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Afrika Matematika

, Volume 29, Issue 3–4, pp 451–462 | Cite as

Propagation of waves in micropolar thermodiffusion elastic half-space

  • Rajneesh Kumar
  • Sachin Kaushal
  • M. Marin
Article
  • 35 Downloads

Abstract

The present paper is devoted to the study of propagation of plane waves in micropolar thermodiffusion elastic half-space in the context of generalized theories of thermoelasticity. The variations of amplitude ratios for plane waves (longitudinal wave, thermal wave and mass diffusive wave) are computed analytically and depicted graphically for longitudinal wave against the angle of incidence. The impact of relaxation times, micropolarity and diffusion have been studied. Some particular cases of interest are also deduced from the present investigation.

Keywords

Micropolar Thermodiffusion Amplitude ratios Plane waves 

Mathematics Subject Classification

74F05 74J05 76R50 

References

  1. 1.
    Eringen, A.C.: In: Lieboneitz, H. (ed.) Theory of micropolar elasticity, In Fracture. Academic, New York (1968)Google Scholar
  2. 2.
    Eringen, A.C.: Plane waves in non-local micropolar elasticity. Int. J. Eng. Sci. 22, 1113–1121 (1984)CrossRefzbMATHGoogle Scholar
  3. 3.
    Touchert, T.R., Claus Jr., W.D., Ariman, T.: The linear theory of micropolar thermoelasticity. Int. J. Eng. Sci. 6, 37–47 (1968)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dost, S., Tabarrok, B.: Genralized micropolar thermoelasticity. Int. J. Eng. Sci. 16(3), 173–183 (1978)CrossRefzbMATHGoogle Scholar
  5. 5.
    Marin, M., Florea, O.: On temporal behaviour of solutions in thermoelasticity of porous micropolar bodies. Ann. Sci. Univ. Ovidius Constanta 22(1), 169–188 (2014)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Sharma, K., Marin, M.: Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids. Ann. Sci. Univ. Ovidius Constanta 22(2), 151–175 (2014)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Marin, M.: On the minimum principle for dipolar materials with stretch. Nonlinear Anal. RWA 10(3), 1572–1578 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Sherief, H.H., Saleh, H., Hamza, F.: The theory of generalized thermoelastic diffusion. Int. J. Eng. Sci. 42, 591–608 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Aouadi, M.: Generalized theory of thermoelasic diffusion for an anisotropic media. J. Therm. Streses 31, 270–285 (2008)CrossRefGoogle Scholar
  10. 10.
    Sherief, H.H., El-Maghraby, N.M.: A thick plate problem in the theory of generalized thermoelastic diffusion. Int. J. Thermophys. 30, 2044–2057 (2009)CrossRefGoogle Scholar
  11. 11.
    Kumar, R., Kaushal, S., Miglani, A.: Elastodynamic response of various sources in micropolar thermodiffusive elastic medium. Int. J. Appl. Mech. Eng. 15(1), 63–98 (2010)zbMATHGoogle Scholar
  12. 12.
    Kumar, R., Kaushal, S., Miglani, A.: Disturbance due to concentrated sources in a micropolar thermodiffusive medium. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 225(2), 437–450 (2011)CrossRefGoogle Scholar
  13. 13.
    Lord, H., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solid 15, 299–309 (1957)CrossRefzbMATHGoogle Scholar
  14. 14.
    Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2, 1–7 (1972)CrossRefzbMATHGoogle Scholar
  15. 15.
    Kumar, R., Singh, B.: Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic half-space with stretch. Indian J. Pure Appl. Math. 29(6), 657–669 (1998)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Singh, B.: Reflection of P and SV waves from free surface of an elastic soild with generalized thermodiffusion. J. Earth Syst. Sci. 114(2), 159–168 (2005)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Thomas, L.: Fundamental of Heat Transfer. Prentice hall Inc-Englewmd Diffs, Newjersey (1980)Google Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsKurukshetra UniversityKurukshetraIndia
  2. 2.Department of Mathematics, School of Chemical Engineering and Physical SciencesLovely Professional UniversityPhagwaraIndia
  3. 3.Department of MathematicsUniversity of BrasovBrasovRomania

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