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Journal of Engineering Mathematics

, Volume 75, Issue 1, pp 139–155 | Cite as

Propagation of magnetoelastic shear waves in an irregular self-reinforced layer

  • Amares Chattopadhyay
  • Abhishek Kumar Singh
Article

Abstract

The propagation of horizontally polarised shear waves in an internal irregular magnetoelastic self-reinforced stratum which is sandwiched between two semi-infinite magnetoelastic self-reinforced media is studied. Two shapes of irregularities on the interface of layer and lower semi-infinite media are considered, namely rectangular and parabolic. The dispersion equation is obtained in closed form. The combined effects of reinforcement, magnetic field and irregularity are also studied. Some important features of the results are highlighted. It is also observed that the dispersion equation is in agreement with the classical Love-type wave equation for an isotropic layer sandwiched between two isotropic half-spaces in the absence of reinforcement, magnetic field and irregularity.

Keywords

Dispersion equation Irregularity Magnetoelastic Perturbation Self-reinforced Shear waves 

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References

  1. 1.
    Belfield AJ, Rogers TG, Spencer AJM (1983) Stress in elastic plates reinforced by fibers lying in concentric circles. J Mech Phys Solids 31(1): 25–54ADSMATHCrossRefGoogle Scholar
  2. 2.
    Verma PDS, Rana OH (1983) Rotation of a circular cylindrical tube reinforced by fibres lying along helices. Mech Mater 2: 353–359CrossRefGoogle Scholar
  3. 3.
    Knopoff L (1955) The interaction between elastic wave motion and a magnetic field in electrical conductors. J Geophys Res 60: 441–456ADSCrossRefGoogle Scholar
  4. 4.
    Dunkin JW, Eringen AC (1963) On the propagation of waves on electromagnetic elastic solids. Int J Eng Sci 1: 461–495MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Yu CP, Tang S (1966) Magneto-elastic waves in initially stressed conductors. J Appl Math Phys ZAMP 17: 766–775CrossRefGoogle Scholar
  6. 6.
    Tomita S, Shindo Y (1979) Rayleigh waves in magneto-thermo-elastic solid with thermal relaxation. Int J Eng Sci 17: 227–232MATHCrossRefGoogle Scholar
  7. 7.
    Verma PDS (1986) Magnetoelastic shear waves in self-reinforced bodies. Int J Eng Sci 24(7): 1067–1073MATHCrossRefGoogle Scholar
  8. 8.
    Chattopadhyay A, Chaudhury S (1990) Propagation reflection and transmission of magnetoelastic shear waves in a self reinforced medium. Int J Eng Sci 28(6): 485–495MATHCrossRefGoogle Scholar
  9. 9.
    Chattopadhyay A, Chaudhury S (1995) Magnetoelastic shear waves in an infinite self-reinforced plate. Int J Numer Anal Methods Geomech 19: 289–304MATHCrossRefGoogle Scholar
  10. 10.
    Bhattacharya J (1962) On the dispersion curve for Love wave due to irregularity in the thickness of the transversely isotropic crustal layer. Gerlands Beitrage zur Geophysik 6: 324–334Google Scholar
  11. 11.
    Chattopadhyay A, Chakraborty M, Pal AK (1983) Effects of irregularity on the propagation of guided SH waves. Jr de Mecanique Theo et Appl 2(2): 215–225MATHGoogle Scholar
  12. 12.
    Chatopadhyay A, Bandyopadhyay UK (1986) Shear waves in an infinite monoclinic crystal plate. Int J Eng Sci 24(10): 1587–1596CrossRefGoogle Scholar
  13. 13.
    Chattopadhyay A, Gupta S, Sharma VK, Kumari P (2008) Propagation of SH waves in an irregular monoclinic crustal layer. Arch Appl Mech 78(12): 989–999MATHCrossRefGoogle Scholar
  14. 14.
    Chattopadhyay A, Gupta S, Sharma VK, Kumari P (2009) Propagation of shear waves in viscoelastic medium at irregular boundaries. Acta Geophys 58(2): 195–214ADSCrossRefGoogle Scholar
  15. 15.
    Eringen AC, Samuels CJ (1959) Impact and moving loads on a slightly curved elastic half space. J Appl Mech 26: 491–498MathSciNetMATHGoogle Scholar
  16. 16.
    Willis HF (1948) A formula for expanding an integral as a series. Phil Mag 39: 455–459MathSciNetMATHGoogle Scholar
  17. 17.
    Tranter CJ (1966) Integral transform in mathematical physics. Methuen and Company Limited, LondonGoogle Scholar
  18. 18.
    Achenbach JD (1975) Wave propagation in elastic solids. North Holland Publication Company, New YorkGoogle Scholar
  19. 19.
    Chattopadhyay A (1975) On the dispersion equation for Love wave due to irregularity in the thickness of non-homogeneous crustal layer. Acta Geophys Polonica 23: 307–317Google Scholar
  20. 20.
    Hool GA, Kinne WS (1924) Reinforced concrete and masonry structure. McGraw-Hill, New YorkGoogle Scholar
  21. 21.
    Markham MF (1970) Measurements of elastic constants of fibre composite by ultrasonics. Composites 1: 145–149CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian School of Mines (ISM)DhanbadIndia

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