Study of Love Waves in a Clamped Viscoelastic Medium with Irregular Boundaries

Document Type: Research Paper

Authors

1 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore -632014, TN, India

2 Department of Mathematics, Madanapalle Institute of Technology & Science Madanapalle-517325, AP, India

10.22034/jsm.2019.667234

Abstract

A mathematical model is presented to investigate the effects of sandiness, irregular boundary interfaces, heterogeneity and viscoelasticity on the phase velocity of Love waves. Geometry of the problem is consisting of an initially stressed viscoelastic layer with corrugated irregular boundaries, which is sandwiched between heterogeneous orthotropic semi-infinite half-space with initial stress and pre-stressed dry sandy half-space. Heterogeneity arises in the upper half-space is due to trigonometric variation in elastic parameters of the orthotropic medium. Inclusion of the concept of corrugated irregular viscoelastic layer clamped between two dissimilar half-spaces under different physical circumstances such as initial stress and heterogeneity brings a novelty to the existing literature related to the study of Love wave. Dispersion equation for Love wave is obtained in closed form. The obtained dispersion relation is found to be in well agreement with classical Love wave equation. Numerical example and graphical illustrations are made to demonstrate notable effect of initial stress, internal friction, wave number and amplitude of corrugations on the phase velocity of Love waves.

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