Radiation of sound waves from a rigid stepped cylindrical waveguide

The radiation of plane harmonic sound waves from a rigid stepped cylindrical waveguide is treated by using the mode-matching method in conjunction with theWiener-Hopf technique. The solution is exact, but formal, since infinite series of unknowns and some branch-cut integrals with unknown integrands are involved. Approximation procedures based on rigorous asymptotics are used and the approximate solution to the Wiener-Hopf equations is derived in terms of infinite series of unknowns, which are determined from infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the directivity of the stepped waveguide is presented.     

Propagation of axisymmetric waves on the surface of a cylindrical cavity in elastic medium

A nondamped axisymmetric mode that propagates in an elastic cylindrical waveguide representing an extended cavity with a circular cross section in an infinite homogeneous medium is described. The wave dispersion in this system is analyzed and the similarity with and differences from other elastic media with one boundary are considered, including an infinite round rod and the surface of a half-space (Rayleigh wave). It is shown that, for axisymmetric waves in the cavity, a boundary frequency dependent on the curvature radius always exists, below which the waves are evanescent. A physical interpretation of results is given.     

Mathematical simulation of semitransparent layered thin-walled waveguides with the use of averaged two-sided boundary conditions

The boundary-value problem on the penetration of electromagnetic waves from a thin-walled cylindrical waveguide into the environment was solved with the use of averaged boundary conditions. The multilayer wall of the waveguide was considered as an ideally thin cylindrical surface, the complex material structure of which was described with the use of special two-sided boundary conditions. The dispersion equation determining the constants of propagation of partial waves in the waveguide was solved by the method of numerical minimization of the function of two variables. Results of calculation of the attenuation of the electromagnetic field penetrating from the waveguide into the environment as compared to the field of the corresponding mode inside the waveguide are presented.     

Two-dimensional scattering from an impenetrable cylindrical obstacle in an acoustic quarterspace

The problem of sound scattering by an infinitely long hard or soft circular cylindrical obstacle suspended near a rigid corner is investigated. The separation of variables technique, the appropriate wave field expansions and the method of images along with the translational addition theorem for cylindrical wave functions are used to derive a closed-form analytical solution in form of infinite series. The analytical results are illustrated with a numerical example in which the cylindrical obstacle is positioned near the rigid boundary of a water-filled acoustic quarter-space. The backscattering form function amplitude and spatial distribution of the total acoustic pressure are evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence and proximity of the cylinder to the rigid boundary are examined. Limiting case involving an infinite cylinder in an acoustic halfspace is considered and fair agreement with a well-known solution is established.     

Sudden twisting of an external circular crack in an infinite medium with a cylindrical inclusion

In this paper the torsional impact response of an external circular crack in an infinite medium bonded to a cylindrical inclusion has been investigated. The infinite medium and cylindrical inclusion are assumed to be of different homogeneous isotropie elastic materials. Laplace and Hankel transforms are used to reduce the problem to the solution of a pair of dual integral equations. These equations are solved by using an integral transform technique and the results are expressed in terms of a Fredhol integral equation of the second kind. By solving Fredholm integral equation of the second kind the numerical results for the dynamic stress-intensity factor are obtained which measure the load transmission on the crack.     

Concentrated force acting on an elastic inclusion in a thick-walled tube

A two-dimensional problem is investigated on the action of a concentrated force applied to the axis of a circular cylindrical, elastic inclusion embedded in an elastic thick-walled tube. This is a generalization of an indentation problem in infinite space, previously studied by Noble and Hussain [4] and revised by Omar and Hassan [5]. The problem is solved using a fast numerical approximation technique and numerical results are presented that allow us to evaluate the angle of contact and to establish a comparison with the case of embedding in an infinite space.     

Transmission of sound waves in a cylindrical duct with an acoustically lined muffler

The propagation of sound in an infinite rigid cylindrical duct with an inserted expansion chamber whose walls are treated with an acoustically absorbent material is investigated rigorously through the Wiener–Hopf technique. By introducing the Fourier transform for the scattered field and applying the boundary conditions in the transform domain, the problem is reduced into a modified Wiener–Hopf equation. The solution involves four sets of infinitely many constants satisfying four infinite systems of linear algebraic equations. An approximate solution of these systems is obtained by means of numerical procedures.     

The temperature field of an infinite solid containing a cylindrical channel with a thermally thin surface coating

The Laplace method of integral transformation is used to find an analytical solution of the problem of unsteady-state heat conduction for an infinite isotropic solid containing a cylindrical channel with a thermally thin surface coating filled with a high-temperature gas.     

Pulse distortion due to eddy currents induced in a multiply excitedcylindrical shell of finite length and thickness

The electromagnetic field due to pulse excitation of two crossed pairs of coils surrounded by a cylindrical conducting shell is determined by accounting for the eddy-current effect. Each coil is modeled as a pair of straight, parallel wires of infinite length; the surrounding conducting shell is a cylindrical tube of finite length and thickness. The problem is formulated in the frequency domain, and the resulting expressions are used to calculate the transient magnetic flux density which originates from the quadruple coil and the eddy currents induced within the metallic shell. The part due to the eddy currents represents an unwanted distortion, which is investigated through a numerical example. The analytical and numerical results are complemented by a brief discussion on compensation techniques and potential applications in magnetic resonance imaging     

Electromagnetic scattering from cylindrical objects above a conductive surface using a hybrid finite-element-surface integral equation method

This work presents a novel finite-element solution to the problem of scattering from a finite and an infinite array of cylindrical objects with arbitrary shapes and materials over perfectly conducting ground planes. The formulation is based on using the surface integral equation with Green's function of the first or second kind as a boundary constraint. The solution region is divided into interior regions containing the cylindrical objects and the region exterior to all the objects. The finite-element formulation is applied inside the interior regions to derive a linear system of equations associated with nodal field values. Using two-boundary formulation, the surface integral equation is then applied at the truncation boundary as a boundary constraint to connect nodes on the boundaries to interior nodes. The technique presented here is highly efficient in terms of computing resources, versatile, and accurate in comparison with previously published methods. The near and far fields are generated for a finite and an infinite array of objects. While the surface integral equation in combination with the finite-element method was applied before to the problem of scattering from objects in free space, the application of the method to the important problem of scattering from objects above infinite flat ground planes is presented here for the first time, to our knowledge.     

The Nonaxisymmetric Contact Thermoelastic Problem for a Half‐Space with a Motionless Rigid Spherical Inclusion

Based on the generalized Fourier method used simultaneously in the spherical and cylindrical systems of coordinates, we suggested an analytical method for solving the contact problem of thermoelasticity for an elastic halfspace with a rigid spherical inclusion. The problem is reduced to an infinite system of linear algebraic equations with the Fredholm operator provided that the boundary surfaces do not intersect. An approximate solution of the system in the form of a series with respect to a small parameter is obtained. The numerical analysis of the problem is presented.     

An axisymmetric external crack problem for an infinite medium with a cylindrical inclusion

Summary This paper deals with the determination of stresses in an infinite medium containing an external crack surrounding a cylindrical inclusion. The two media are assumed to be homogeneous, isotropic and elastic but with different elastic constants. The continuity of stresses and displacements is assumed at the common cylindrical surface due to perfect bonding. The problem is reduced to the solution of a Fredholm integral equation of the second kind. A closed-form expression is obtained for the stress-intensity factor. The integral equation is solved numerically and the results are used to obtain the numerical values of the stress-intensity factor which are displayed graphically.The authors thank the National Research Council of Canada for supporting this research through NRC Grant No. A-4177.     

A non-axisymmetric cylindrical contact problem

The contact problem under investigation is one whereby a solid circular elastic cylinder of infinite length is rigidly indented by a two piece collar of finite length, each piece being diametrically opposed and extending only partially around one half of the circumference. This case is practically significant in relation to the axisymmetric cylindrical contact problem since in many cases attachment of a component to a cylindrical shaft is achieved by means of a two piece clamp.Shear stresses on the contact interface are taken zero and a radial displacement influence coefficient technique is used to model the integral equation governing this contact problem. Adopting the Papkovich-Neuber solution for the non-axisymmetric cylindrical coordinate case and substituting the appropriate boundary conditions leads to a combined Fourier series, Fourier integral representation for the desired displacements. Convergence of this series—integral is studied and results of interference contact pressure are presented for an illustrative range of the various parameters involved.     

Cylindrical phase change approximation with effective thermal diffusivity

No exact, general, solution exists for phase change in a cylindrical geometry. In fact, even approximate solutions are rare and limited in applicability. The use of the effective thermal diffusivity concept has allowed a closed form approximate solution to be generated for phase change around a circular cylinder in an infinite medium. The effective diffusivity method permits solutions to be found for phase change problems merely by solving the usually linear, zero latent heat problem analogous to the phase change problem. Phase change problems are often intractable with the usual mathematical methods. The cylindrical formulae given here are shown to be of acceptable accuracy, for most engineering purposes, over a wide range of parameters. No other simple, closed form, approximation is known for the cylindrical system. Although the accuracy of the effective diffusivity method has been demonstrated for the cylindrical geometry, application to other geometries must be verified.     

Stress analysis of a penny-shaped crack locted between two oblate spheroidal cavities in an infinite solid

The problem of a penny-shaped crack located between two oblate spheroidal cavities in an infinite solid subjected to uniaxial loads is considered. Using transformations between harmonic functions in cylindrical coordinates and those in oblate spheroidal ones, the problem is reduced to non-homogeneous linear equations. The obtained equations are solved numerically and the stress intensity factors at the penny-shaped crack tip under the influence of the two oblate spheroidal cavities are shown graphically.     

Effect of fluid viscosity on wave propagation in a cylindrical bore in micropolar elastic medium

Wave propagation in a cylindrical bore filled with viscous liquid and situated in a micropolar elastic medium of infinite extent is studied. Frequency equation for surface wave propagation near the surface of the cylindrical bore is obtained and the effect of viscosity and micropolarity on dispersion curves is observed. The earlier problems of Biot and of Banerji and Sengupta have been reduced as a special case of our problem.     

Extension of the residual variable method to propagation problems and its application to the diffusion equation in spherical coordinates

Summary We consider a partial differential equation in spherical (cylindrical) coordinates describing a dynamic process in an infinite medium with an inner spherical (cylindrical) boundary. If an analytical solution is not possible to obtain, then one resorts to numerical techniques. In this case it becomes necessary to discretize the infinite domain even if the solution is required on the inner spherical (cylindrical) surface or at a limited number of points in the domain only. The Residual Variable Method (RVM) circumvents the difficulty of discretizing the infinite domain. The governing equation is integrated once in radial direction. The number of the spatial dimensions is, thus, reduced by one. It is now possible to determine the solution on the inner boundary without having to deal with the infinite domain. The RVM is amenable to marching solutions in a finite-difference implementation and it is suitable for the analysis of propagation into the infinite medium from the inner surface. There is no need to discretize the infinite domain in its entirety at all. The propagation analysis can be terminated at any point in the radial direction without having to consider the rest.     

Optimization of a variable mouth acoustic horn

By using boundary shape optimization on the end part of a semi‐infinite waveguide for acoustic waves, we design transmission‐efficient interfacial devices without imposing an upper bound on the mouth diameter. The boundary element method solves the Helmholtz equation modeling the exterior wave propagation problem. A gradient‐based optimization algorithm solves the resulting least‐squares problem and the adjoint method provides the necessary gradients. The results demonstrate that there appears to be a natural limit on the optimal mouth diameter. Copyright © 2010 John Wiley & Sons, Ltd.     

Non‐reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow

We consider a time‐harmonic acoustic scattering problem in a 2D infinite waveguide with walls covered with an absorbing material, in the presence of a mean flow assumed uniform far from the source. To make this problem suitable for a finite element analysis, the infinite domain is truncated. This paper concerns the derivation of a non‐reflecting boundary condition on the artificial boundary by means of a Dirichlet‐to‐Neumann (DtN) map based on a modal decomposition. Compared with the hard‐walled guide case, several difficulties are raised by the presence of both the liner and the mean flow. In particular, acoustic modes are no longer orthogonal and behave asymptotically like the modes of a soft‐walled guide. However, an accurate approximation of the DtN map can be derived using some bi‐orthogonality relations, valid asymptotically for high‐order modes. Numerical validations show the efficiency of the method. The influence of the liner with or without mean flow is illustrated. Copyright © 2011 John Wiley & Sons, Ltd.     

多铁性非均匀空心层合柱圆弧界面的反平面断裂分析

讨论反平面载荷作用下多铁性非均匀空心层合柱的圆弧界面裂纹问题,层合柱由梯度铁电层和梯度铁磁层粘接而成,界面处存在圆弧型裂纹。采用分离变量和Cauchy核奇异积分方程方法求解该断裂问题。通过讨论断裂参数的数值解,分析了梯度非均匀参数、几何与材料参数变动等对应力强度因子的影响。