Diffraction of sound pulses by a rigid cylinder in an inhomogeneous medium

We consider the problem of scattering of two-dimensional sound pulses by a rigid circular cylinder embedded in a cylindrically stratified inhomogeneous medium. The line source is parallel to the axis of the cylinder. It is assumed that the velocity of soundc is given byc ^?1=pr ^q, wherep andq are real constants andp>0. The method of dual integral transformation developed by Friedlander is used. The solution in terms of pulse propagation modes gives the diffracted pulse and the method of steepest descents yields the geometrical acoustic field.     

Scattering of sound by an inhomogeneous thermoelastic spherical layer

The diffraction of sound by a radially layered isotropic thermoelastic spherical shell is considered. The system of equations for small perturbations of a hollow thermoelastic sphere is reduced to a system of ordinary differential equations, the boundary-value problem for which is solved by a spline-collocation method. Expressions are obtained which describe the wave fields outside the spherical layer. The results of calculations of the frequency and angular dependences of the amplitude of the scattered sound field in the far zone are presented.     

Propagation of sound pulses in a semiinfinite stratified medium

We consider the propagation of sound pulses due to a line source in the inhomogeneous, semi-infinite mediumy ≥ 0 with the boundary conditionφ=0 or?φ/(?y)=0 aty=0, whereφ is the acoustic velocity potential. We suppose that the velocity of wave propagation,c, is given byc ^?2=p ?qe ^?ay , wherep, q, α are real and positive andp>q. The method of dual integral transformation is used. The solution in terms of pulse propagation modes yields the diffracted pulse and the method of steepest descents gives the geometrical acoustic field.     

Sound field of a source moving in an inhomogeneous layer on a homogeneous halfspace

Equations are suggested in the present paper for the amplitudes and instantaneous frequencies of sound waves generated by a moving source. The equations are derived by means of the Space-Time Ray (STR) method and by the two-scale expansion method (the method of horizontal rays and vertical modes).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 35–48, 1986.     

Models of layer deformation of an elastic half space

Applied modes of the deformation of an inhomogeneous elastic bed consisting of a layer of finite thickness and a semi-infinite space, the elastic constants of which differ markedly, are proposed. An explicit form of the equations describing the theory of deformation is established. An evaluation of the error of the resultant equations is made, and the range of their application determined.Translated from Dinamicheskie Sistemy, No. 5, pp. 11–20, 1986.     

A method of calculating interference waves in a vertically inhomogeneous half space

Calculation of the complex roots of the dispersion equations by the sweep-out method is discussed for the case of SH waves in a layered inhomogeneous medium. The roots obtained define the phase speeds and the damping coefficients of interference waves as functions of the frequency. Results of numerical computations are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 162–173, 1974.     

Interference transverse sh waves in a transversally,isotropic, inhomogeneous half space

In the paper Love waves in a transversally, Isotropic, inhomogeneous half space are investigated in the case where the plane of isotropy does not coincide with the boundary plane. The dependence on the angle between them is established to the solution obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 104, pp. 228–234, 1981.     

Electroelastic state of an inhomogeneous piezoceramic layer under symmetric loading

A procedure for solving three-dimensional mixed symmetric problems of electroelasticity theory for a piezoceramic layer with an inclusion, which is weakened with a through hole, is proposed. The boundary-value problem is reduced to a system of 12k (k = 1, 2, …) integrodifferential equations. Expressions for stresses characterizing the stress state of the inhomogeneous layer are found. Calculation results for characteristic stresses are presented.     

Propagation of shear waves in homogeneous and inhomogeneous fibre-reinforced media on a cylindrical Earth model

The present paper is concerned with the propagation of shear wave in a cylindrical structure comprised of two concentric media by two distinct cases. In first case, media are homogeneous and in second case, media are heterogeneous. The heterogeneities are caused due to the radial variation in both the media distinctly. The dispersion relation for shear wave propagation in homogeneous and heterogeneous, fibre-reinforced media have been derived analytically in the closed form using Debye Asymptotic Expansion and verified with the existing literature and classical results. Numerical computation and graphical demonstration have been carried out to show the remarkable effect of various parameter viz. fibre-reinforcement, heterogeneities and radii ratio of the media on the intensity of frequency of shear wave propagation against the dimensionless wave number. A comparative study between the reinforcement and isotropic material with or without heterogeneity has been discussed extensively and unravel some important peculiarities.     

Propagation of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space

In the present paper, the dispersion equation which determines the velocity of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space has been obtained. The dispersion equation obtained is in agreement with the classical result of Love wave when the initial stresses and inhomogeneity parameters are neglected. Numerical results analyzing the dispersion equation are discussed and presented graphically. The result shows that the initial stresses have a pronounced influence on the propagation of torsional surface waves. It has also been shown that the effect of density, directional rigidities and non-homogeneity parameter on the propagation of torsional surface waves is prominent.     

The boundary layer analysis for stokes equations on a half space

The time dependent Stokes equations on a half space are considered. We decompose the solution of these equations in an inviscid solution: a boundary layer solution and a correction. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction is shown to be of the same order of magnitude of the square root of the viscosity.     

Propagation of SH‐wave in an initially stressed orthotropic medium sandwiched by a homogeneous and an inhomogeneous semi‐infinite media

The paper presents a study of propagation of shear wave (SH‐wave) in an orthotropic elastic medium under initial stress sandwiched by a homogeneous semi‐infinite medium and an inhomogeneous half‐space. The technique of separation of variables has been adopted to get the analytical solutions for the dispersion relation in a closed form. The propagation of SH‐waves is influenced by inhomogeneity parameters and initial stress parameter. Velocities of SH‐waves are calculated numerically for different cases. As a special case when the intermediate layer and half‐space are homogeneous, computed frequency equation coincides with general equation of Love wave. To study the effect of inhomogeneity parameters and initial stress parameter, we have plotted the velocity of SH‐wave in several figures and observed that the velocity of wave decreases with the increases of non‐dimensional wave number. It can be found that the phase velocity decreases with the increase of inhomogeneity parameters. We observed that the velocity of SH‐wave decreases with the increases of initial stress parameter in both homogeneous and inhomogeneous media. GUI has been developed by using MATLAB to generalize the effect of the parameters discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Inverse scattering by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem: one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.     

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Based on the methods of complex function, conformal mapping, and multipolar coordinate system, dynamic response of an elliptical inclusion embedded in an anisotropic half space is investigated. In order to find the solution of SH waves, the governing equation is transferred into its normalized form. Then, the scattering wave induced by the inclusion and the standing wave in the inclusion is deduced. Different incident wave angles and the corresponding anisotropy of the half space are considered to obtain the reflected waves. The elliptical inclusion is transferred into a unit circle by conformal mapping method, and then the undetermined coefficients in scattering wave and standing wave are solved by using the continuous condition at the boundary of the inclusion. Subsequently, the dynamic stress concentration factor (DSCF) around the inclusion is calculated and analyzed. Numerical results demonstrate that the distribution of the DSCF is mainly influenced by the incident wave angle and the incident wave number. It is affected by anisotropic parameters as well.     

Indentation of an incompressible inhomogeneous layer by a rigid circular indenter

This work deals with an incompressible inhomogeneous layer bondedto a rigid substrate and indented without friction by a rigidcircular indenter. The corresponding mixed boundary-value problemof elasticity is reduced to equivalent dual integral equations.It is shown that the pliability function in these equationsmay be found from a system of nonlinear differential equationsand that its behaviour is peculiar when the elastic medium isincompressible. A novel technique taking into account this peculiarityis developed in order to reduce the dual integral equationsto Fredholm integral equations of the second kind with symmetricstrictly coercive operators. For a homogeneous layer and a flatindenter, the structure of the Fredholm integral equations permitsan approximate analytical solution which is very accurate forany layer thickness. For an indenter of three-dimensional profile,leading asymptotic terms of the solution are derived in thecase of a thin inhomogeneous layer.     

Strong evaporation into a half space

Evaporation of a liquid into a vacuum occupying a half space is investigated on the basis of the one-dimensional BGK model linearized about a drifting Maxwellian distribution. A unique solution is shown to exist if the downstream speed remains subsonic. Exact analysis is used, and numerical results are given.

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Zusammenfassung Auf der Basis eines eindimensionalen BGK-Modells, das über eine driftende Maxwell-Verteilung linearisiert ist, wird die Verdampfung einer Flüssigkeit in ein einen Halbraum ausfüllendes Vakuum untersucht. Es wird gezeigt, daß nur eine einzige Lösung existiert, wenn die Geschwindigkeit im Unterschallbereich bleibt. Exakte Analysis wird verwendet und numerische Resultate angegeben.