Diffraction of an arbitrary acoustic wave by a strip of finite width

The problem of the diffraction of an arbitrary acoustic wave by a strip of finite width is solved. The solution is constructed by means of a generalization of the previously obtained integral for the problem of the diffraction of acoustic waves by a half-plane [5]. The problem of the diffraction of an arbitrary acoustic wave by the Riemannian manifold corresponding to the strip of finite width is first found. After this, by substitution of the values of the polar angle a solution is obtained for the reflected wave associated with diffraction on the Riemannian manifold, and then the boundary conditions on the surface of the strip are satisfied by means of a linear combination of these solutions. The problem of the diffraction of an arbitrary acoustic wave by a slit of finite width could be constructed in exactly the same way.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–175, March–April, 1991.     

Action of an acoustic wave on a system of two spherical bodies in an ideal fluid

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 5, pp. 102–108, May, 1990.     

Diffraction of a plane acoustic wave by a rigid sphere in a cylindrical cavity: An axisymmetric problem

The paper studies the interaction of a rigid spherical body and a cylindrical cavity filled with an ideal compressible fluid in which a plane acoustic wave of unit amplitude propagates. The solution is based on the possibility of transforming partial solutions of the Helmholtz equation between cylindrical and spherical coordinates. Satisfying the interface conditions between the cavity and the acoustic medium and the boundary conditions on the spherical surface yields an infinite system of algebraic equations with indefinite integrals of cylindrical functions as coefficients. This system of equations is solved by reduction. The behavior of the system is studied depending on the frequency of the plane wave     

Diffraction of a sound wave by a slit

The diffraction of a sound wave by a slit in an unbounded plane is analyzed as an initial-boundary-value problem with a moving boundary for the two-dimensional wave equation. The initial-boundary-value problem is solved by the formation and inversion of Volterra integral equations. A solution is obtained in closed form in quadratures for an arbitrary angle of inclination of the incident wave front relative to the plane. The solution is presented in the form of recursion formulas, which take into account the influence of diffraction waves occurring in succession at the boundaries of the slit.     

Effect of acoustic radiation on a spherical drop of liquid

The effect of radiation force on a drop of liquid in an acoustic field is examined. It is established that the force depends on the ratio of the densities of the liquid and the drop and on their adiabatic elastic moduli __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 26–34, July 2007.     

Broadband optimization of a pentamode-layered spherical acoustic waveguide

Transformational acoustics offers the theoretical possibility of cloaking obstacles within fluids, provided metamaterials having continuously varying bulk moduli and densities can be found or constructed. Realistically, materials with the proper, continuously varying anisotropies do not presently exist. Discretely layered cloaks having constant material parameters within each layer are a viable alternative, but due to their discrete nature, may become ineffective outside of narrow frequency ranges. Because of such limitations, there is interest in finding discretely layered systems that can be effective in as wide as possible bandwidth without the need for unrealizable material properties within each layer. The present work introduces a novel methodology for finding optimal material parameters for use in such layered cloaks. In principle, the technique could be applied to any acoustic or electromagnetic scattering problem, but for purposes of demonstration, this paper considers a fluid-loaded acoustically hard sphere with a cloak that comprised layered pentamodes, whose material properties are constrained to lie within reasonable ranges relative to the density and bulk modulus of water.     

Diffraction of a solitary wave by a thin wedge

The diffraction of a solitary wave by a thin wedge with vertical walls is studied when the incident solitary wave is directed along the wedge axis. The method of multiple scales is extended to this problem and reduces the task to that of solving the two-dimensional KdV equation with proper boundary and initial conditions. The finite-difference numerical procedure is carried out with the fractional step algorithm in which difference schemes are all implicit. Except the maximum run-up at the wall, the results in this paper are found to corroborate the Melville's experiments not only qualitatively but also quantitatively. The maximum run-up of our results agrees well with Funakoshi's numerical one but it is considerably larger than that in Melville's experiment. An important reason for this discrepancy is believed to be the effect of viscous boundary layer on the vertical side wall.     

Diffraction of a sound wave by a nonmoving plate

The problem of determining the velocity field excited by a sound wave impinging on a plate at rest is analyzed as an initial- and boundary-value problem with a movable boundary for the two-dimensional wave equation. The latter problem is solved by the formulation and inversion of integral equations of the Volterra type. The solution is obtained in closed form for any angle of inclination of the incident wave relative to the plate surface and is represented by recursion relations allowing for the influence of any number of diffracted waves generated in succession at the plate boundary.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 123–130, March–April, 1972.     

Diffraction of an elastic wave in a disc

A numerical solution is constructed for the axisymmetric problem of the diffraction of a plane longitudinal wave in a rigid disc (cylinder) of finite thickness. The disc is enclosed in an unbounded elastic medium; at the contact surface, the tangential stresses are limited by some constant. The incident wave moves along the axis of the cylinder and has the form of a semiinfinite washed-out step. At the same time, a solution is obtained to the corresponding static problem. A study was made of the dependence of the rate of motion of the cylinder and the stress field on the parameters of the problem. In particular, it is shown that the contact conditions have a considerable effect on the stress field only near the lateral surface. The results obtained can be useful for evaluating the errors in measurement of the stresses and velocities in an elastic medium, and possibly also in certain other cases.Deceased.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, No. 3, pp. 139–150, May–June, 1972.     

The reflection of a shock wave over a cone

An investigation was made of the reflection of planar shock waves from cones. 86 cones, the half apex angle of which varied from 10° to 52° at every 0.5°, were installed in a 60 mm×150 mm diaphragmless shock tube equipped with holographic interferometry. The diaphragmless shock tube had a high degree of reproducibility with which the scatter of shock wave Mach number was within ±0.25% for shock wave Mach number ranging from 1.16 to approximately 2.0. The reflection of shock waves over cones was visualized using double exposure holographic interferometry. Whitham's geometrical shock wave dynamics was used to analyse the motion of Mach stems over cones. It is found that for relatively smaller apex angles of cones trajectory angles of resulting irregular reflections coincide with the so-called glancing incidence angles and their Mach stems appear to be continuously curved from its intersection point with the incident shock wave, which shows the chractericstic of von Neumann reflection. The domain of the existence of the von Neumann reflection was analytically obtained and was found to be broadened much more widely than that of two-dimensional reflections of shock waves over wedges.     

Modal acoustic impedance force on a spherical source near a rigid interface

The modal acoustic radiation load on a spherical surface undergoing angularly periodic axisymmetric harmonic vibrations while immersed in an acoustic halfspace with a rigid (infinite impedance) planar boundary is analyzed in an exact fashion using the classical technique of separation of variables. The formulation utilizes the appropriate wave field expansions, the classical method of images and the appropriate translational addition theorem to simulate the relevant boundary conditions for the given configuration. The associated acoustic field quantities such as the modal impedance matrix and the modal acoustic radiation force acting on the spherical surface are determined. The analytical results are illustrated with a numerical example in which the spherical surface, excited in vibrational modes of various orders, is immersed near an impervious rigid wall. The presented solution could eventually be used to validate those obtained by numerical approximation techniques.