thermal Stresses, vol.28, pp.1-20.
• Sharma J.N., Chand R. and Chand D. (2006): Forced vibrations due to mechanical loads in thermo-viscoelastic half spaces. - Int. J. Applied Mech. and Eng., vol.11, pp.105-121.
• Strunin D.V. (2001): On characteristics times in generalized thermoelasticity. - J. Applied Maths, vol.68, pp.816-817.
• Voigt W. (1887): Theortische student uberdie Elasticitats Verhalinisse Krystalle. - Abs. Ges. Wiss. Goettingen 34.