Advertisement

Meccanica

, 44:305 | Cite as

Lamb waves in micropolar thermoelastic solid plates immersed in liquid with varying temperature

  • J. N. Sharma
  • Satish Kumar
Article

Abstract

In the present paper the theory of micropolar generalized thermoelastic continua has been employed to study the propagation of plane waves in micropolar thermoelastic plates bordered with inviscid liquid layers (or half-spaces) with varying temperature on both sides. The secular equations in closed form and isolated mathematical conditions are derived and discussed. Thin plate and short wave length results have also been deduced under different cases and situations and discussed as special cases of this work. The results in case of conventional coupled and uncoupled theories of thermoelasticity can be obtained both in case of micropolar elastic and elastokinetics from the present analysis by appropriate choice of relevant parameters. The various secular equations and relevant relations have been solved numerically by using functional iteration method in order to illustrate the analytical developments. Effect of characteristic length and coupling factors have also been studied on phase velocity. The computer simulated results in case of phase velocity, attenuation coefficient and specific loss of symmetric and skew symmetric are presented graphically.

Keywords

Micropolar Interfacial waves Generalized thermoelasticity Characteristic length Continuum mechanics 

References

  1. 1.
    Voigt W (1887) Theoretishe studien uber die ebstiZitatsverhaltnisse der Kristalle. Abh Ges Wiss Gottingen 34 Google Scholar
  2. 2.
    Cosserat E, Cosserat F (1909) Theorie des corps deformable. Hermann, Paris Google Scholar
  3. 3.
    Eringen AC, Suhubi ES (1964) Nonlinear theory of simple micro-elastic solids. Int J Eng Sci 2:189–203 MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Mindlin RD (1964) Microstructure in linear elasticity. Arch Ration Mech Anal 16:51–78 MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Eringen AC (1966) Linear theory of micropolar elasticity. J Math Mech 15:909–923 MATHMathSciNetGoogle Scholar
  6. 6.
    Fatemi J, Van Keulen F, Onck PR (2002) Generalized continuum theories: application to stress analysis in bone. Meccanica 37:385–396 MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Anderson WB, Lakes RS (1994) Size effects due to Cosserat elasticity and surface damage in closed-cell polymethacrylimide foam. J Mater Sci 29:6413–6419 CrossRefADSGoogle Scholar
  8. 8.
    Di Carlo A, Rizzi N, Tatone A (1990) Continuum modelling of beam like latticed truss: identification of the constitutive functions for the contact and inertial actions. Meccanica 25:168–174 MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Masiani R, Rizzi N, Trovalusci P (1995) Masonry as structured continuum. Meccanica 30:673–683 MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Masiani R, Trovalusci P (1996) Cauchy and Cosserat materials as continuum models of brick masonry. Meccanica 31:421–432 MATHCrossRefGoogle Scholar
  11. 11.
    Lord HW, Shulman Y (1967) The generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15:299–307 MATHCrossRefADSGoogle Scholar
  12. 12.
    Green AE, Lindsay KA (1972) Thermoelasticity. J Elast 2:1–7 MATHCrossRefGoogle Scholar
  13. 13.
    Ackerman CC, Betman B, Fairbank HA, Guyer RA (1966) Second sound in helium. Phys Rev Lett 16:789–791 CrossRefADSGoogle Scholar
  14. 14.
    Guyer RA, Krumhansal JA (1966) Thermal conductivity, Second sound phonon hydrodynamics phenomenon in non metallic crystals. Phys Rev Lett 148:778–788 ADSGoogle Scholar
  15. 15.
    Ackerman CC, Overtone WC (1969) Second sound in helium-3. Phys Rev Lett 22:764–766 CrossRefADSGoogle Scholar
  16. 16.
    Chanderasekharaiah DS (1986) Thermoelasticity with second sound-a review. Appl Mech Rev 39:355–376 CrossRefGoogle Scholar
  17. 17.
    Dost S, Tabarrok B (1978) Generalized micropolar thermoelasticity. Int J Eng Sci 16:173–178 MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Eringen AC (1970) Foundation of micropolar thermoelasticity. Course of lectures No 23, CISM Udine Springer Google Scholar
  19. 19.
    Kumar R, Choudhary S (2003) Response of orthotropic micropolar elastic medium due to various sources. Meccanica 38:349–368 MATHCrossRefGoogle Scholar
  20. 20.
    Wu J, Zhu Z (1992) The propagation of Lamb waves in a plate bordered with layers of a liquid. J Acoust Soc Am 91:861–867 CrossRefADSGoogle Scholar
  21. 21.
    Sharma JN, Pathania V (2003) Generalized thermoelastic Lamb waves in a plate bordered with layers of inviscid liquid. J Sound Vib 268:897–916 CrossRefADSGoogle Scholar
  22. 22.
    Sharma JN, Pathania V (2005) Crested waves in Thermoelastic plates Immersed in liquid. J Vib Control 11:347–370 CrossRefMathSciNetGoogle Scholar
  23. 23.
    Sharma JN, Kumar S, Sharma YD (2008) Propagation of Rayleigh surface waves in microstretch thermoelastic continua under inviscid fluid loadings. J Therm Stress 31:18–39 CrossRefGoogle Scholar
  24. 24.
    Strunin DV (2001) On characteristics times in generalized thermoelasticity. J Appl Math 68:816–817 MATHGoogle Scholar
  25. 25.
    Graff KF (1991) Wave motion in elastic solids. Dover, New York Google Scholar
  26. 26.
    Sharma JN, Singh D (2002) Circular crested thermoelastic waves in homogeneous isotropic plate. J Therm Stress 25:1179–1193 CrossRefGoogle Scholar
  27. 27.
    Sharma JN, Singh D, Kumar R (2000) Generalized thermoelastic waves in homogeneous isotropic thermoelastic plate. J Acoust Soc Am 108:848–851 CrossRefADSGoogle Scholar
  28. 28.
    Gauthier RD (1982) Experimental investigation on micropolar media. In: Brulin O, Hsieh RKT (eds) Mechanics of micropolar media. World Scientific, Singapore, pp 395–463 Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Applied SciencesNational Institute of TechnologyHamirpurIndia
  2. 2.Department of MathematicsLovely Professional UniversityPhagwaraIndia

Personalised recommendations