Green's function for the vector wave equation in a mildly heterogeneous continuum

Manolis, George D.; Shaw, Richard Paul

doi:10.1016/0165-2125(96)00006-6

Cited by 69 publications

(22 citation statements)

References 28 publications

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“…(20), (25), free-field, time-harmonic displacements in a vertically inhomogeneous half-space depend on the type and degree of inhomogeneity, as well as on the direction of propagation and frequency of the incident wave. …”

Section: E-materials Inhomogeneitymentioning

confidence: 99%

“…We consider restricted types of inhomogeneities, where all material parameters vary proportionally and Poisson's ratio is fixed [20]. As such, this work is a continuation of earlier efforts by the authors focusing on the inhomogeneous half-plane [21] and on the inhomogeneous half-space where the incoming wave has normal incidence only [22].…”

Section: Introductionmentioning

confidence: 99%

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Free-field dynamic response of an inhomogeneous half-space

2008

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In this work, elastic wave propagation in the inhomogeneous half-space is solved by an analytical approach based on plane wave decomposition in conjunction with appropriate functional transformations for the displacement vector. Specifically, free-field motions are recovered at the surface of a half-space with either quadratic or exponential type of depth-dependent material parameters. The incident wave is a time harmonic, planar pressure wave and the resulting free-field motions are obtained in closed form, first for the full-space and then for the half-space by adding the reflected waves. Parametric studies show marked differences in the results when compared against the corresponding ones for a homogeneous background. Finally, sensitivities of the free-field waves on the basic characteristics of the underlying inhomogeneous material and of the incoming wave are investigated.

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Section: E-materials Inhomogeneitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free-field dynamic response of an inhomogeneous half-space

2008

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“…Manolis and Shaw [36] A fundamental solution is derived for time-harmonic elastic waves originating from a point source and propagating in a three-dimensional unbounded heterogeneous medium with Poisson's ratio = 0.25…”

Section: C-d Wang Et Almentioning

confidence: 99%

Wave propagation in an inhomogeneous cross‐anisotropic medium

Wang

Lin

Jeng

et al. 2009

Num Anal Meth Geomechanics

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SUMMARYAnalytical solutions for wave velocities and wave vectors are yielded for a continuously inhomogeneous cross-anisotropic medium, in which Young's moduli (E, E ) and shear modulus (G ) varied exponentially as depth increased. However, for the rest moduli in cross-anisotropic materials, and remained constant regardless of depth. We assume that cross-anisotropy planes are parallel to the horizontal surface. The generalized Hooke's law, strain-displacement relationships, and equilibrium equations are integrated to constitute governing equations. In these equations, displacement components are fundamental variables and, hence, the solutions of three quasi-wave velocities, V P , V SV , and V SH , and the wave vectors, l P l SV , and l SH , can be generated for the inhomogeneous cross-anisotropic media. The proposed solutions and those obtained by Daley and Hron, and Levin correlate well with each other when the inhomogeneity parameter, k, is 0. Additionally, parametric study results indicate that the magnitudes and directions of wave velocity are markedly affected by (1) the inhomogeneous parameter, k; (2) the type and degree of geomaterial anisotropy (E/E , G /E , and / ); and (3) the phase angle, . Consequently, one must consider the influence of inhomogeneous characteristic when investigating the behaviors of wave propagation in a cross-anisotropic medium.

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“…However, defects and cracks are commonly present in FGM, both during the manufacturing process and afterwards under service conditions. Up to now, relatively little research seems to have been carried out for devising effective methods, both analytical and numerical, in order to solve static and dynamic problems involving inhomogeneous media [1][2][3][4][5][6][7][8]. The same holds true regarding work that focuses on studying formation of defects and development of cracks in these materials [9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Elastic Wave Propagation in a Class of Cracked, Functionally Graded Materials by BIEM

2006

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Elastic wave propagation in cracked, functionally graded materials (FGM) with elastic parameters that are exponential functions of a single spatial co-ordinate is studied in this work. Conditions of plane strain are assumed to hold as the material is swept by time-harmonic, incident waves. The FGM has a fixed Poisson's ratio of 0.25, while both shear modulus and density profiles vary proportionally to each other. More specifically, the shear modulus of the FGM is given as μ(x) = μ 0 exp (2ax 2 ), where μ 0 is a reference value for what is considered to be the isotropic, homogeneous material background. The method of solution is the boundary integral equation method (BIEM), an essential component of which is the Green's function for the infinite inhomogeneous plane. This solution is derived here in closed-form, along with its spatial derivatives and the asymptotic form for small argument, using functional transformation methods. Finally, a non-hypersingular, traction-type BIEM is developed employing quadratic boundary elements, supplemented with special edge-type elements for handling crack tips. The proposed methodology is first validated against benchmark problems and then used to study wave scattering around a crack in an infinitely extending FGM under incident, time-harmonic pressure (P) and vertically polarized shear (SV) waves. The parametric study demonstrates that both far field displacements and near field stress intensity factors at the crack-tips are sensitive to this type of inhomogeneity, as gauged against results obtained for the reference homogeneous material case.

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Green's function for the vector wave equation in a mildly heterogeneous continuum

Cited by 69 publications

References 28 publications

Free-field dynamic response of an inhomogeneous half-space

Free-field dynamic response of an inhomogeneous half-space

Wave propagation in an inhomogeneous cross‐anisotropic medium

Elastic Wave Propagation in a Class of Cracked, Functionally Graded Materials by BIEM

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