Shear Waves in an Inhomogeneous Viscoelastic Layer Resting over a Prestressed Orthotropic Substrate

AbstractThis paper intends to study the dispersive nature of shear waves transmitting in an inhomogeneous viscoelastic layer embedded over a prestressed orthotropic substrate. The frequency equations obtained under the combined effect of viscoelasticity and inhomogeneity were analyzed. It has been observed that the phase velocity of the shear wave is influenced by the prestress present in the half-space. The method of separation of variables has been incorporated to deduce the dispersion equation of the shear wave. Consequently, it has been found that the dispersion equations from the real and damped parts converged with the classical Love wave equation under certain suitable conditions. The graphical representations show that inhomogeneity, viscoelasticity, prestress, and shear moduli had a remarkable effect on the phase velocity of the shear wave.

[1]  A. Singh,et al.  Influence of corrugated boundary surfaces, reinforcement, hydrostatic stress, heterogeneity and anisotropy on Love-type wave propagation , 2015 .

[2]  P. Pal,et al.  Reflection and Transmission of Plane SH-Waves Through an Anisotropic Magnetoelastic Layer Sandwiched Between Two Semi-Infinite Inhomogeneous Viscoelastic Half-Spaces , 2015, Pure and Applied Geophysics.

[3]  S. Kundu,et al.  SH-type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi-infinite media , 2014 .

[4]  S. A. Sahu,et al.  SH-waves in viscoelastic heterogeneous layer over half-space with self-weight , 2014 .

[5]  V. Sharma,et al.  Effect of point source and heterogeneity on the propagation of SH-Waves in a viscoelastic layer over a viscoelastic half space , 2012, Acta Geophysica.

[6]  S. S. Singh,et al.  Love Wave at a Layer Medium Bounded by Irregular Boundary Surfaces , 2011 .

[7]  N. Mahanti,et al.  Love waves in a fluid-saturated porous layer under a rigid boundary and lying over an elastic half-space under gravity , 2010 .

[8]  A. Chattopadhyay,et al.  Propagation of shear waves in viscoelastic medium at irregular boundaries , 2010 .

[9]  A. M. Abd-Alla,et al.  Rayleigh waves in a magnetoelastic half-space of orthotropic material under influence of initial stress and gravity field , 2004, Appl. Math. Comput..

[10]  Vlastislav Červený,et al.  Inhomogeneous Harmonic Plane Waves in Viscoelastic Anisotropic Media , 2004 .

[11]  M. Romeo.  Interfacial viscoelastic SH waves , 2003 .

[12]  M. Destrade.  Surface waves in orthotropic incompressible materials , 2001, 1305.7019.

[13]  G. Manolis,et al.  Harmonic wave propagation through viscoelastic heterogeneous media exhibiting mild stochasticity — II. Applications , 1996 .

[14]  J. Carcione.  Wave propagation in anisotropic linear viscoelastic media: theory and simulated wavefields , 1990 .

[15]  M. Schoenberg.  Transmission and Reflection of Plane Waves at an Elastic-Viscoelastic Interface , 1971 .

[16]  J. Bhattacharya.  The possibility of the propagation of Love type waves in an intermediate heterogeneous layer lying between two semi-infinite isotropic homogeneous elastic layers , 1969 .

[17]  Arabinda Biswas.  Propagation ofSH-waves in a heterogeneous visco-elastic layer overlying a homogeneous voigt medium , 1969 .

[18]  R. Shaw,et al.  On the Transmission of Plane Waves through Layered Linear Viscoelastic Media , 1969 .