Spatial Modes in Periodically Inhomogeneous Media

A method is proposed to determine wave modes in periodically inhomogeneous media. Quantitative results for longitudinal waves across a structure in the first four transmission zones for a medium formed of repeating two isotropic layers are analyzed__________Translated from Prikladnaya Mekhanika,Vol. 41, No. 5, pp. 3–8, May 2005.     

Spatial Shear Modes in Periodically Inhomogeneous Media

A method is proposed to determine shear wave modes of arbitrary direction in periodically inhomogeneous media. Quantitative results for the two first transmission zones of a medium formed of repeating two layers are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 51–57, August 2005.     

Propagation of Coupled Waves Interacting with an Electromagnetic Field in Periodically Inhomogeneous Media

The paper is concerned with coupled (electroelastic, electromagnetoelastic, and magnetoelastic) waves in inhomogeneous media     

Seismic Wave Propagation in Composite Elastic Media

It has been known since the time of Biot–Gassman theory (Biot, J Acoust Soc Am 28:168–178, 1956, Gassmann, Naturf Ges Zurich 96:1–24, 1951) that additional seismic waves are predicted by a multicomponent theory. It is shown in this article that if the second or third phase is also an elastic medium then multiple p and s waves are predicted. Futhermore, since viscous dissipation no longer appears as an attenuation mechanism and the media are perfectly elastic, these waves propagate without attenuation. As well, these additional elastic waves contain information about the coupling of the elastic solids at the pore scale. Attempts to model such a medium as a single elastic solid causes this additional information to be misinterpreted. In the limit as the shear modulus of one of the solids tends to zero, it is shown that the equations of motion become identical to the equations of motion for a fluid filled porous medium when the viscosity of the fluid becomes zero. In this limit, an additional dilatational wave is predicted, which moves the fluid though the porous matrix much similar to a heart pumping blood through a body. This allows for a connection with studies which have been done on fluid-filled porous media (Spanos, 2002).     

Propagation of magnetoelastic shear waves across layers in a periodically layered medium

The paper is concerned with magnetoelastic shear waves propagating in regularly layered magnetostrictive media at a right angle to the layer interfaces __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 54–60, June 2006.     

Homogenization and Global Responses of Inhomogeneous Spherical Nonlinear Elastic Shells

Homogenization of radially inhomogeneous spherical nonlinear elastic shells subject to internal pressure is studied. The equivalent homogeneous material is defined in such a way that it gives rise to exactly the same global response to the pressure load as that of the inhomogeneous shell. For a shell with general strain–energy function and inhomogeniety, the strain–energy function of the equivalent homogeneous material is determined explicitly. The resulting formula is used to study layered composite shells. The equivalent homogeneous material for an infinitely fine layered composite shell is examined, and is found to give not only the same global response, but also the same average stress field as the composite shell does.     

Propagation of the Energy of Nonlinearly Elastic Plane Waves

The propagation of the energy of nonlinearly elastic plane waves in a Murnaghan material is simulated on a computer. The velocity of energy propagation is found in an explicit form. A procedure of determining the critical values of the time and space coordinates for the given material is described. The resultant plots are discussed and analyzed     

Solitary Elastic Waves and Elastic Wavelets

A new group of wavelets that have the form of solitary waves and are the solutions of the wave equations for dispersive media is proposed to call elastic wavelets. That this group includes well-known Mexican-hat wavelets is proved. It is proposed to use elastic wavelets to study local features of the profile evolution of a solitary wave in an elastic dispersive medium     

Propagation of Harmonic Waves in an Orthotropic Cylindrical Shell on Elastic Foundation

An equation is derived, using Timoshenko shell theory, to analyze axisymmetric strain fields in an orthotropic cylindrical shell on an elastic foundation. Also a dispersion equation is derived to study the natural harmonic waves in a shell depending on the properties of the elastic foundation. The wave velocities computed by the numerical method proposed are in agreement with the analytical solutions, which confirms the reliability of the results     

Finite-Amplitude Inhomogeneous Plane Waves of Exponential Type in Incompressible Elastic Materials

It is proved that elliptically polarized finite-amplitude inhomogeneous plane waves may not propagate in an elastic material subject to the constraint of incompressibility. The waves considered are harmonic in time and exponentially attenuated in a direction distinct from the direction of propagation. The result holds whether the material is stress-free or homogeneously deformed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Propagation of nonlinear waves in an inhomogeneous gas-liquid medium. Derivation of wave equations in the Korteweg-de Vries approximation

Equations describing the propagation of waves of small but finite amplitude in a liquid with gas bubbles are derived. The bubble distribution density is a continuous function of bubble size and spatial coordinates. It is found that, for a uniform bubble distribution, the obtained equations become the Korteweg-de Vries, Kadomtsev-Petviashvili and Khokhlov-Zabolotskaya equations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 188–197, March–April, 2009.     

Bending Solutions for Inhomogeneous and Laminated Elastic Plates

A procedure has been developed in previous papers for constructing exact solutions of the equations of linear elasticity in a thick plate of inhomogeneous isotropic linearly elastic material in which the elastic moduli depend in any specified manner on a coordinate normal to the plane of the plate. The essential idea is that any solution of the classical thin plate or classical laminate theory equations (which are two-dimensional theories) generates, by straightforward substitutions, a solution of the three-dimensional elasticity equations for the homogeneous material. Recently this theory has been formulated in terms of functions of a complex variable. It was shown that the displacement and stress fields in the inhomogeneous material could be expressed in terms of four complex potentials that are analytic functions of the complex variable ζ = x + iy in the mid-plane of the plate. However, the analysis performed so far applies only to the case of a plate with traction-free upper and lower faces. The present paper extends these solutions to the case where the plate is bent by a pressure distribution applied to a face.     

Wave Propagation along Axes of Symmetry in Linearly Elastic Media with Initial Stress

The proofs of the Fedorov–Stippes and Fedorov's theorems, which hold for linearly elastic homogeneous bodies in natural configurations, remain valid for any linearly elastic medium with initial stress provided that Hooke's tensor be replaced by a suitable elasticity tensor.     

Propagation of Normal Axisymmetric Waves in Compliant Elastic Cylinders Filled with and Immersed in a Fluid

The paper studies the relationship between the physical characteristics of a cylinder and the properties of normal axisymmetric waves in elastic–liquid waveguides. The cylinder is made of a compliant material in which the velocity of shear waves is less than the sonic velocity in a perfect compressible liquid. The complete system of dynamic elasticity equations and the wave equation are used to describe the wave fields in the elastic cylinder and fluid, respectively. This approach allows obtaining the dispersion characteristics of coupled normal waves in compound waveguides over wide ranges of frequencies and wavelengths. The curves of real, imaginary, and complex wave numbers versus frequency are plotted for specific pairs of waveguide materials. Computations are carried out for a thick-walled cylinder filled with a fluid and immersed in either vacuum or a fluid. It is found out that compliant and rigid materials of the cylinder affect differently the wave interaction process in elastic–liquid waveguides     

A Numerical Method for Wave Propagation in Viscoelastic Stratified Porous Media

This paper presents a numerical method, a transmission matrix method, for the wave propagation in viscoelastic stratified saturated porous media. The wave propagation in saturated media, based on Biot theory, is a coupled problem. In this stratified three-dimensional model we do the Laplace transform for the time variable and the Fourier transform for the horizontal space coordinate. The original problem is transformed into ordinary differential equations with six independent unknown variables, which are only the function of the coordinate of depth. Thus, we get a transmission matrix of the wave problem for each layer. In the process of solution we use numerical method to calculate the eigenvalues and the eigenvectors of the transmission matrices. In the first step of the solution process we can obtain the wave field in the transformed space. The fast Fourier transform (FFT) method is used to do the inverse Laplace and the inverse Fourier transforms to get the solution in the time space. The detailed formulae are derived and some numerical examples are given.     

On the Existence of Longitudinal Plane Waves in General Elastic Anisotropic Media

We give a new proof of Kolodner's result that longitudinal waves can propagate in at least three directions in a hyperelastic anisotropic medium. We give examples of an orthotropic hyperelastic tensor with exactly three such directions, of a monoclinic elastic (but not hyperelastic) tensor with only one, and of a monoclinic elastic (elliptic, but not uniformly elliptic) tensor with no direction for longitudinal waves. This revised version was published online in August 2006 with corrections to the Cover Date.     

含有随机夹杂非均匀体的有效弹性模量

在对含有随机夹杂的非均匀体求有效弹性模量时,一般多根据Eshelby的等效夹杂法,但由于该方法没有充分考虑非均匀体内部的微结构,所以其理论具有一定的局限性。本文认为Kunin的微结构理论与Eshelby的等效夹杂法相比更具一般性,因而本文采用了文[9]中一些合理的思想,摒弃了其中不合理的假设,并且建立了一种新的理论模型.最后,本文针对球夹杂的情况给出了非均匀体有效弹性模量依赖于夹杂体积份数的关系,并将该结果与文[10]中的结果进行了比较.     

Equivalence Theorems on the Propagation of Small-Amplitude Waves in Prestressed Linearly Elastic Materials with Internal Constraints

By extending the procedure of linearization for constrained elastic materials in the papers by Marlow and Chadwick et al., we set up a linearized theory of constrained materials with initial stress (not necessarily based on a nonlinear theory). The conditions of propagation are characterized for small-displacement waves that may be either of discontinuity type of any given order or, in the homogeneous case, plane progressive. We see that, just as in the unconstrained case, the laws of propagation of discontinuity waves are the same as those of progressive waves. Waves are classified as mixed, kinematic, or ghost. Then we prove that the analogues of Truesdell"s two equivalence theorems on wave propagation in finite elasticity hold for each type of wave. This revised version was published online in August 2006 with corrections to the Cover Date.     

Properties of Elastic Waves in a Non-Newtonian (Maxwell) Fluid-Saturated Porous Medium

The present study investigates novelties brought into the classic Biot's theory of propagation of elastic waves in a fluid-saturated porous solid by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. Based on our previous results (Tsiklauri and Beresnev, 2001), we investigated the propagation of rotational and dilatational elastic waves by calculating their phase velocities and attenuation coefficients as a function of frequency. We found that the replacement of an ordinary Newtonian fluid by a Maxwell fluid in the fluid-saturated porous solid results in: (a) an overall increase of the phase velocities of both the rotational and dilatational waves. With the increase of frequency these quantities tend to a fixed, higher level, as compared to the Newtonian limiting case, which does not change with the decrease of the Deborah number . (b) The overall decrease of the attenuation coefficients of both the rotational and dilatational waves. With the increase of frequency these quantities tend to a progressively lower level, as compared to the Newtonian limiting case, as decreases. (c) Appearance of oscillations in all physical quantities in the deeply non-Newtonian regime.