Eur. Phys. J. Plus (2018) 133: 112
https://doi.org/10.1140/epjp/i2018-11923-2

Regular Article

Wave analysis at frictional interface: A case wise study

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

^* e-mail: mathsakanksha@gmail.com

Received: 8 October 2017
Accepted: 9 February 2018
Published online: 19 March 2018

Abstract

The present article deals with the propagation of a Stoneley wave and with the reflection as well as refraction of an incident P -wave at the frictional bonded interface between an initially stressed isotropic viscoelastic semi-infinite superstratum and an initially stressed isotropic substratum as case I and case II, respectively. The complex form of the velocity equation has been derived in closed form for the propagation of a Stoneley wave in the said structure. The real and imaginary parts of the complex form of the velocity equation correspond to the phase velocity and damped velocity of the Stoneley wave. Phase and damped velocity have been analysed against the angular frequency. The expressions of the amplitude ratios of the reflected and refracted waves are deduced analytically. The variation of the amplitude ratios is examined against the angle of incidence of the P -wave. The influence of frictional boundary parameters, initial stress, viscoelastic parameters on the phase and damped velocities of the Stoneley wave and the amplitude ratios of the reflected as well as refracted P - and SV -wave have been revealed graphically through numerical results.