Propagation of inhomogeneous plane waves in dissipative anisotropic poroelastic solids

Sharma, M. D.

doi:10.1111/j.1365-246x.2005.02701.x

Cited by 24 publications

(36 citation statements)

References 24 publications

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“…For an isotropic medium, the wave number is a scalar quantity and the phase velocity v is constant for any direction n. For an anisotropic medium, the wave number k becomes a vector k(k 1 ,k 2 ,k 3 ) and the associated phase velocity vector v(v 1 ,v 2 ,v 3 ) varies with the direction of wave propagation n. An alternate approach to the solution of Eq. (6), for the squares of the wave speeds v 2 and the two 3D vectors a and b, has been undertaken by Sharma (2005Sharma ( , 2008 who uses Eq. (6) to solve the relationship between the two 3D vectors a and b and then obtains a 3 by 3 matrix equation equivalent to Eq.…”

Section: Fabric Dependence Of Tensors Appearing In the Poroelastmentioning

confidence: 99%

Fabric dependence of quasi-waves in anisotropic porous media

Cardoso

Cowin

2011

The Journal of the Acoustical Society of America

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Assessment of bone loss and osteoporosis by ultrasound systems is based on the speed of sound and broadband ultrasound attenuation of a single wave. However, the existence of a second wave in cancellous bone has been reported and its existence is an unequivocal signature of poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as bone mineral density (BMD), a fabric-dependent anisotropic poroelastic wave propagation theory was recently developed for pure wave modes propagating along a plane of symmetry in an anisotropic medium. Key to this development was the inclusion of the fabric tensor-a quantitative stereological measure of the degree of structural anisotropy of bone-into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of mixed wave modes along an arbitrary direction in anisotropic porous media called quasi-waves. It was found that differences between phase and group velocities are due to the anisotropy of the bone microarchitecture, and that the experimental wave velocities are more accurately predicted by the poroelastic model when the fabric tensor variable is taken into account. This poroelastic wave propagation theory represents an alternative for bone quality assessment beyond BMD.

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Section: Fabric Dependence Of Tensors Appearing In the Poroelastmentioning

confidence: 99%

Fabric dependence of quasi-waves in anisotropic porous media

Cardoso

Cowin

2011

The Journal of the Acoustical Society of America

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“…In the absence of dissipation in the APP medium, the real coefficients c j , (j = 0, 1, 2, 3, 4) are derived (Sharma 2005) from matrices D j in equation ( Then the phase velocities of the four waves, given by v j = Rh j /r, (j = 1, 2, 3, 4), will vary with the phase direction (n 1 , n 2 , n 3 ). Keeping in mind the propagation of compressional and shear waves in an isotropic poroelastic medium, the waves represented by j = 1, 2, 3 and 4, are called the qP1, qS 1, qS 2 and qP2 waves, respectively.…”

Section: Phase Velocitymentioning

confidence: 99%

“…It is also assumed that the properties of the pore-fluid are unaffected by its proximity to the walls of the solid. Another representation of viscous loss in terms of permeability, the pore size and the fluid-solid inertial coupling is also used (Sharma 2005). Wave propagation is discussed for two different frequency regimes.…”

Section: (A) Dissipation In Porous Mediummentioning

confidence: 99%

“…Recently Wang & Yuan (2007) investigated, theoretically and experimentally, the propagation characteristics of Lamb waves in composites with emphasis on group velocity and characteristic wave curves. Green's functions for piezoelectric composites were obtained by Pan & Han (2004, 2005. The evaluation of Green's function for an elastic medium is a fundamental problem in the field wave propagation.…”

Section: Introductionmentioning

confidence: 99%

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

Sharma

2010

Proc. R. Soc. A.

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A mathematical model for mechanical and electrical dynamics in an anisotropic piezoporoelastic (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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“…An earlier study of author (Sharma, 2005b) shows that, compared to velocity, the attenuation is more sensitive to the inhomogeneity of waves propagating in dissipative anisotropic poroelastic medium. Much earlier, Winterstein (1987) related the quality factor (Q) variations in a multilayered medium to the inhomogeneity (angle between propagation direction and direction of maximum attenuation) of the attenuating waves.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic attenuation from inhomogeneous waves in a dissipative anisotropic poroelastic medium

Sharma

Vashishth

2011

Earth Planet Sp

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A procedure is suggested to translate the quality factor of a plane harmonic attenuating wave in a general anisotropic elastic medium into its phase velocity and two finite non-dimensional attenuation parameters. A chosen value of the quality factor of an attenuated wave in the dissipative medium is used to specify its complex slowness vector for a general direction of propagation. In this specification, one of the attenuation parameter identifies the component of intrinsic attenuation along the direction of propagation of wave, i.e., homogeneous propagation of wave. Another parameter represents the component of attenuation in the direction orthogonal to propagation direction. It measures the deviation from homogeneous propagation and is termed as the inhomogeneity strength of the attenuated wave. These attenuation parameters alongwith phase velocity are used to calculate the rate of decay of amplitude of the attenuated wave along any given direction in propagationattenuation plane. Biot's theory is used to study the propagation of four attenuating waves in an anisotropic poroviscoelastic medium in the presence of initial stress. For each wave, the specification of complex slowness vector is obtained in terms of its phase velocity and two attenuation parameters. Numerical results show that the attenuation contribution from the homogeneous propagation (of any of the three faster waves) is only a little in the total attenuation of any of these attenuated waves. The effects of the changes in anisotropy-type, initial-stress, frequency, fluid-viscosity, viscous characteristic length, and anelasticity of porous frame on the attenuation are also studied. It is found that though they affect the phenomenon of wave propagation and wave characteristics, major contribution to total intrinsic attenuation comes from the inhomogeneous propagation of the attenuated wave.

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Propagation of inhomogeneous plane waves in dissipative anisotropic poroelastic solids

Cited by 24 publications

References 24 publications

Fabric dependence of quasi-waves in anisotropic porous media

Fabric dependence of quasi-waves in anisotropic porous media

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

Intrinsic attenuation from inhomogeneous waves in a dissipative anisotropic poroelastic medium

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