Reflection of harmonic elastic waves from a convex cylindrical cavity of arbitrary section

We describe an approach to the solution of problems of reflection of harmonic elastic waves from a convex indrical cavity of arbitrary section, on the basis of Debye ray, series. We obtain a system of linear algebraic equations to determine the constants of integration and expressions for determining the stresses in the elastic medium surrounding the convex cylindrical cavity. We give the results of computation of the stresses that arise as a result of the action of a planar harmonic rarefaction wave on a cylindrical cavity in the shape of elliptic and parabolic cylinders and on a cylindrical cavity whose section is a Munger oval. Four figures. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 10–16, 1991.     

Axial-radial acoustic eigenoscillations near a thin-walled obstacle in a cylindrical channel with stepped narrowings

The dependencies are investigated of eigenfrequencies and eigenfunctions of acoustic axial-radial oscillations near a thin-walled obstacle in a channel with stepped narrowings on the geometric parameters of the oscillation region. It is discovered that, near the thin-walled cylindrical obstacles in an inhomogeneous cylindrical channel with the stepped two-sided cylindrical narrowing, the number of eigenfrequencies of the acoustic axial-radial oscillations of a gas may increase. The dependencies are obtained of eigenfrequencies on the geometric parameters of obstacles and the inhomogeneities of the channel.     

Homogenization of transmission conditions for analysis of acoustic waves in domains with perforated barriers

We consider structures like the muffler of the engine exhaust, where the acoustic waves propagate through periodically perforated barriers. Recently we proposed a homogenized model [6] of the acoustic transmission through the layer with embedded rigid obstacles of arbitrary shapes, which represent the perforation. The homogenized model describes relationship between jump of the acoustic pressures p⁺ and p⁻ at the discontinuity interface Γ₀ and the transverse acoustic velocity g^0±, on introducing in–layer acoustic pressure p⁰ which describes wave propagation along the interface. The coupling between the transversely and the tangential acoustic velocities may become important for certain types of perforations. A sensitivity study was done which reveals remarkable dependence of wave transmission losses on the geometry of the perforation. Examples of 3D perforation geometries were treated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reflection of plasma waves from a plane boundary

We state and analytically solve the linearized problem of the reflection of plasma waves from the half-space boundary in gas plasma for the first time. We consider mirror and diffusion boundary conditions and find the reflection coefficient as a function of the original problem parameters. We analyze the long-wave limit. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 3, pp. 498–510, March, 2007.     

Averaging of densely perforated cylindrical shells

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 46, pp. 136–139, 1986.     

Propagation of waves from spherical and cylindrical cavities

Résumé L'auteur examine la propagation des ondes d'une cavité sphérique ou cylindrique dans une substance avec une isotropie transversale et curviligne. Il traite d'une manière assez détaillée le cas particulier d'un solide infini dans lequel existe un trou sphérique ou cylindrique, et les résultats numériques sont donnés sous une forme graphique pour le trou cylindrique avec un démarrage à fonction type unitaire.     

Propagation of kelvin waves from a channel into a semibounded tank

The problem of propagation of Kelvin waves from a channel into a semibounded tank is considered. An exact solution of the problem is constructed using the Wiener — Hopf method. The solution is analyzed asymptotically and numerically. The Wiener — Hopf method was used in /1,2/ to solve the problem of diffraction of the Kelvin waves in tanks bounded by the infinite and semiinfinite parallel walls. Below a generalized method of matching /3/ is used to solve the problem of diffraction of Kelvin waves in the case when the walls confining the fluid meet at the right angles.     

Reflection and transmission of plane acoustic waves in an infinite annular duct with a finite gap on the inner wall

The diffraction of acoustic waves by an infinitely long annular duct having a finite gap on the inner wall is investigated rigorously. The related boundary‐value problem is formulated into a modified Wiener–Hopf equation, which is then reduced to a pair of simultaneous Fredholm integral equations of the second kind. At the end of the analysis, numerical results illustrating the effects of the width of the coaxial cylindrical waveguide and the gap length on the diffraction phenomenon are presented. Copyright © 2010 John Wiley & Sons, Ltd.     

Reflection of plane waves from the boundary of a pre-stressed compressible elastic half-space

The effect of pre-stress on the propagation and reflection ofplane waves in an incompressible isotropic elastic half-spacehas been examined recently by the authors (Ogden & Sotiropoulos,1997). In the present paper the corresponding analysis for compressiblematerials is detailed. In the two-dimensional context consideredfor incompressible materials the (homogeneous) plane waves werenecessarily shear waves. By contrast, in the compressible contextpure shear waves can propagate only in specific directions inthe considered principal plane and, in a general direction,a quasi-shear wave may be accompanied by a quasi-longitudinalwave, as is the case in the anisotropic linear theory. The dependenceof the (in-plane) slowness section on the pre-stress (and finitedeformation) and on the choice of constitutive law is elucidated.This information is used to determine the reflection coefficientsfor reflection of either a (quasi-) shear wave or a (quasi-)longitudinal wave from the boundary of the half-space and tocharacterize the different cases which arise depending on thegeometry of the slowness section. The theoretical results are illustrated by numerical calculationsfor the range of possible types of behaviour with referenceforms of strain-energy function and different states of finitedeformation and to the question of stability of the half-space.     

The propagation of non-stationary waves from a spherical cavity in an acoustic layer

The axisymmetric problem of the propagation of non-stationary waves from a spherical cavity in the plane of an infinite layer filled with an acoustic medium is considered. Using methods of incomplete separation of the variables in the space of Laplace transformation in time, the problem is reduced to an infinite system of linear algebraic equations, the solution of which is investigated in the form of series in exponential functions.     

Vector acoustic solitons from the coupling of long and short waves in a paramagnetic crystal

We investigate the propagation of a longitudinal-transverse elastic pulse in a statically deformed crystal containing paramagnetic impurities and placed in an external magnetic field. We derive a system of three nonlinear wave equations describing the interaction of the pulse with the paramagnetic impurities in the quasiresonance approximation in the Faraday geometry. We assume that the transverse components of the pulse, which cause quantum transitions, have carrier frequencies and are short-wave (acoustic), while the longitudinal component has no carrier frequency and is long-wave. We show that in the case of an equilibrium initial distribution of populations of quantum levels of paramagnetic impurities, the coupling between the longitudinal and transverse components is weak, the pulse is therefore strictly transverse, and its dynamics are described by the Manakov system. With a nonequilibrium initial distribution of populations, conditions of effective interaction between all components of the elastic pulse can be reached, and their nonlinear dynamics are described by a vector generalization of the Zakharov equations. In the case of a unidirectional propagation of the pulse, these equations reduce to the Yajima-Oikawa vector system. We show that the obtained system of equations and its version with an arbitrary number of short-wave components can be integrated using the inverse scattering transform. We construct infinite hierarchies of solutions of the Yajima-Oikawa vector system (including a solution on a nontrivial background). We consider stationary (complex-valued Garnier system) and self-similar reductions of that system, also admitting a representation in the form of compatibility conditions.     

Compressible gas flow inside a cylindrical channel with a source on the channel axis

The article solves the problem of compressible nonviscous gas flow inside a cylindrical channel in the presence of a source on the channel axis. The cases considered include a supersonic spherically symmetrical source and a hypersonic source modeling jet flow. The numerical solution is obtained by two methods: one method treats the flow singularities (shocks, etc.) in explicit form, while the other uses the “through calculation” procedure. The solution is applied to analyze the physical flow pattern and the distribution of gasdynamic parameters in the shock layer, in particular on the channel walls. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 169–180.     

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.     

Scattering of acoustic waves on a sloping beach

A classical problem of acoustics is considered by the Sommerfeld-Maliuzhinets method. All geometric waves are computed explicitly. For diffracted waves, a numerical procedure based on a uniquely solvable Fredholm integral equation is elaborated. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 57–64. Translated by B. V. Budaev.     

Diffraction of water waves by a slotted cylindrical breakwater

Permeable and slotted breakwaters are becoming more popular, in order to reduce the drawback of rigid coastal structures: namely large reflections, forces and overtopping. The linearized theory of water waves is used to examine the diffraction of incident regular waves by a vertically slotted cylindrical breakwater that consists of a number of distinct rigid cylindrical panels. Under the assumption that the wavelength is much greater than the thickness, each segment is replaced by a thin structure and the permeability is modelled by suitable boundary conditions. The first condition is the matching pressure and normal velocity conditions between two internal and external fluid regions and the second condition is zero normal velocity on rigid panels. The mixed boundary–value problem is transformed to dual series relations and the least–square method is applied to get the forces on the structure. The results are presented to illustrate the effects of permeability. Numerical results compare well with McCamy and Fuchs predictions for the limiting case of an impermeable rigid cylinder. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interaction of acoustic waves with shock waves in elastic solids

Summary Transmission and reflexion of plane acoustic waves through a longitudinal shock wave in elastic isotropic solids are investigated. As a result, the amplitude of the transmitted and reflected waves and the jump of the acceleration of the shock are explicitly determined.

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Résumé On envisage la transmission et la réflexion d'une onde acoustique plane par une onde de choc longitudinale dans les solides élastiques isotropes. On détermine explicitement l'amplitude des ondes transmises et réflechies et le saut de l'acceleration du choc.

     

Nonlinear propagation of coupled electromagnetic waves in a circular cylindrical waveguide

The problem of the propagation of coupled surface electromagnetic waves in a two-layer cylindrical circular waveguide filled with an inhomogeneous nonlinear medium is considered. A nonlinear coupled TE-TM wave is characterized by two (independent) frequencies ω_e and ω_m and two propagation constants \({\widehat \gamma _e}\) and \({\widehat \gamma _m}\). The physical problem reduces to a nonlinear two-parameter eigenvalue problem for a system of nonlinear ordinary differential equations. The existence of eigenvalues (\({\widehat \gamma _e}\), \({\widehat \gamma _m}\)) in proven and intervals of their localization are determined.     

Reflection of plane waves from a rigid wall and a free surface in a transverse isotropic medium

For the general solution of two-dimensional equations of dynamics of a transverse isotropic medium with the Carrier–Gassmann condition, we give a representation in terms of two resolvent functions satisfying two separate wave equations. The problem of reflection of plane waves from a rigid wall and a free surface is solved. The coefficients of reflection and transformation of the plane waves are found. These formulas yield a solution for isotropic media too. Some special cases are consideredwhere the shapes (amplitudes) of the reflectedwaves are not uniquely determined, but linearly related with the shape of the incident wave.