Propagation of acoustic waves in a fibrous fluid-filled material

The homogenization method is used for the analysis of acoustic wave propagation in a unidirectional fibrous material for the acoustic control of the fiber arrangement in manufacturing composites. Acoustic equations for a rigid periodic structure filled by a nonviscous fluid are obtained by two-dimensional asymptotic expansions. A regular square and triangular arrangement of the fibers with a round cross-section are considered. The analysis reveals that the velocity of acoustic waves is significantly affected by both the volume content and the fiber arrangement.Moscow State Academy of Chemical Engineering, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 651–655 September–October, 1997.     

Diffraction on a semi-infinite screen of a plane nonstationary wave the amplitude of which increases linearly along the front set

An exact analytic solution of the two-variables nonstationary problem of diffraction on an ideal half-infinite screen is obtained by the Smirnov-Sobolev method. The source of the field is an incident plane acoustic wave with a δ-function profile. The wave amplitude is a linear function increasing along the front set. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 138–152.     

An axially asymmetric problem of diffraction of a cylindrical wave on an ideal cylinder

The nonstationary scattering problem of a cylindrical wave on an absolutely rigid cylinder is considered in the case when the axes of an emitter and a disperser are arranged in crossed systems of coordinates, are not parallel, and do not lie in one plane. It is shown analytically that in the case of nonparallel axes of the emitter and the disperser, perturbations will be propagated along a spiral near the cylinder and along its axis.Translated from Dinamicheskie Sistemy, No. 9, pp. 33–37, 1990.     

Shortwave scattering by a diffraction echelette-grating

The two-dimensional problem of the scattering of a plane wave by a periodic perfectly conducting grating, an echelette with a right angle, is considered in the case of a high-frequency approximation (the wavelength is assumed to be small as compared with the period of the grating). The situation where the incident plane wave glides along one of the faces of a wedge is discussed. A ray-optical solution of the problem (a shortwave asymptotic result) is derived by the method of summing multiple diffracted fields, which is well known in the geometric theory of diffraction. The main result of this paper consists of obtaining simple formulas for the efficiency e_n of a diffraction order with maximal value of e_n, derived in the shortwave approximation. Numerical results are presented, and important optical properties obtained by asymptotic analysis are described. Bibliography: 10 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 109–135. Translated by V. V. Zalipaev.     

Wood's anomalies in the scattering problem of a plane wave on a smooth periodic boundary

A series of multiple diffracted fields in a high-frequency asymptotic expansion of the solution to the problem of grazing scattering of a plane wave by a smooth periodic boundary is summed in the case of appearance of Wood's anomalies. Bibliography: 8 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 87–100, 1990. Translated by V. V. Zalipaev.     

Evaluation of fluid-filled fractures during acoustic measurements on tube waves

The problem of reflection, transmission, and conversion of the tube wave on a fracture intersecting a borehole is investigated. We consider the case where an acoustic sonde is placed inside a borehole and the fracture separates two different elastic half-spaces and is filled with a porous material. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 324, 2005, pp. 121–128.     

Dynamics of a rigid body on rockers

We study the dynamics of a rigid body on rockers with a nonspherical contact surface. It is shown that in the case of small oscillations the equations of motion contain strong nonlinearity, which makes it possible to avoid resonance (nonperiodic) oscillations. We study free and forced oscillations under a harmonic force on the plane of whose parameters bifurcation curves are constructed separating the periodic and nonoscillatory processes. Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 51–55.     

Diffraction of a plane wave by a narrow cone

The problem of diffraction of a plane scalar wave by a narrow cone is considered. The shape of the cone is arbitrary. The boundary condition is the Dirichlet or Neumann one. The wave scattered by the cone vertex arises as a result of the diffraction process. The subject of this paper is to calculate the wave amplitude. If the cone is narrow, it is possible to obtain simpler approximate formulas in comparison with Smyshlayev's one. The exactness of the approximate formulas is checked numerically. The etalon is a solution in explicit form in the axially symmetric case. The calculation shows that our formula is more exact in the case of the Dirichlet boundary condition than Felsen's formula. The approximate formula is a generalization of Felsen's one for circular cone to an arbitrary narrow cone in the case of the Neumann boundary condition. Bibliography: 6 titles. Dedicated to N. N. Uraltseva on her jubilee Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 67–74. Translated by D. B. Dement'ev.     

Asymptotic expansion of the coefficients of radiating plane waves in the scattering problem on a smooth periodic boundary

High-frequency asymptotic expansion of the coefficients of radiating plane waves in the problem of grazing scattering of a plane wave on a smooth periodic boundary is derived. Bibliography: 8 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 71–86, 1990. Translated by V. V. Zalipaev.     

The acoustic field of an elastic band in contact with a liquid

We propose a method of computation and analyze the acoustic field of an elastic plate under forced vibrations over the shapes of a cylindrical bend on an infinite rigid screen at the interface of liquid media. The problem is reduced to solving a system of algebraic equations with respect to the real and imaginary components of the acoustic pressure at a series of fixed points of the plate.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 102–105.     

The motion of a rigid spherical inclusion in an elastic medium under the action of plane waves

Two problems on the motion of a rigid spherical inclusion in an elastic medium under the action of a nonstationary, longitudinal, plane, compressional wave and a harmonic shear wave are considered. Using the method of vector eigenfunctions and the integral Laplace transform with respect to time their precise solutions are constructed. Numerical results are given which illustrate the dependence of characteristics of motion of the inclusion on parameters of the falling wave.Translated from Dinamicheskie Sistemy, No. 9, pp. 37–47, 1990.     

Application of the matrix riemann problem to the study of excitation of natural waves in an acoustic waveguide by a piston radiator

Stationary excitation of natural waves in a flat acoustic waveguide with absolutely soft lateral walls by a piston radiator is investigated. In the case where the length of the radiator is equal to the halved width of the waveguide, the exact analytic solution is obtained. The representation of the acoustic field in the waveguide in the form of an expansion over the natural waves of the waveguide is provided.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 129–132.     

Diffraction of a plane wave by a step discontinuity in an impedance plane

In the present paper, the high-frequency diffraction of a plane wave by a right-angle step discontinuity in an impedance plane is analyzed with the help of the uniform geometric theory of diffraction, beginning with the Maluzhenets solution. The principal term of an asymptotic solution of the problem, which is uniform with respect to the angle of incidence of the plane wave and the angle of observation, is derived. The excitation of primary and multiply diffracted fields radiated from the upper edge, as well as surface waves, is considered (the lower edge does not radiate cylindrical or surface waves owing to a right-angle step). For simplicity, the details of computation are given here for a right-angle step discontinuity. A similar procedure is applied to other examples with more complicated geometry. Bibliography: 7 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 97–108. Translated by V. V. Zalipaev.     

Radiation of short waves by a pair of plates backed by a semi-infinite set of ribbed stiffeners

The following acoustic diffraction problem is considered. The upper half-space is filled by an acoustic medium. Two semi-infinite thin plates are situated on the boundary of the upper half-space. One of the plates is backed by a semi-infinite periodical set of ribbed stiffeners. The source of an acoustic field is positioned on the other plate. The problem is reduced to an infinite system of linear algebraic equations. Such a system can be solved in a shortwave approximation. An expression for the acoustic field at a large distance from the junction of the plates is obtained. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 38–46. Translated by A. V. Badanin.     

Scattering of waves by an expanding surface

In the present paper, the perturbance of a harmonic plane wave by an expanding surface originating at a fixed point is considered. This surface generates a wave with spherical front. An analytic expression of the wave field in the vicinity of the wave front is obtained both in the scalar and in the electromagnetic case. Bibliography: 7 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 35–48. Translated N. S. Zabavnikova.     

The spectral characteristics of an acoustic pressure field scattered by a nondeformable solid of revolution

We carry out a numerical analysis of the solution of scattering problems for acoustic waves by acoustically soft and rigid bodies whose shape is close to spherical. We obtain the absolute value of the scattering amplitude as a function of the wave number. Four figures. One table. Bibliography: 8 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 8–13.     

Investigation of wave propagation velocities in fluid mixtures

In order to determine the wave propagation velocities in fluid mixtures, the mixtures are approximated by block structures. These structures consist of identical cells containing eight blocks. The blocks may be filled with different fluids. In block structures, the passage to the limit is carried out under the conditions that the sizes of blocks tend to zero but the relative sizes of blocks remain constant. In the general case, the average wave field satisfies the equations of anisotropic fluids. Two special cases of mixtures of two fluids are considered. In the first case, both fluids are intermixed completely. In the second case, there are periodic inclusions of one fluid into the other. In both cases, the fluid mixtures are homogeneous and isotropic, and formulas for the velocities are obtained. These formulas determine the dependence of the velocities on the percent composition and the parameters of two mixed fluids. The velocity of propagation in the fluid mixture does not exceed the greatest velocity but may be less than the least velocity in mixed fluids. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 332, 2006, pp. 149–162.     

On diffraction of high-frequency waves by a cone of arbitrary shape. Neumann case

In this paper, we consider the problem of diffraction of an acoustic wave by a cone of arbitrary shape. The problem is to calculate in a high frequency approximation the wave scattered by the cone vertex. The calculation is based on a formula of Smyshlyaev. The acoustic wave satisfies the Newmann boundary conditions. The same problem for the Dirichlet boundary conditions was considered by Babich, Dement'ev, and Samokish. In this paper, we apply a similar method. We calculate the direction diagram for the wave scattered by the cone vertex, in the so-called Smyshlyaev oasis. Calculations show that for the case when the exact solution can be written explicitly (axisymmetric wave on a circular cone), the approximate solution is very close to the exact one. Bibliography: 8 titles. Dedicated to N. N. Uraltseva on her jubilee Published inZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 75–82. Translated by D. B. Dement'ev.     

The acoustic field of a high-frequency source moving in a waveguide

The acoustic field of a source moving at a subsonic velocity in a regular waveguide with perfectly reflecting boundaries is considered. The acceleration of the source is assumed to be small. In a moving coordinate system, the asymptotics of the wave field is obtained. This asymptotics is inapplicable near the critical cross sections, for which the Doppler frequency of the source coincides with the frequency of the waveguide mode under consideration. It is demonstrated that, in this case, the wave field can be represented locally by a special type of integral, which is analyzed by the saddle-point method.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 71–78.This work was supported in part by the Russian Foundation for Basic Research under grant 95-01-01285a.     

The transmission of a plane acoustic wave through a non-uniform thermoelastic layer

The reflection and refraction of a plane acoustic wave by a thermoelastic plane layer, non-uniform in thickness, bounded by non-viscous heat-conducting liquids, generally different, is considered. The system of equations for small perturbations of the thermoelastic medium is reduced to a system of ordinary differential equations, the boundary-value problem for which is solved by two methods: the spline-collocation method and the power-series method. Analytic expressions are obtained which describe the wave fields outside the layer. The results of calculations of the intensity transmission coefficient of the acoustic wave are presented.