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2010 | Vol. 15, no 4 | 1169-1184
Tytuł artykułu

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

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Warianty tytułu
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 and Shulman (1967) is applied. The material of the semi-infinite medium is an 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. 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.
Wydawca

Rocznik
Strony
1169-1184
Opis fizyczny
Bibliogr. 23 poz., wykr.
Twórcy
autor
autor
  • Department of Mathematics, Faculty of Science Zagazig University P.O. Box 44519, Zagazig EGYPT, khlotfy_1@yahoo.com
Bibliografia
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  • 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 (Ph.D. thesis of S. Chakraborty, Jadavpur University).
  • 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 Ignazack J. (1999): Generalised thermo-elasticity. - J. Thermal Stresses, vol.22, pp.541-570.
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  • 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 heat source. - Acta Physica Polonica A, vol.116, pp.186-192.
  • Othman M.I. and Lotfy K.H. (2009): Two-dimensional problem of generalized magneto-thermoelasticity under the effect of temperature dependent properties for different theories. - MMMS, vol.5, pp.235-242.
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Typ dokumentu
Bibliografia
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