Scattering of torsional waves by a spherical cavity in a long circular elastic cylinder

Summary. The axisymmetric wave equation is solved for the problem of torsional elastic waves scattered by a spherical cavity located symmetrically in an infinitely long circular cylinder. Using Fourier transforms, the problem is reduced to the solution of an infinite system of simultaneous equations, which is suitable for the numerical solution. The numerical results on the transmission and reflection coefficients are shown for various values of sphere radius and frequency. Equation of energy conservation is utilized to check the numerical procedure.     

Energy distribution and radiation loading of a cylindrical source suspended within a nonconcentric fluid cylinder

Acoustic radiation from a cylindrical source undergoing angularly periodic and axially-dependent harmonic surface vibrations while eccentrically suspended within a fluid cylinder, which is submerged in an infinite fluid medium, is analyzed in an exact manner. This configuration, which is a realistic idealization of a cylindrical liquid-filled acoustic lens with focal point inside the lens when used as a sound projector, is of practical importance with applications in underwater and biomedical ultrasonics. The formulation utilizes the appropriate wave-field expansions along with the pertinent translational addition theorem to develop an infinite series solution. The analytical results are illustrated with a numerical example in which the basic acoustic quantities, such as the modal acoustic radiation impedance load on the source, on-axis pressure magnitude, radiated far-field pressure directivity patterns, and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system. Numerical results clearly illustrate that, in addition to source frequency and surface velocity distribution, its position (eccentricity) can be of great significance in sound radiation.     

Déplacements engendrés par des ondes élastiques incidentes sur une sphère multi-couches

In an infinite space, we study the propagation of elastic spherical waves emitted by a source point placed outside a given finite set of concentric elastic spherical layers. The exact solution (displacements fields) of this problem is determined by a new method which avoids solving the totality of equations and boundary conditions. From these results we deduce those corresponding to some particular cases.     

Stokes resistance of a porous spherical particle in a spherical cavity

The boundary effect on the asymmetrical motion of a porous spherical particle in an eccentricspherical cavity is investigated in the quasi-steady limit under creeping flow conditions. The porous particletranslates and rotates in the viscous fluid, located within the spherical cavity, normal to the line connectingtheir centers. The fluid inside the porous particle is governed by the Brinkman equation. A tangential stressjump condition at the interface between the fluid and the porous particle is applied. A semi-analytical approachbased on a collocation technique is used. Due to the linearity of the present problem, the flow variables for theclear fluid region are constructed by superposing basic solutions of two problems: the first one is the regularsolution inside the cavity region in the absence of the porous particle where a first system of coordinates has itsorigin at the center of the cavity, while the second problem is the regular solution in the infinite region outsidethe spherical porous particle where a second coordinate system with its origin at the center of the porousparticle is used. Numerical results displaying the resistance coefficients acting on the particle are obtainedwith good convergence for various values of the physical parameters of the problem. The results are tabulatedand represented graphically. The findings demonstrate that the collocation results of the resistance coefficientsare in good agreement with the corresponding results for the impermeable solid particle.     

Eccentricity effects on acoustic radiation from a spherical source suspended within a thermoviscous fluid sphere

Acoustic radiation from a spherical source undergoing angularly periodic axisymmetric harmonic surface vibrations while eccentrically suspended within a thermoviscous fluid sphere, which is immersed in a viscous thermally conducting unbounded fluid medium, is analyzed in an exact fashion. The formulation uses the appropriate wave-harmonic field expansions along with the translational addition theorem for spherical wave functions and the relevant boundary conditions to develop a closed-form solution in form of infinite series. The analytical results are illustrated with a numerical example in which the vibrating source is eccentrically positioned within a chemical fluid sphere submerged in water. The modal acoustic radiation impedance load on the source and the radiated far-field pressure are evaluated and discussed for representative values of the parameters characterizing the system. The proposed model can lead to a better understanding of dynamic response of an underwater acoustic lens. It is equally applicable in miniature transducer analysis and design with applications in medical ultrasonics.     

Modal vibrations of an infinite cylinder in an acoustic halfspace

Acoustic radiation from an infinite cylindrical surface vibrating with an arbitrary, time-harmonic surface velocity distribution while positioned near the rigid/compliant boundary of a semi-infinite ideal compressible fluid medium is determined in an exact fashion using the classical method of separation of variables. The formulation utilizes the appropriate wave-field expansions and the method of images along with the pertinent translational addition theorem to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which the cylindrical source, vibrating in the monopole and dipole-like modes, is positioned near the rigid/compliant boundary of a water-filled acoustic halfspace. Subsequently, the basic acoustic field quantities such as the modal acoustic radiation impedance load, radiated far-field pressure and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system.     

Waves Past Porous Structures in a Two-layer Fluid

Havelock’s type of expansion theorems, for an integrable function having a single discontinuity point in the domain where it is defined, are utilized to derive analytical solutions for the radiation or scattering of oblique water waves by a fully extended porous barrier in both the cases of finite and infinite depths of water in two-layer fluid with constant densities. Also, complete analytical solutions are obtained for the boundary-value problems dealing with the generation or scattering of axi-symmetric water waves by a system of permeable and impermeable co-axial cylinders. Various results concerning the generation and reflection of the axisymmetric surface or interfacial waves are derived in terms of Bessel functions. The resonance conditions within the trapped region are obtained in various cases. Further, expansions for multipole-line-source oblique-wave potentials are derived for both the cases of finite and infinite depth depending on the existence of the source point in a two-layered fluid.     

Numerical Solution of a Problem of Thermal Stresses of a Magnetothermoelastic Cylinder with Rotation by Finite-Difference Method

The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation, open or closed circuit, thermal and mechanical boundary conditions. The outer and inner surfaces of the cylinder are subjected to both mechanical and thermal boundary conditions. A The transient coupled thermoelasticity in an infinite cylinder with its base abruptly exposed to a heat flux of a decaying exponential function of time is devised solve by the finite-difference method. The fundamental equations’ system is solved by utilizing an implicit finite-difference method. This current method is a second-order accurate in time and space; it is also unconditionally stable. To illustrate the present model’s efficiency, we consider a suitable material and acquire the numerical solution of temperature, displacement components, and the components of stresses with time t and through the radial of an infinite cylinder. The results indicate that the effect of coupled thermoelasticity, magnetic field, and rotation on the temperature, stresses, and displacement is quite pronounced. In order to illustrate and verify the analytical developments, the numerical solution of partial differential equations, stress components, displacement components and temperature is carried out and computer simulated results are presented graphically. This study is helpful in the development of piezoelectric devices.     

旋转点声源声场的数值仿真计算

旋转声源辐射声场的计算是利用点源模型预测风扇离散噪声的关键所在,对叶片式机械气动噪声的研究具有重要参考价值.提供了在任意边界条件下计算旋转点声源辐射卢场的数值仿真计算方法.将连续的旋转声源离散化,处理为分布于旋转轨迹上的有限个固定点声源.利用离散化处理后的声源,通过边界元法分别计算旋转单极子和旋转点力源的辐射声场.在自由空间内的计算结果与理论解进行了对比验证,得到较为理想的结果:另外进行了有限长圆管内旋转点声源辐射声场的数值计算,由此对不同长度圆管的结果进行对比,分析了管道长度对声场分布以及指向性的影响规律.     

Far-field radiation of a vibrating point source in anisotropic media

In this paper, Lamb's technique,⁽¹⁾ which was used to study acoustic radiation due to an external force acting in an infinite isotropic solid or over the surface of an isotropic solid, has been extended to the case of general anisotropic media. The far-field radiation is numerically calculated for a vibrating point source in an infinite anisotropic solid or on the free surface of a semi-infinite anisotropic solid. The directivity patterns of a point source are obtained for the three different elastic modes, and a brief discussion of the main features of the numerical results is presented.     

The residual variable method and its applications

Summary We consider a partial differential equation in spherical coordinates which describes a dynamic process going on in an infinite medium with an inner spherical boundary. If an analytical solution to the problem is not possible to obtain then one would have to resort to numerical techniques. It becomes necessary to discretize the infinite domain even if the solution is required on the inner spherical surface only. The numerical difficulties associated with the discretization of an infinite medium are well known. The Residual Variable Method (RVM) is a rigorous method which essentially reduces the number of the spatial dimensions of the problem by one. The governing differential equation is integrated once in the radial direction and, thus, it becomes possible to determine the solution on the inner boundary without having to deal with the infinite domain. The applications of the RVM to the wave equations in acoustic and viscous media and to the diffusion equation are shown.With 4 Figures     

有限长圆柱绕流气动噪声源特性分析

气动噪声源的能级、分布特性及其产生根源还不够清晰。以有限长三维圆柱绕流为研究对象,基于声源方程分析气动噪声源的种类构成及其与气动参数的关系,通过数值计算得到可压非定常流场,利用气动参数定量计算圆柱顶部、中部和底部的声源大小分布,研究声源的分布特性和产生根源。结果表明,在有限长圆柱绕流场中,以偶极子声源为主,单极子声源可以忽略不计,四极子源项的值比偶极子小1～2个数量级。偶极子主要分布在来流分离点及圆柱后壁面湍流涡二次碰撞区域,四极子主要分布在来流分离点及其向后拖曳区域。偶极子声源主要由于圆柱两侧涡脱落处的脉动压力在横向(y方向)上的二阶梯度引起。以上结果为气动噪声控制的进一步研究提供了借鉴和参考。     

Scattering of a gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results

We present numerical results concerning the properties of the electromagnetic field scattered by an infinite circular cylinder illuminated by a circular Gaussian beam. The cylinder is arbitrarily located and arbitrarily oriented with respect to the illuminating Gaussian beam. Numerical evaluations are provided within the framework of a rigorous electromagnetic theory, the generalized Lorenz-Mie theory, for infinite cylinders. This theory provides new insights that could not be obtained from older formulations, i.e., geometrical optics and plane-wave scattering. In particular, some emphasis is laid on the waveguiding effect and on the rainbow phenomenon whose fine structure is hardly predictable by use of geometrical optics.     

A boundary spectral method for elastostatic problems with multiple spherical cavities and inclusions

The problem of an infinite solid containing an arbitrary number of non-overlapping spherical cavities and inclusions with arbitrary sizes and locations is considered. The infinite solid and the spherical inclusions are made of different isotropic, linearly elastic materials. The spherical cavities are assumed to carry arbitrary tractions, and the spherical inclusions are assumed to be perfectly bonded to the infinite solid. The boundary and interfacial displacements and tractions are represented by truncated series of surface spherical harmonics. The problem involving multiple spherical features is replaced by a sequence of problems involving a single spherical feature via Schwarz's alternating method which accounts for the interactions in the course of an iterative process. Problems involving a single spherical feature are solved by employing the Papkovich–Neuber functions, and the interactions are evaluated by applying a least squares method. A robust scheme is introduced to control the total errors on the spherical boundaries and interfaces and to choose the number of terms in the series expansions. Several numerical examples are given to address the efficiency and the accuracy of the proposed method.     

Light scattering from a sliced target through use of the internal field of infinite cylinders: comparison between Mie theory and a sliced sphere

Light scattering from a particle that can be sectioned into circular slices is calculated by performing a coherent integration of the internal field over the volume of the target. The internal field in each slice is taken to be the internal-field solution of an infinite cylinder of radius equal to the radius of the slice. It is shown that for a spherical scatterer with size parameters up to 1.4, the integration leads to results that are in good agreement with those predicted by the Mie theory. Thus, we show the remarkable result that the internal field from an infinite cylinder can reproduce scattering intensities for such a radically different shape as a sphere. This being the case, a wide variety of target shapes between a sphere and a cylinder should be open to evaluation by this technique. The approach also has the benefit of being computationally efficient, requiring a double integration of the internal field over a disk and then coherently adding these calculations. The computations demonstrated in this paper are performed relatively quickly on a computer such as the Macintosh Centris 650, and this efficiency allows us to obtain the scattered fields for many target shapes.     

An integral equation method for the diffraction of oblique waves by an infinite cylinder

A hybrid integral equation method is formulated to study the diffraction of oblique waves by an infinite cylinder. The water depth and the geometry of the floating cylinder are assumed to be uniform in the y-direction (one of the horizontal axes). Numerical discretization and integrations are performed in the vertical plane. Analytical solutions are used in far fields such that radiation boundary conditions are satisfied. Numerical results are obtained for the case of wave scattering by a floating rectangular cylinder in a constant water depth. The accuracy and efficiency of present method are compared with those obtained by other numerical techniques.     

Transfert de chaleur par convection naturelle dans une couche poreuse limitée par deux cylindres coaxiaux horizontauxHeat transfer by natural convection in a porous layer bounded by two coaxial horizontal cylinders

Natural convection in a porous medium is studied for the geometrical configuration defined by two concentric horizontal cylinders with isothermal and impermeable surfaces, representing a cylinder or a pipe insulated by a layer of porous material. Two methods of investigation are used to approach the phenomenon: experiments on a cell of large aspect ratio (cylinder length to outside diameter), and a numerical model on a two-dimensional plane area. The experimental results reveal three different regimes according to the value of the Rayleigh number. For a finite radial gradient, thermoconvective phenomena develop in the annular layer, but as long as these are not amplified too much, the isotherms remain practically concentric with the cylinders, and heat transfer occurs essentially through conduction. At higher Rayleigh numbers natural convection develops in the form of two-dimensional counter-rotational vortices which are symmetrical with respect to a vertical plane containing the axis common to both cylinders. The third regime, observed at higher Rayleigh numbers, corresponds to a fluctuating evolution of the temperature field which becomes three-dimensional. As the inside cylinder is warmer, instabilities occur in the upper part of the model causing some periodicity of the temperature distribution along a generatrix, with a period of about the radius difference. A relative increase in the heat transfer between the cylinders due to the instabilities is observed. A two-dimensional numerical model, using the method of finite differences, enables us to describe the first two regimes observed experimentally, and to define the temperature field and the streamlines for a given Rayleigh number. The total heat transfer calculated is represented by a correlation between the Nusselt and the rayleigh numbers for many values of the ratio of the radii.The different results are then compared and analysed from a physical point of view.     

基于Fresnel-Kirchhoff理论的无限大声屏障绕射声衰减

从实际工业噪声控制中大面积有壁障噪声源的噪声控制问题出发,应用Fresnel-Kirchhoff理论和Babinet原理,建立计算无限大声屏障绕射声衰减的理论模型。通过数值求解,分析了声源、接收点位置,声波频率和地面反射等对声屏障绕射声衰减的影响。     

Vibro-acoustic behavior of a hollow FGM cylinder excited by on-surface mechanical drives

The linear three-dimensional elasticity theory in conjunction with the powerful transfer matrix solution technique is employed to investigate the steady-state nonaxisymmetric sound radiation characteristics of an arbitrarily thick functionally graded hollow cylinder of infinite length subjected to arbitrary time-harmonic on-surface concentrated mechanical drives. A formal integral expression for the radiated pressure field in the frequency domain is obtained by utilizing the spatial Fourier transform along the shell axis and Fourier series expansion in the circumferential direction. The method of stationary phase is subsequently employed to evaluate the integral for an observation point in the far-field. The analytical results are illustrated with numerical examples in which water-submerged metal-ceramic FGM cylinders are driven by harmonic concentrated radial/transverse surface forces and circumferential moment. The far-field radiated pressure amplitudes and directivities are calculated and compared with those of equivalent bi-laminate hollow cylinders with comparable volume fractions of constituent materials. The effects of FGM material profile, cylinder thickness, excitation frequency and type on the radiated far-field are examined. Limiting cases are considered and the validity of results is established by comparison with the data in the existing literature as well as with the aid of a commercial finite element package.     

Acoustical multipole source in a hollow fluid-filled cylinder

The propagation of elastic waves generated by an impulse multipole source in a hollow fluid-filled cylinder was studied. The general solution of the problem is illustrated by calculations for monopole and dipole sources applied in geophysical and geoecological measurement practice. The analysis of the outer boundary influence on the waveforms registered by receivers located in the fluid was performed. The estimation has been carried out to determine a cylinder wall thickness under which its influence on cinematic parameters of the waveforms can be neglected.