A Study on Propagation of Waves in a Transversely Isotropic Poroelastic Layer Bounded between Two Viscous Liquids

Nageswaranath Chinta,Venkata Ramanamurthy Mangipudi,Ahmed Shah Syed,Ramesh Modem

doi:10.4236/oja.2019.91001

Abstract

Propagation of Love waves in a transversely isotropic poroelastic layer bounded between two compressible viscous liquids is presented. The equations of motion in a transversely isotropic poroelastic solid are formulated in the framework of Biot’s theory. A closed-form solution for the propagation of Love waves is obtained in a transversely isotropic poroelastic layer. The complex frequency equation for phase velocity and attenuation of Love waves is derived for a transversely isotropic poroelastic layer when it is bounded between two viscous liquids and the results are compared with that of the poroelastic layer. The effect of viscous liquids on the propagation of Love waves is discussed. It is observed that the presence of viscous liquids decreases phase velocity in both transversely isotropic poroelastic layer and poroelastic layer. Results related to the case without viscous liquids have been compared with some of the earlier results and comparison shows good agreement.

Highlights

Deresiewicz [1] [2] discussed propagation of elastic waves in non-dissipative porous solid
The frequency equation for Love waves in a transversely isotropic poroelastic layer bounded between two viscous liquids is obtained and the results are compared with that of poroelastic layer
A study of propagation of Love waves in an infinite poroelastic layer bounded by viscous liquids leads to the following conclusions: 1) Presence of upper and lower viscous liquids decreases phase velocity of Love waves for both transversely isotropic poroelastic layer and poroelastic layer

Summary

Introduction

Deresiewicz [1] [2] discussed propagation of elastic waves in non-dissipative porous solid. The effect of viscosity on propagation of Love waves in a fluid loaded transversely isotropic poroelastic layered half-space was studied by Nageswarnath et al [8]. Phase velocity of Love waves is more for higher values of coefficients of viscosity in case of fluid loaded transversely isotropic poroelastic layered half-space. Nageswaranath et al [9] discussed propagation of Love waves in viscous liquid layer bounded between poroelastic layer and half-space which was transversely isotropic. The frequency equation for Love waves in a transversely isotropic poroelastic layer bounded between two viscous liquids is obtained and the results are compared with that of poroelastic layer. The effect of presence of viscous liquids is studied and it is observed that presence of viscous liquids decreases phase velocity of Love waves in transversely isotropic poroelastic layer and in poroelastic layer.

Frequency Equation

Numerical Work

Conclusions