Journal of Engineering Mathematics

, Volume 114, Issue 1, pp 159–176 | Cite as

Impact of inhomogeneous fiber-reinforced layer with frictional interface on Rayleigh-type wave propagation

  • Akanksha SrivastavaEmail author
  • Amares Chattopadhyay
  • Abhishek Kumar Singh


The effect of frictional boundary on the propagation of Rayleigh-type wave in an initially stressed inhomogeneous fiber-reinforced layer overlying an initially stressed homogeneous semi-infinite medium has been analyzed by an approximate analytical method. A realistic model has been considered for sliding boundary friction at the interface. The frequency equation has been obtained in closed form. The substantial effects of various affecting parameters, viz. reinforcement, inhomogeneity, bonding parameter, spectral decay parameter, and horizontal initial stress on phase and damped velocity have been discussed graphically in detail. The remarkable observation has been obtained through the comparative study in the presence and the absence of reinforcement in the layer.


Fiber-reinforcement Frequency equation Frictional bonding Heterogeneity Initial stress Rayleigh-type wave 



The authors convey their sincere thanks to the Indian Institute of Technology (ISM), Dhanbad for providing JRF to Ms. Akanksha Srivastava and also facilitating us with its best facility for research.


  1. 1.
    Spencer AJM (1972) Deformations of fibre-reinforced materials. Oxford University Press, LondonzbMATHGoogle Scholar
  2. 2.
    Belfield AJ, Rogers TG, Spencer AJM (1983) Stress in elastic plates reinforced by fibres lying in concentric circles. J Mech Phys Solids 31(1):25–54CrossRefzbMATHGoogle Scholar
  3. 3.
    Verma PDS (1986) Magnetoelastic shear waves in self-reinforced bodies. Int J Eng Sci 24(7):1067–1073CrossRefzbMATHGoogle Scholar
  4. 4.
    Chattopadhyay A, Venkateswarlu RL, Saha S (2002) Reflection of quasi-P and quasi-SV waves at the free and rigid boundaries of a fibre-reinforced medium. Sãdhanã 27(6):613–630zbMATHGoogle Scholar
  5. 5.
    Kundu S, Pandit DK, Gupta S, Manna S (2016) Love wave propagation in a fiber-reinforced medium sandwiched between an isotropic layer and gravitating half-space. J Eng Math 100(1):109–119MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Singh AK, Lakshman A, Chattopadhyay A (2016) The plane waves at the edge of a uniformly pre-stressed fiber-reinforced plate. J Vib Control 22(10):2530–2541MathSciNetCrossRefGoogle Scholar
  7. 7.
    Kaur T, Sharma SK, Singh AK (2016) Effect of reinforcement, gravity and liquid loading on Rayleigh-type wave propagation. Meccanica 51(10):2449–2458MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Bullen KE (1940) The problem of the Earth’s density variation. Bull Seismol Soc Am 30(3):235–250Google Scholar
  9. 9.
    Biot MA (1965) Mechanics of incremental deformations. Wiley, New YorkCrossRefGoogle Scholar
  10. 10.
    Chatterjee M, Dhua S, Chattopadhyay A, Sahu SA (2016) Seismic waves in heterogeneous crust-mantle layers under initial stresses. J Earthq Eng 20(1):39–61CrossRefGoogle Scholar
  11. 11.
    Sezawa K, Kanai K (1940) A fault surface or a block absorbs seismic wave energy. Bull Earthq Res Inst Tokyo Univ 18:465–482zbMATHGoogle Scholar
  12. 12.
    Kanai K (1961) A new problem concerning surface waves. Bull Earthq Res Inst Tokyo Univ 39:359–366MathSciNetGoogle Scholar
  13. 13.
    Iwan WD (1973) A generalization of the concept of equivalent linearization. Int J Nonlinear Mech 8(3):279–287MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Miller RK (1979) An estimate of the properties of Love-type surface waves in a frictionally bonded layer. Bull Seismol Soc Am 69(2):305–317Google Scholar
  15. 15.
    Miller RK (1977) An approximate method of analysis of the transmission of elastic waves through a frictional boundary. J Appl Mech 44(4):652–656CrossRefzbMATHGoogle Scholar
  16. 16.
    Murty GS (1975) A theoretical model for the attenuation and dispersion of Stoneley waves at the loosely bonded interface of elastic half spaces. Phys Earth Planet Inter 11(1):65–79MathSciNetCrossRefGoogle Scholar
  17. 17.
    Singh AK, Parween Z, Das A, Chattopadhyay A (2017) Influence of loosely-bonded sandwiched initially stressed visco-elastic layer on torsional wave propagation. J Mech 33(3):351–368CrossRefGoogle Scholar
  18. 18.
    Mistri KC, Singh AK, Yadav RP, Chattopadhyay A (2017) Stresses due to moving load on the surface of an irregular magneto-elastic monoclinic half-space under hydrostatic initial stress. Mech Adv Mater Struct 24(13):1094–1108CrossRefGoogle Scholar
  19. 19.
    Xia J, Miller RD, Park CB (1999) Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves. Geophysics 64(3):691–700CrossRefGoogle Scholar
  20. 20.
    Mallick PK (2007) Fibre-reinforced composites: materials, manufacturing, and design. CRC Press, Boca RatonCrossRefGoogle Scholar
  21. 21.
    Loeb J (1961) Attenuation des ondes sismiques dans les solides. Geophys Prospect 9(3):370–381CrossRefGoogle Scholar
  22. 22.
    Markham MF (1970) Measurement of the elastic constants of fibre composites by ultrasonics. Composites 1(3):145–149CrossRefGoogle Scholar
  23. 23.
    Gubbins D (1990) Seismology and plate tectonics. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)DhanbadIndia

Personalised recommendations