Eur. Phys. J. Plus (2017) 132: 8
https://doi.org/10.1140/epjp/i2017-11282-6

Regular Article

Influence of prestress and periodic corrugated boundary surfaces on Rayleigh waves in an orthotropic medium over a transversely isotropic dissipative semi-infinite substrate

Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad - 826004, Jharkhand, India

^* e-mail: shishir_ism@yahoo.com

Received: 30 August 2016
Accepted: 6 December 2016
Published online: 12 January 2017

Abstract

The paper environs the study of Rayleigh-type surface waves in an orthotropic crustal layer over a transversely isotropic dissipative semi-infinite medium under the effect of prestress and corrugated boundary surfaces. Separate displacement components for both media have been derived in order to characterize the dynamics of individual materials. Suitable boundary conditions have been employed upon the surface wave solutions of the elasto-dynamical equations that are taken into consideration in the light of corrugated boundary surfaces. From the real part of the sixth-order complex determinantal expression, we obtain the frequency equation for Rayleigh waves concerning the proposed earth model. Possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. Numerical computations have been performed in order to graphically demonstrate the role of the thickness of layer, prestress, corrugation parameters and dissipation on Rayleigh wave velocity. The study may be regarded as important due to its possible applications in delay line services and investigating deformation characteristics of solids as well as typical rock formations.