Advertisement

Sadhana

, Volume 19, Issue 2, pp 337–346 | Cite as

Magneto-visco-elastic surface waves in stressed conducting media

  • Samar Das Chandra
  • D P Acharya
  • P R Sengupta
Article

Abstract

The present paper is concerned with magneto-visco-elastic surface waves in conducting media involving time rate of strain and stress of first order, the media being under an initial stress of hydrostatic tension or compression. The theory of magneto-visco-elastic surface waves in a conducting medium involving time rate of strain and stress of first order is derived under an initial stress. The above general theory is then employed to characterise Rayleigh, Love and Stoneley waves. Results obtained in the above cases reduce to well-known classical results when viscosity and magnetic field are absent.

Keywords

Magneto-visco-elastic first order surface waves initial stress hydrostatic tension or compression 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Acharya D P, Sengupta P R 1978 Magneto-thermo-elastic surface waves in initially stressed conducting media.Acta Geophys. Polon. 26(4):Google Scholar
  2. Banos A 1956 Normal modes characterising magneto-elastic plane waves.J. Phys. Rev. 104: 300–305CrossRefMathSciNetGoogle Scholar
  3. Bland D R 1960The theory of linear visco-elasticity (London: Pergamon) (This monograph on the subject contains many cases of stress analysis)Google Scholar
  4. Chadwick P 1957 Elastic wave propagation in a magnetic field.IX Congress Int. Mech. Appl. 7: 143–158Google Scholar
  5. Das T K, Sengupta P R 1990a Surface waves in general viscoelastic media of higher order.Indian. J. Pure Appl. Math. 21(7): 661–675MATHMathSciNetGoogle Scholar
  6. Das T K, Sengupta P R 1990b Surface waves in thermo-visco-elastic media considering time rate of stress and strain of higher order.Gerlands Beitr. Geophys. Leipzig 99: 337–448Google Scholar
  7. Das T K, Sengupta P R 1992 Effect of gravity on visco-elastic surface waves in solids involving time rate of strain and stress of first order.Sādhanā 17: 315–323Google Scholar
  8. De S N, Sengupta P R 1971 Surface waves in magneto-elastic initially stressed conducting media.Pure Appl. Geophys. 88: 44–52CrossRefGoogle Scholar
  9. De S N, Sengupta P R 1972 Magneto-elastic waves and disturbances in initially stressed conducting media.Pure Appl. Geophys. 93: 41–54CrossRefGoogle Scholar
  10. Ewing W M, Jardetzky W S, Press F 1957Elastic waves in layered media (London: McGraw-Hill)MATHGoogle Scholar
  11. Flugge W 1967Visco-elasticity (London: Blaisdell)Google Scholar
  12. Hunter S C 1960Visco-elastic waves. Progress in solid mechanics (eds) I N Snedon, R Hill (Amsterdam, New York: North Interscience)Google Scholar
  13. Jeffreys H 1959The earth 4th edn (Cambridge: University Press)Google Scholar
  14. Knopoff L 1955 The interaction between elastic wave motions and a magnetic field in electric conductors.J. Geophys. Res. 60: 441–456CrossRefGoogle Scholar
  15. Rayleigh Lord 1885 On waves propagated along the plane surface of an elastic solid.Proc. London Math. Soc. 17: 4–11CrossRefGoogle Scholar
  16. Roy S K, Sengupta P R 1983a Rotatory vibration of a sphere of general visco-elastic solid.Gerlands Beitr. Geophys. Leipzig 92: 70–76Google Scholar
  17. Roy S K, Sengupta P R 1983b Radial vibration of a sphere of general visco-elastic solid.Gerlands Beitr. Geophys. Leipzig 92: 435–442Google Scholar
  18. Stoneley R 1924 Elastic waves at the surface of separation of two solids.Proc. R. Soc., London 106: 416–428CrossRefGoogle Scholar
  19. Suhubi E S 1965 Small torsional oscillations of a circular cylinder with finite electric conductivity in a constant axial magnetic field.Int. J. Eng. Sci. 2: 441–459CrossRefMathSciNetGoogle Scholar
  20. Voigt W 1887 Theoretische Studien uber die Elasticitats Verhaltnisse der Krystalle.Abh. Ges. Wiss. Gottingen 34Google Scholar
  21. Yu C P, Tang S 1966 Magneto-elastic waves in initially stressed conductors.Z. Angew. Math. Phys. 17: 766CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 1994

Authors and Affiliations

  • Samar Das Chandra
    • 1
  • D P Acharya
    • 2
  • P R Sengupta
    • 3
  1. 1.Indian Institute of Mechanics of ContinuaCalcuttaIndia
  2. 2.Department of MathematicsMahadevananda CollegeBarrackporeIndia
  3. 3.Department of MathematicsUniversity of KalyaniKalyaniIndia

Personalised recommendations