# Axially Symmetric Vibrations of a Liquid-Filled Poroelastic Thin Cylinder Saturated with Two Immiscible Liquids Surrounded by a Liquid

Document Type: Research Paper

Authors

1 Department of Mathematics, Osmania University, Hyderabad, India

2 Department of Mathematics, Kakatiya University, Warangal, India

10.22034/jsm.2019.665907

Abstract

This paper studies axially symmetric vibrations of a liquid-filled poroelastic thin cylinder saturated with two immiscible liquids of infinite extent that is surrounded by an inviscid elastic liquid. By considering the stress free boundaries, the frequency equation is obtained. Particular case, namely, liquid-filled poroelastic cylinder saturated with single liquid is discussed.  When the wavenumber is large, the frequency equation is reduced to that of Rayleigh-type surface wave at the plane boundary of a poroelastic half-space. In this case, the asymptotic expressions of Bessel functions and modified Bessel functions are used. In both general and particular cases, the case of the propagation of Rayleigh waves in a poroelastic half-space is obtained.  The parameter values of Columbia fine sandy loam saturated with air-water mixture are used for the numerical evaluation.  In all the cases, phase velocity as a function of  wavenumber is computed and presented graphically. From the numerical results, some inferences are drawn.

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