Inhomogeneous Waves in Solids and Fluids

Caviglia, Giacomo; Morro, Angelo

doi:10.1142/1519

Cited by 70 publications

(42 citation statements)

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“…An extensive literature (Hayes, 1980;Caviglia and Morro, 1992;Carcione, 2001;Cerveny and Psencik, 2005) is available on the propagation of inhomogeneous waves in dissipative anisotropic media. A different method (Sharma, 2007), explained in this section, constructs the complex slowness vector for the inhomogeneous waves with given propagation and attenuation directions in unbounded medium.…”

Section: Inhomogeneous Plane Wavesmentioning

confidence: 99%

Inhomogeneous waves at the boundary of a generalized thermoelastic anisotropic medium

Sharma

2008

International Journal of Solids and Structures

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The Christoffel equation is derived for the propagation of plane harmonic waves in a generalized thermoelastic anisotropic (GTA) medium. Solving this equation for velocities implies the propagation of four attenuating waves in the medium. The same Christoffel equation is solved into a polynomial equation of degree eight. The roots of this equation define the vertical slownesses of the eight attenuating waves existing at a boundary of the medium. Incidence of inhomogeneous waves is considered at the boundary of the medium. A finite non-dimensional parameter defines the inhomogeneity of incident wave and is used to calculate its (complex) slowness vector. The reflected attenuating waves are identified with the values of vertical slowness. Procedure is explained to calculate the slowness vectors of the waves reflected from the boundary of the medium. The slowness vectors are used, further, to calculate the phase velocities, phase directions, directions and amounts of attenuations of the reflected waves. Numerical examples are considered to analyze the variations of these propagation characteristics with the inhomogeneity and propagation direction of incident wave. Incidence of each of the four types of waves is considered. Numerical example is also considered to study the propagation and attenuation of inhomogeneous waves in the unbounded medium.

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Section: Inhomogeneous Plane Wavesmentioning

confidence: 99%

Inhomogeneous waves at the boundary of a generalized thermoelastic anisotropic medium

Sharma

2008

International Journal of Solids and Structures

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“…It is also valid for inhomogeneous waves and for noncoplanar P inc P inc , A inc A inc and n n. In the seismological literature, considerable attention has been devoted to the R/T laws in viscoelastic isotropic media, assuming the coplanar case. See Borcherdt (1977Borcherdt ( , 1982, Aki and Richards (1980), Krebes (1983), Wennerberg (1985), Caviglia and Morro (1992), where many other references can be found.…”

Section: 5 I S O T R O P I C V I S C O E L a S T I C M E D I Amentioning

confidence: 99%

Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

Červený

2007

Stud Geophys Geod

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The reflection/transmission laws (R/T laws) of plane waves at a plane interface between two homogeneous anisotropic viscoelastic (dissipative) halfspaces are discussed. Algorithms for determining the slowness vectors of reflected/transmitted plane waves from the known slowness vector of the incident wave are proposed. In viscoelastic media, the slowness vectors of plane waves are complex-valued, p = P + iA p = P + iA, where P P is the propagation vector, and A A the attenuation vector. The proposed algorithms may be applied to bulk plane waves (A = 0 A = 0), homogeneous plane waves (A 6 = 0 A 6 = 0, P P and A A parallel), and inhomogeneous plane waves (A 6 = 0 A 6 = 0, P P and A A non-parallel). The manner, in which the slowness vector is specified, plays an important role in the algorithms. For unrestricted anisotropy and viscoelasticity, the algorithms require an algebraic equation of the sixth degree to be solved in each halfspace. The degree of the algebraic equation decreases to four or two for simpler cases (isotropic media, plane waves in symmetry planes of anisotropic media). The physical consequences of the proposed algorithms are discussed in detail.

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“…Plane waves of the form u ¼ Ae jðkÁxÀxtÞ , (j 2 ¼ À1), with complex valued A and k are called inhomogeneous waves (see [1]). Here, the A is the wave amplitude and the k is the wave vector.…”

Section: Introductionmentioning

confidence: 99%

“…It is pointed out in Ref. [1] that, plane wave solutions do not exist for heterogeneous elastic bodies. However, as is shown previously ( [3]), this work also describes a particular case, when the notion of wave number can be retained both exactly and approximately.…”

Section: Introductionmentioning

confidence: 99%

A spectral finite element for axial-flexural-shear coupled wave propagation analysis in lengthwise graded beam

Chakraborty

Gopalakrishnan

2005

Comput Mech

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A new spectral element (SE) is formulated to analyse wave propagation in anisotropic inhomogeneous beam. The inhomogeneity is considered in the longitudinal direction. Due to this particular pattern of inhomogeneity, the governing partial differential equations (PDEs) have variable coefficients and an exact solution for arbitrary variation of material properties, even in frequency domain, is not possible to obtain. However, it is shown in this work that for exponential variation of material properties, the equations can be solved exactly in frequency domain, when the same parameter governs the variation of elastic moduli and density. The SE is formed using this exact solution as interpolating polynomial. As a result a single element can replace hundreds of finite elements (FEs), which are essential for all wave propagation analysis and also for accurate representation of the inhomogeneity. The developed element is used for eliciting several advantages of the gradation, including mode selection, mode blockage and smoothening of stress waves.

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Inhomogeneous Waves in Solids and Fluids

Cited by 70 publications

References 0 publications

Inhomogeneous waves at the boundary of a generalized thermoelastic anisotropic medium

Inhomogeneous waves at the boundary of a generalized thermoelastic anisotropic medium

Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

A spectral finite element for axial-flexural-shear coupled wave propagation analysis in lengthwise graded beam

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