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Transient thermo-elastic disturbances in a visco-elastic semi-space due to a moving internal heat source

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Języki publikacji
EN
Abstrakty
EN
This paper investigates the transient disturbances created by an internal line heat source that suddenly starts moving uniformly inside a visco-elastic half-space. The generalised theory of thermo-elasticity with relaxation time proposed by Lord-Shulman (1967) is applied. The material of the semi-infinite medium is isotropic visco-elastic solid of Kelvin-Voight type. Applying the Fourier and Laplace transform technique, expressions for displacement components in the transformed domain are found out. These expressions prove the existence of three waves - a modified thermal wave, a visco-elastic wave of defused nature and a transverse visco-elastic wave. Surface displacement components are evaluated on the boundary for small time only. Numerical results are given and illustrated graphically to highlight the variations of surface displacement components with distance for different values of time, source depth and velocity of the source.
Rocznik
Strony
747--762
Opis fizyczny
Bibliogr. 23 poz., wykr.
Twórcy
autor
  • Department of Mathematics, Faculty of Science Zagazig University, P.O. Box 44519, Zagazig EGYPT, khlotfy_1@yahoo.com
Bibliografia
  • Baksi A. and Bera R.K. (2005): Eigenfunction expansion method for the solution of magneto-thermo-elastic problems with thermal relaxation and heat source in three dimensions. - Mathematical and Computer Modelling, vol.42, pp.533-552.
  • Banerjee S. and Roychoudhuri S.K. (1995): Spherically symmetric thermo-visco-elastic waves in a visco-elastic medium with a spherical cavity. - Computers Math. Applic., vol.30, No.1, pp.91-98.
  • Chandrasekharaiah D.S. (1986): Thermo-elasticity with second sound, a review. - Appl. Mech. Rev., vol.39, No.3, pp.354-376.
  • Chandrasekharaiah D.S. (1996): Thermo-elastic plane waves without energy dissipation. - Mech. Res. Comm., vol.23, pp.549-555.
  • Chakraborty S. (1998): Transient disturbances in a relaxing thermo-elastic half-space due to a suddenly moving internal line heat source. - Int. J. Maths. And Maths. Sci., vol.21. No.3, pp.595-602.
  • Eringen A.C. (1967): Mechanics of Continua - New York: Wiley.
  • Ezzat M.A., Othman M.I. and El-Karmany A.S. (2001): Electro-magneto-thermo-elastic plane waves with thermal relaxation in a medium of perfect conductivity. - Journal of Thermal Stresses, vol.24, pp.411-432.
  • Ezzat M.A. and Othman M. (2000): Electromagneto-thermo-elastic plane waves with two relaxation times in a medium of perfect conductivity. - Int. J. Eng. Sci., vol.38, pp.107-120.
  • Green A.E. and Lindsay K.A. (1972): Thermo-elasticity. - J. Elasticity, vol.2. No.1, pp.1-7.
  • Green A.E. and Naghdi P.M. (1992): On undamped heat waves in an elastic solid. - J. Thermal Stresses, vol.15, pp.253-254.
  • Green A.E. and Naghdi P.M. (1993): Thermo-elasticity without energy dissipation. - J. Elasticity, vol.31, pp.189-208.
  • Hetnarski R.B. and Ignaczak J. (1999): Generalised thermo-elasticity. - J. Thermal Stresses, vol.22, pp.541-570.
  • Ignaczak J. (1991): Domain of influence results in generalised thermo-elasticity - a survey. - Appl. Mech. Rev., vol.44, No.9, pp.375-382.
  • Lord H.W. and Shulman Y. (1967): A generalised dynamical theory of thermo-elasticity. - J. Mech. Phys. Solids, vol.15, No.5, pp.299-309.
  • Mukhopadhyay B. and Bera R.K. (1992): Effect of thermal relaxation on electro-magneto-thermo-visco-elastic plane waves in rotating media. - Int. J. Eng. Sci., vol.30, No.3, pp.350-369.
  • Nayfeh A. and Nemat-Nasser S. (1972): Transient thermo-elastic waves in a half-space with thermal relaxation. - J. Appl. Math. Phys., (ZAMP), vol.23, pp.50-68.
  • Othman M.I. (2004): Relaxation effects on thermal shock problem in an elastic half-space of generalised magneto-thermo-elastic waves. - Mechanics and Mechanical Eng., vol.7, No.2, pp.165-178.
  • Othman M.I. and Song Y. (2006): The effect of rotation on the reflection of magneto-thermoelastic waves under thermoelasticity without energy dissipation. - Acta Mechanica, vol.184, pp.189-204.
  • Othman M.I., Lotfy K.H. and Farouk R.M. (2009): Transient disturbance in a half- space under generalized magneto- thermoelasticity due to moving internal heats source. - Acta Physica Polonica A, vol.116, pp.186-192.
  • Othman M.I. and Lotfy K.H. (2009): Two-dimensional problem of generalized magnetothermoelasticity under the effect of temperature dependent properties for different theories. - MMMS, vol.5, pp.235-242.
  • Roy Choudhuri S.K. and Chatterjee G. (1990): Spherically symmetric thermo-elastic waves in a temperature-rate dependent medium with a spherical cavity. - Computers Math. Applic., vol.20. No.11, pp.1-12.
  • Song Y.Q. and Zhang Y.C. (2006): Magneto-thermo-visco-elastic wave propagation at the interface between two micropolar visco-elastic media. - Appl. Maths. and Computation, vol.176, pp.785-802.
  • Tiersten H.F. (1964): Coupled magneto-mechanical equations for magnetically saturated insulator. - J. Math. Phys., vol.5, No.9, pp.1-21.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ5-0017-0029
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