On the dynamic behavior of a functionally graded viscoelastic-piezoelectric composite substrate subjected to a moving line load

  • Abhishek Kumar Singh
  • Siddhartha Koley
  • Anil NegiEmail author
  • Anusree Ray
Regular Article


The present study bestows the analytical investigation of incremental mechanical stresses (compressive stress, shear, and tensile) and electrical displacements (vertical and horizontal components) induced due to a moving line load on an irregular transversely isotropic functionally graded viscoelastic-piezoelectric material (FGVPM) substrate. The closed form expressions of said induced mechanical stresses and induced electrical displacements are deduced and validated with pre-established results for electrically open and short conditions. The elastic moduli (stiffness tensors), piezoelectric moduli, dielectric moduli, elastic loss moduli, piezoelectric loss moduli, and dielectric loss moduli for a viscoelastic-piezoelectric composite are computed and used for numerical computation and graphical demonstration. The effectuality of diverse physical parameters (viz. maximum depth of irregularity, friction due to rough upper surface, functional gradient parameter, irregularity factor associated with different types of irregularity viz. rectangular irregularity, parabolic irregularity and no irregularity) on said induced stresses and electrical displacements in the aforementioned composite substrate has also been discussed. A comparative analysis has also been made to examine the impact of piezoelectricity and viscoelasticity on theon said induced mechanical stresses and induced electrical displacements. In particular, some special peculiarities are also sketched by means of graphs.


  1. 1.
    A. Kothari, A. Kumar, R. Kumar, R. Vaish, V.S. Chauhan, Polym. Compos. 37, 1895 (2016)CrossRefGoogle Scholar
  2. 2.
    R. Newnham, D. Skinner, L. Cross, Mater. Res. Bull. 13, 525 (1978)CrossRefGoogle Scholar
  3. 3.
    J. Li, M.L. Dunn, J. Appl. Phys. 89, 2893 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    Y. Amini, M. Heshmati, P. Fatehi, S.E. Habibi, Appl. Math. Model. 49, 1 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    K.K. Chawla, Composite Materials: Science and Engineering (Springer Science & Business Media, 2012)Google Scholar
  6. 6.
    L.P. Kollár, G.S. Springer, Mechanics of Composite Structures (Cambridge University Press, 2003)Google Scholar
  7. 7.
    X.Y. Li, Z.K. Wang, S.H. Huang, Int. J. Solids Struct. 41, 7309 (2004)CrossRefGoogle Scholar
  8. 8.
    J.D. Achenbach, S.P. Keshava, G. Herrmann, J. Appl. Mech. 34, 910 (1967)ADSCrossRefGoogle Scholar
  9. 9.
    R.G. Payton, Int. J. Eng. Sci. 5, 49 (1967)CrossRefGoogle Scholar
  10. 10.
    W.L. Luo, Y. Xia, X.Q. Zhou, J. Sound Vib. 369, 109 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    M. Olsson, J. Sound Vib. 145, 299 (1991)ADSCrossRefGoogle Scholar
  12. 12.
    Z. Dimitrovová, J. Sound Vib. 366, 325 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    S. Mukherjee, Pure Appl. Geophys. 72, 45 (1969)ADSCrossRefGoogle Scholar
  14. 14.
    A. Mukhopadhyay, Pure Appl. Geophys. 60, 29 (1965)ADSCrossRefGoogle Scholar
  15. 15.
    S. Itou, Int. J. Solids Struct. 100, 411 (2016)CrossRefGoogle Scholar
  16. 16.
    A.K. Singh, A. Negi, A. Chattopadhyay, A.K. Verma, Int. J. Geomech. 17, 04017022 (2017)CrossRefGoogle Scholar
  17. 17.
    A.K. Singh, A. Negi, A.K. Verma, S. Kumar, J. Eng. Mech. 143, 04017096 (2017)CrossRefGoogle Scholar
  18. 18.
    T. Kaur, S.K. Sharma, A.K. Singh, Appl. Math. Model. 40, 3535 (2016)MathSciNetCrossRefGoogle Scholar
  19. 19.
    P. Kumari, C. Modi, V.K. Sharma, Wave Random Complex Media 28, 601 (2018)ADSCrossRefGoogle Scholar
  20. 20.
    A.K. Singh, S. Kumar, R. Kumari, Eur. Phys. J. Plus 133, 120 (2018)ADSCrossRefGoogle Scholar
  21. 21.
    W.Q. Chen, H.J. Ding, Acta Mech. 153, 207 (2002)CrossRefGoogle Scholar
  22. 22.
    A.K. Singh, S. Kumar, A. Chattopadhyay, Int. J. Eng. Sci. 89, 35 (2015)CrossRefGoogle Scholar
  23. 23.
    J. Du, X. Jin, J. Wang, K. Xian, Ultrasonics 46, 13 (2007)CrossRefGoogle Scholar
  24. 24.
    G.G. Sheng, X. Wang, J. Sound Vib. 323, 772 (2009)ADSCrossRefGoogle Scholar
  25. 25.
    J.F. Lu, D.S. Jeng, Int. J. Solids Struct. 44, 573 (2007)CrossRefGoogle Scholar
  26. 26.
    G. Tondreau, S. Raman, A. Deraemaeker, Smart Struct. Syst. 13, 547 (2014)CrossRefGoogle Scholar
  27. 27.
    H.A. Dieterman, V. Metrikine, Eur. J. Mech. A Solids 16, 295 (1997)Google Scholar
  28. 28.
    K.Y. Lam, T.Y. Ng, Smart Mater. Struct. 8, 223 (1999)ADSCrossRefGoogle Scholar
  29. 29.
    Z. Zhang, H. Xiang, Z. Shi, J. Intell. Mater. Syst. Struct. 27, 567 (2016)CrossRefGoogle Scholar
  30. 30.
    M.A. Trindade, Smart Mater. Struct. 16, 2159 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    A. Chattopadhyay, S. Gupta, V.K. Sharma, P. Kumari, Acta Mech. 221, 271 (2011)CrossRefGoogle Scholar
  32. 32.
    J.V. Uspensky, Theory of Equations (McGraw-Hill Book Company, Inc., 1948)Google Scholar
  33. 33.
    J. Cole, J. Huth, J. Appl. Mech. 25, 433 (1958)MathSciNetGoogle Scholar
  34. 34.
    C.N. Della, D. Shu, Sensors Actuat. A: Phys. 140, 200 (2007)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

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

Personalised recommendations