Generalised surface waves at the boundary of piezo-poroelastic medium with arbitrary anisotropy

M. D. Sharma

doi:10.1121/10.0002851

Generalised surface waves at the boundary of piezo-poroelastic medium with arbitrary anisotropy

The Journal of the Acoustical Society of America ◽

10.1121/10.0002851 ◽

2020 ◽

Vol 148 (6) ◽

pp. 3544-3552

Author(s):

M. D. Sharma

Keyword(s):

Surface Waves ◽

Poroelastic Medium ◽

Arbitrary Anisotropy

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Piezoelectric effect on the velocities of waves in an anisotropic piezo-poroelastic medium

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2009.0534 ◽

2010 ◽

Vol 466 (2119) ◽

pp. 1977-1992 ◽

Cited By ~ 16

Author(s):

M. D. Sharma

Keyword(s):

Phase Velocity ◽

Velocity Vector ◽

Plane Waves ◽

Three Dimensional ◽

Directional Derivatives ◽

Poroelastic Medium ◽

Arbitrary Phase ◽

Phase Direction ◽

Arbitrary Anisotropy ◽

Derivatives Of

A mathematical model for mechanical and electrical dynamics in an anisotropic piezo-poroelastic (hereafter referred to as APP) medium is solved for three-dimensional propagation of harmonic plane waves. A system of modified Christoffel equations is derived to explain the existence and propagation of four waves in the medium of arbitrary anisotropy. This system is solved to calculate the phase velocities of four waves in an unbounded APP medium. Directional derivatives of phase velocity are derived analytically and are used to calculate the components of the ray velocity vector. A hypothetical numerical model is considered to compute the phase velocity for given (arbitrary) phase direction and then the ray velocity vector. Surfaces are plotted for the phase velocity and ray velocity of each wave in a saturated poroelastic medium in the absence/presence of piezoelectricity. The contributions of the piezoelectric activeness of the solid frame and pore-fluid to the phase and ray velocities are identified and analysed for each of the four waves in the medium.

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Rayleigh wave at the surface of a general anisotropic poroelastic medium: derivation of real secular equation

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2017.0589 ◽

2018 ◽

Vol 474 (2211) ◽

pp. 20170589 ◽

Cited By ~ 3

Author(s):

M. D. Sharma

Keyword(s):

Porous Media ◽

Phase Velocity ◽

Rayleigh Wave ◽

Surface Waves ◽

Rayleigh Waves ◽

Secular Equation ◽

Poroelastic Medium ◽

Numerical Example ◽

True Surface

A secular equation governs the propagation of Rayleigh wave at the surface of an anisotropic poroelastic medium. In the case of anisotropy with symmetry, this equation is obtained as a real irrational equation. But, in the absence of anisotropic symmetries, this secular equation is obtained as a complex irrational equation. True surface waves in non-dissipative materials decay only with depth. That means, propagation of Rayleigh wave in anisotropic poroelastic solid should be represented by a real phase velocity. In this study, the determinantal system leading to the complex secular equation is manipulated to obtain a transformed equation. Even for arbitrary (triclinic) anisotropy, this transformed equation remains real for the propagation of true surface waves. Such a real secular equation is obtained with the option of boundary pores being opened or sealed. A numerical example is solved to study the existence and propagation of Rayleigh waves in porous media for the top three (i.e. triclinic, monoclinic and orthorhombic) anisotropies.

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