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An isotropic elastic solid reinforced with a family of parallel fibres behaves anisotropic to any deformation. With orientation of all fibres along a coordinate axis in rectangular Cartesian system, this anisotropy reduces to transverse isotropy. Else with arbitrary orientation of fibre‐family, induced anisotropy lacks any symmetry. In this composite medium with arbitrary anisotropy, three‐dimensional wave motion decaying with depth propagates as a surface wave along all directions on plane boundary. Real phase velocity for this surface wave lies implicit in a system of three equations with complex coefficients. An appropriate transformation of this system yields a real characteristic equation, which is solved to get the anisotropic phase velocity of generalised surface wave. This phase velocity defines a complex slowness vector, which is used to calculate the particle motion at any point in the medium. Effects of fibre‐orientation are analysed, numerically, on the phase velocity and polarisation of surface wave. For example, in the reinforced fibres alters the contours of particle motion through increased ellipticity. However, in the presence of fibres, the decay of particle motion with depth slows down. [ABSTRACT FROM AUTHOR]

Mathematical model for mechanical and electrical dynamics is solved for three‐dimensional propagation of harmonic plane waves in a piezoelectric medium with arbitrary anisotropy. A system of modified Christoffel equations is derived to explain the existence and propagation of bulk waves or decaying phases in the considered medium. At the free plane boundary, a superposition of decaying phases form a generalised Rayleigh wave, which is governed by a linear system of four homogeneous equations. A complex determinantal secular equation ensures a solution to this system. True surface wave at the boundary of the considered medium demands a real solution of this complex secular equation. The linear system of four equations is then transformed to replace the complex secular equation with a real one, which can be solved by standard numerical methods. A real solution of this real secular equation provides the phase velocity for generalised Rayleigh wave at the boundary of piezoelectric medium with arbitrary anisotropy. This phase velocity defines a complex slowness vector, which is used to calculate the motion of material particles and the wave‐induced electric field. A numerical example is considered to compute the phase velocity as well as group velocity for given (arbitrary) propagation directions of Rayleigh wave at the boundary. Variations in particle motion and electric field, induced by Rayleigh wave, are analysed at different depths for different propagation directions at the boundary. [ABSTRACT FROM AUTHOR]

This study considers to solve the complex dispersion equation for propagation of Rayleigh waves in a dissipative porous composite. This porous medium is a viscoelastic porous solid frame saturated with a viscous fluid. Seepage of fluid at the boundary is controlled through pore-fluid pressure and its normal gradient. A complex irrational equation governs the propagation, attenuation and dispersion of the Rayleigh waves. A complex analysis technique is used to solve this equation into an explicit expression for complex phase velocity. Effects of porosity and seepage from surface pores are analyzed numerically on the velocity of Rayleigh wave in a saturated poroelastic material. [ABSTRACT FROM AUTHOR]

An attenuating wave field in an anisotropic poroviscoelastic medium is represented through the three‐dimensional inhomogeneous propagation of four bulk waves. Propagation of each wave is governed by a complex slowness vector, which specifies its phase direction, phase velocity and coefficients for homogeneous/inhomogeneous attenuation. Partially opened surface pores restrict the seepage of pore fluid at the boundary. A generalized reflection phenomenon is illustrated for incidence of inhomogeneous waves at this boundary. Horizontal slowness of this incidence derives the slowness vectors of four inhomogeneous waves reflected into the medium. Slowness vectors and polarizations of incident and reflected waves are used to calculate the amplitudes, phase shifts and energy fluxes of reflected waves in comparison to the incident wave. A particular example illustrates the numerical implementation of the derived mathematical model for anisotropic poroviscoelastic reflection. [ABSTRACT FROM AUTHOR]

This study considers the propagation of surface waves along all directions on the plane boundary of piezo-poroelastic half-space with arbitrary anisotropy. This generalised propagation is characterized through an anisotropic phase velocity, which should ensure the decay of wave-field with depth into the medium. A linear homogeneous system of six equations with complex coefficients governs the existence and propagation of surface waves in the considered medium. The real phase velocity of surface waves lies implicit in a complex determinantal equation, which ensures a non-trivial solution to the system of equations. Through a specific transformation, the system of complex equations is modified to yield a real secular equation, with phase velocity being the only unknown. This equation can always be solved numerically for phase velocity of surface wave along any direction on the plane boundary of anisotropic piezo-poroelastic medium. The phase velocity has been used further to calculate the components of energy flux at the boundary. Horizontal components of energy flux define the group velocity and ray direction for the surface wave. A numerical example is solved to analyse the phase/group velocity curves at the boundary of the medium. [ABSTRACT FROM AUTHOR]

The propagation of harmonic plane waves is considered in a general anisotropic elastic medium, in the presence of prestress. A system of three homogeneous equations governs the existence of a Rayleigh wave at the stress-free plane boundary of the medium. This requires solving a complex secular equation for the implicit real phase velocity of the Rayleigh wave. For the presence of the radical, this irrational equation is never easy to solve by any standard analytical or numerical method. In this study, the system of three equations is transformed to get a real secular equation for the propagation of a Rayleigh wave, which can always be solved numerically for the real phase velocity of the Rayleigh wave. This phase velocity defines a complex slowness vector, which is used to calculate the polarisation of the Rayleigh wave at different depths in an elastic half-space. Effects of prestress and anisotropic symmetry on the phase velocity of the Rayleigh wave and associated particle motion are analysed by a numerical example. [ABSTRACT FROM AUTHOR]

A method is presented to decompose the complex slowness vector for the propagation of inhomogeneous plane harmonic waves in a general anisotropic medium. Phase velocity and attenuation coefficient are obtained along the arbitrary directions of propagation and attenuation, in 3-D space. The method is applied to study the propagation of inhomogeneous waves in an anisotropic poroelastic solid saturated with a viscous fluid. The variations of phase velocities and attenuation factors with the directions of propagation and attenuations are computed, for a realistic numerical model. Effects of these directions are discussed for low- and high-frequency propagation regimes of Biot's theory. The attenuations are found to be much more sensitive to the change in angle between the directions of propagation and attenuation, as compared to propagation velocities. [ABSTRACT FROM AUTHOR]

This is an attempt to study 3-D wave propagation in a general anisotropic poroelastic medium. Biot's theory is used to derive a modified Christoffel equation for the propagation of plane harmonic waves in an anisotropic fluid-saturated porous solid. This equation is solved further to obtain a biquadratic equation, the roots of which represent the phase velocities of all the four quasi-waves that may propagate in such a medium. These phase velocities vary with the direction of phase propagation. Expressions are derived to calculate the group velocities of all the four quasi-waves without using numerical differentiation. The eigensystem of modified Christoffel equation is used to calculate the polarizations of all the quasi-waves. The particle motion of each wave is a function of the direction of phase propagation. Some fundamental differences between wave propagation in anisotropic poroelastic medium and anisotropic elastic medium are suggested, an interesting one is that in an anisotropic poroelastic medium, the polarizations of different quasi-waves need not be mutually orthogonal. In the anisotropic poroelastic medium, the motion of fluid particles deviates from solid particles and this deviation varies, also, with the matrix porosity. Propagation regimes for an isotropic medium, giving velocities and polarizations of both compressional and shear waves, are obtained as special cases. The variations of phase velocity, group velocity, ray direction with phase direction (in 3-D space), are plotted for a numerical model of general anisotropic poroelastic solid. The same numerical model is used to plot the deviations of polarizations from phase direction and ray direction. The deviations among the motion in fluid of the particles and solid parts of porous aggregate are also plotted. [ABSTRACT FROM AUTHOR]