, Volume 27, Issue 6, pp 613–630 | Cite as

Reflection of quasi-P and quasi-SV waves at the free and rigid boundaries of a fibre-reinforced medium

  • A. Chattopadhyay
  • R. L. K. Venkateswarlu
  • S. Saha


The propagation of plane waves in fibre-reinforced media is discussed. The expressions of phase velocities of quasi-P (qP) and quasi-SV (qSV) waves propagating in plane symmetry are obtained in terms of propagation vectors. We have established a relation from which the displacement vector can be obtained in terms of the propagation vector. Expressions for the reflection coefficients of qP and qSV waves are obtained. Numerical results of reflection coefficients are obtained and presented graphically. The partition of energy between qP and qSV waves reflected on free and rigid boundaries due to incident qP and qSV waves are also obtained and presented graphically.


Reflection of waves quasi-P waves quasi-SV waves quasi-SH waves fibre-reinforced media reflection coefficients 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Achenbach J D 1976Wave propagation in elastic solids (New York: North Holland)Google Scholar
  2. Chattopadhyay A, Choudhury S 1995 The reflection phenomena of P-waves in amedium of monoclinic type.Int. J. Eng. Sci. 33: 195–207MATHCrossRefGoogle Scholar
  3. Chattopadhyay A, Venkateswarlu R L K 1998 Stresses produced in fibre-reinforced half space due to a moving load.Bull. Cal. Math Soc. 90: 337–342MATHGoogle Scholar
  4. Chattopadhyay A, Saha S, Chakraborty M 1996 Reflection of SV waves in a monoclinic medium.Indian J. Pure Appl. Math. 27: 1029–1042MATHGoogle Scholar
  5. Crampin S 1975 Distinctive particle motion of surface waves as a diagnostic of anisotropic layering.Geophs. J.R. Astron. Soc. 40: 177–186Google Scholar
  6. Crampin S, Taylor D B 1971 The propagation of surface waves in anisotropic media.Geophys. J.R. Astron. Soc. 25: 71–87Google Scholar
  7. Dey S, Addy S K 1979 Reflection and refraction of plane waves under initial stresses at an interface.Int. J. Non-linear Mech. 14: 101–110MATHCrossRefGoogle Scholar
  8. Gutenberg B 1944 Energy ratio of reflected and refracted seismic waves.Bull. Seismol. Soc. Am. 34: 85–112Google Scholar
  9. Henneke E G 1972 Reflection-refraction of stress waves at a plane boundary between anisotropic media.J. Acoust. Soc. Am. 51: 210–217CrossRefGoogle Scholar
  10. Keith C M, Crampin S 1977a Seismic body waves in anisotropic media, reflection and refraction at a plane interface.Geophys. J. R. Astron. Soc. 49: 181–208Google Scholar
  11. Keith C M, Crampin S 1977b Seismic body waves in anisotropic media: propagation through a layer.Geophys. J. R. Astron. Soc. 49: 209–223Google Scholar
  12. Keith C M, Crampin S 1977c Seismic body waves in anisotropic media, synthetic seismograms.Geophys. J. R. Astron. Soc. 49: 225–243Google Scholar
  13. Knott C G 1899 Reflection and refraction of elastic waves with seismological applications.Philos. Mag. 48: 64–97Google Scholar
  14. Markham M F 1970 Measurements of elastic constants of fibre composites by ultrasonics.Composites. 1: 145–149CrossRefGoogle Scholar
  15. Norris A N 1983 Propagation of planes waves in a pre-stressed elastic medium.J. Accoust. Soc. Am. 74: 1642–1643CrossRefGoogle Scholar
  16. Pal A K, Chattopadhyay A 1984 The reflection phenomena of plane waves at a free boundary in a prestressed elastic half-space.J. Accoust. Soc. Am. 76: 924–925CrossRefGoogle Scholar
  17. Richter C F 1958Elementary seismology (San Francisco and London: W H Freeman)Google Scholar
  18. Singh S J, Khurana S 2002 Reflection of P and SV waves at the interface of a monoclinic elastic half-space.Proc. Indian Acad. Sci. (Earth Planet. Sci.) 111: 401–412Google Scholar
  19. Spencer A J M 1972Deformations of fibre-reinforced materials (London: Oxford University Press)MATHGoogle Scholar
  20. Thapliyal V 1974 Reflection of SH waves from anisotropic transition layer.Bull. Seismol. Soc. Am. 65: 1979–1991Google Scholar
  21. Tolstoy I 1982 On elastic waves in pre-stressed solids.J. Geophy. Res. 87: 6823–6827Google Scholar
  22. Udias A 1999Principles of seismology (Cambridge: University Press)Google Scholar

Copyright information

© Indian Academy of Sciences 2002

Authors and Affiliations

  • A. Chattopadhyay
    • 1
  • R. L. K. Venkateswarlu
    • 1
  • S. Saha
    • 1
  1. 1.Department of Applied MathematicsIndian School of MinesDhanbadIndia

Personalised recommendations