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Green’s function and surface waves in a viscoelastic orthotropic FGM enforced by an impulsive point source

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  • Kumhar, Raju
  • Kundu, Santimoy
  • Pandit, Deepak Kr.
  • Gupta, Shishir

Abstract

Analytical and numerical approach are taken into consideration to analyze the propagation behavior of horizontally polarized shear surface waves (SH-wave) influenced by an impulsive point source in pre-stressed heterogeneous Voigt-type viscoelastic orthotropic functionally graded (FGM) layered structure. The mechanical properties of the material of viscoelastic functionally graded layer vary with respect to a certain depth as a hyperbolic function, while it varies as a quadratic function for the viscoelastic functionally graded half-space. The complex wave velocity of SH-wave has been achieved by the method of Green’s function and Fourier transformation under the appropriate boundary conditions of the adopted model. The derived wave velocity of SH-waves has been reduced to the classical equation of Love wave when both the viscoelastic orthotropic FGM layer and half-space are considered to be homogeneous isotropic elastic, as depicted in the section of particular cases and validation. Moreover, numerical computation of the obtained velocity equation has been performed and the substantial effects of viscoelasticity and heterogeneity on phase velocity as well as attenuation coefficient for both the cases of absence and presence of initial stress in the media have been perceived by the means of graphs. The final results of this work may be relevant to understand the useful information of SH-wave propagation in the considered layered structure.

Suggested Citation

  • Kumhar, Raju & Kundu, Santimoy & Pandit, Deepak Kr. & Gupta, Shishir, 2020. "Green’s function and surface waves in a viscoelastic orthotropic FGM enforced by an impulsive point source," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    • Handle: RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320302915
    DOI: 10.1016/j.amc.2020.125325
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    References listed on IDEAS

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    1. Assari, Pouria & Dehghan, Mehdi, 2017. "A meshless discrete collocation method for the numerical solution of singular-logarithmic boundary integral equations utilizing radial basis functions," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 424-444.
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