Influences of Heterogeneities and Initial Stresses on the Propagation of Love-Type Waves in a Transversely Isotropic Layer Over an Inhomogeneous Half-Space

Subject Areas : Engineering

P Alam ¹ , S Kundu ²

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

Received: 2017-07-17 Accepted : 2017-09-20 Published : 2017-12-30

Keywords: Phase velocity, Isotropic, Initial stress, Heterogeneity, Transversely,

Abstract :

In the present paper, we are contemplating the influences of heterogeneities and pre-stresses on the propagation of Love-type waves in an initially stressed heterogeneous transversely isotropic layer of finite thickness lying over an inhomogeneous half space. The material constants and pre-stress have been taken as space dependent and arbitrary functions of depth in the respective media. To simplify the problem, we have used Whittaker’s function and separation of variables method. We present a general dispersion relation to describe the impacts on the propagation of Love-type waves in the structure. The present dispersion relation is analyzed case wise and also validated by comparison of the standard Love wave equation. Further, numerical computations are demonstrated graphically for the set of dimensionless parameters between dimensionless phase velocity and dimensionless wave number of the wave.

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