Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

The general integral expressions for on-axis nonparaxial vectorial spherical waves diffracted at a circular aperture

Based on the vectorial Rayleigh-Sommerfeld integrals, the general propagation integral expressions for on-axis nonparaxial vectorial spherical wave diffracted at a circular aperture are derived. The results are strict integral formulae for the light field on the axis, valid for either strong or weak focusing, both far and near zones, and for the systems in which the size of the aperture is comparable to or smaller than the wavelength. Thus, it has the advantage for general application. For convergent spherical waves, the numerical calculation results are compared with those obtained by using the integral formulae of scalar paraxial approximation and scalar nonparaxial approximation, confirming the consistence in the situation of scalar approximation.     

Modeling the quasicompressional wave field of a rectangular transducer in a transversely isotropic solid

A fast model for simulating the transient quasicompressional wave field of a rectangular ultrasonic transducer directly coupled to a transversely isotropic elastic half-space of general orientation is developed. The so-called two-tier asymptotic approach and the uniform stationary phase method are used to derive the high-frequency asymptotics of time-harmonic displacements. Then, transient fields are modeled by means of harmonic synthesis. In geometrical regions, the formulas involve elementary and inside boundary layers, well-known special functions (Fresnel integral and generalized Fresnel integral), and are applicable in the radiating near field. The asymptotics elucidate the physics in terms of various arrivals and give explicit dependence of the radiated waves upon model parameters. The asymptotic code is tested against a direct numerical solution. It is at least a thousand times faster but describes accurately both arrival times and amplitudes of various pulses radiated by the transducer.     

Diffraction of electromagnetic waves by a resistive half-plane in magneto-ionic plasma

The interaction of magnetic polarized electromagnetic wave with a resistive half-plane in magneto-ionic plasma is investigated. The method of transition boundary is used for the evaluation of the diffracted wave. The excitation of surface waves is examined in the medium and their diffracted fields are derived by using the diffraction theory for grazing incidence. The uniform field expressions are obtained with the aid of the uniform theory for evanescent waves. The behaviours of the derived scattered waves are studied numerically.     

会聚球面波圆孔衍射的一般积分式

 分别从菲涅尔-基尔霍夫和瑞利-索莫非衍射积分公式出发,导出了考虑倾斜因子后会聚球面波经圆孔衍射的一般衍射积分表达式。所得公式不仅可计算衍射场的焦移,而且对弱聚焦和强聚焦情况均适用。并与Li和Wolf公式的结果进行了比较,结果证实所得公式适用广泛。     

Fringe waves radiated by a half-plane for the boundary conditions of Neumann

The fringe waves of the physical theory of diffraction are obtained in terms of Fresnel integrals for a half-plane satisfying the Neumann boundary condition. The approximate expressions of the radiated waves are also evaluated for sufficiently large wavenumbers. The fields are plotted and compared numerically.     

Boundary diffraction wave theory of resistive surfaces with edge discontinuities

The line integral of the boundary diffraction wave theory is derived by considering the exact diffracted fields of a resistive half-plane. The line integral is generalized for arbitrary resistive surface with edge discontinuity. The method is applied to the diffraction problem of waves by a convex resistive spherical reflector and the resultant field expressions are investigated numerically.     

The anomalous propagation of phase in the focus: A re-examination

The classical theory for focusing predicts that when a converging spherical wave is diffracted at an aperture on an opaque screen, the light ray undergoes a rapid π radian phase change in passing through its focus. In the present note, an objection to this prediction is put forward which embodies evidence that when the Fresnel number of the focusing system is of the order of unity or smaller, the phase change near the focus is neither rapid enough nor large enough to reach π radian and that, as a result, the anomalous propagation of the phase near focus is a specific phenomenon which is apparent only in systems of conventional optics, i.e., in systems with considerably large Fresnel numbers.     

矩形表面波探头声场的高斯声束叠加法

利用矩形压电晶片和有机玻璃楔块折射可激励出超声表面波,广泛用于固体近表面缺陷检测和材料特性测量.由于描述表面波三维声场的理论方法还鲜有报道,因而主要采用简化的表面波二维声场模型来定量分析这类问题.高斯声束模型近些年被广泛应用于解决超声体波传播的各种复杂问题,然而,目前还没有将其扩展应用到超声表面波的声场的计算中.通过结合表面波格林方程和矩形换能器的高斯声束模型,推导出基于高斯声束叠加的表面波三维声场解析解.进一步,将该方法与点源叠加的数值解进行了分析比较,计算结果表明表面波声场的高斯声束叠加方法在具有较好计算精度的同时,还具有更快的计算效率.     

Intensity distributions near focus of strongly converging spherical waves diffracted at a circular aperture

Based on the Rayleigh–Sommerfeld diffraction integral, the diffraction of converging spherical waves at a circular aperture is studied in a general case. The expression for the intensity near focus of strongly converging spherical diffracted waves is derived, which reduces to the well known result expressed in terms of Lommel functions for the case of weakly converging spherical diffracted waves. The intensity distributions at the geometrical focal plane and along the axis are given. Numerical comparative examples are presented to illustrate the more general applicability of our results.     

半球封闭圆柱体表面绕射声场研究

基于一致性几何绕射理论,对半球封闭圆柱体上半球表面的高频绕射声场进行了数值计算与分析。获得了单个点声源作用下,半球表面声场的声压分布图,其中包括一些干涉条纹,干涉条纹的区域及形状与点声源的位置和频率有关;在多个点声源作用下,发现在接近半球顶点的附近,多个声波经多途传播后在该区域的叠加声压由衰减转为增强的现象。     

Modal vibrations of a cylindrical radiator over an impedance plane

The problem of acoustic radiation from an infinite cylinder undergoing harmonic modal surface vibrations near a locally reacting planar boundary is considered. The formulation utilizes the appropriate wave field expansions, the classical method of images, and the translational addition theorem for cylindrical wave functions, along with a simple local surface reaction model involving a complex amplitude wave reflection coefficient applied to simulate the relevant boundary conditions for the given configuration. The analytical results are illustrated with a numerical example in which the cylindrical surface is immersed near a layer of fibrous material set on an impervious rigid wall. The numerical results reveal the important effects of interface local surface reaction and source position on the computed modal impedance component values and the radiated on-axis far-field pressure. The benchmark solution presented can lead to a better understanding of acoustic radiation from near-interface two-dimensional sources, which are commonly encountered problems in outdoor acoustics and noise control engineering. Eventually, it could be used to validate those found by numerical approximation techniques.     

The method of the boundary diffraction wave for impedance surfaces

The line integral of the boundary diffraction wave theory is extended for the diffraction process of waves by the impedance surfaces with edge discontinuities. With this aim, the exact diffraction field expression of Maliuzhinets is transformed into a line integral. The method is applied to the scattering problems of waves by a spherical reflector with edge discontinuity and the diffracted fields are evaluated asymptotically. The resultant expressions of the waves are examined numerically.     

Acoustic manipulation of active spherical carriers: Generation of negative radiation force

This paper examines theoretically a novel mechanism of generating negative (pulling) radiation force for acoustic manipulation of spherical carriers equipped with piezoelectric actuators in its inner surface. In this mechanism, the spherical particle is handled by common plane progressive monochromatic acoustic waves instead of zero-/higher- order Bessel beams or standing waves field. The handling strategy is based on applying a spatially uniform harmonic electrical voltage at the piezoelectric actuator with the same frequency of handling acoustic waves, in order to change the radiation force effect from repulsive (away from source) to attractive (toward source). This study may be considered as a start point for development of contact-free precise handling and entrapment technology of active carriers which are essential in many engineering and medicine applications.     

采用球面波叠加法还原自由声场的方法

为解决非自由声场中近场声全息重建时,干扰声在目标声源表面产生的散射影响,提出一种基于球面波叠加法的自由场还原技术。该技术首先采用基于球面波叠加法的声场分离技术获得向内和向外传播的声场,然后以目标声源的表面导纳作为边界条件,实现目标声源辐射声和散射声的分离,从而获得等效于自由声场的测量条件。该技术为准确实现非自由声场中的噪声源识别创造了条件。文中首先详细描述了该技术的基本原理,并提出一种最优球面波展开项数选取方法,最后通过数值仿真说明了该技术的有效性。结果表明:在频率较低时,散射声影响较小,采用声场分离技术和自由场还原技术效果相当;但随着频率升高,散射声影响逐步增强,必须采用自由场还原技术才能准确获得目标声源辐射声。      

Recovery of the free field in noisy environment by using the spherical wave superposition method

To remove the scattering effect of the disturbing sound on the target source when implementing nearfield acoustic holography in a non-free field, a free field recovery technique based on the spherical wave superposition method is proposed. In the method, the sound field separation technique based on the spherical wave superposition method is first used to separate the incoming and outgoing fields, and a further step for separating the radiated and scattered fields is performed by utilizing the surface admittance of the target source as the boundary condition. The technique makes it possible to correctly identify noise sources in a non-free sound field. The basic principle of the technique is described firstly, a method for choosing the optimal number of spherical wave expansion terms is given, and two numerical simulations are used to demonstrate the validity of this technique. It is shown that, for the lower frequency, the scattering effect can be neglected, and the radiated field of the target source can be obtained by the sound field separation technique, however, as the increasing of the frequency, the scattering effect cannot be neglected, and the free field recovery technique has to be used to obtain the radiated field of the target source.     

The MTPO/Malyughinetz hybrid method for the scattering analysis of parabolic impedance reflectors

The scattering process of cylindrical waves, radiated by a line source, from a parabolic reflector is investigated with the MTPO/Malyughinetz hybrid method. The geometrical optics and diffracted waves are evaluated asymptotically from the radiation integral. The scattered, diffracted and geometrical optics waves are plotted numerically for different impedance values.     

Computation of aeolian tone from a circular cylinder using source models

The generation of aeolian tones from a two-dimensional circular cylinder situated in a uniform cross-flow is investigated. The major emphasis here is placed on identifying the important noise generation mechanisms. Acoustic-viscous splitting techniques are utilized to compute modelled acoustic source terms and their corresponding acoustic fields. The incompressible Reynolds averaged Navier-Stokes equation is used to compute the near-field viscous flow solution, from which modelled acoustic source terms are extracted based on an approximation to the Lighthill’s stress tensor. Acoustic fields are then computed with an acoustic solver to solve the linearized Euler equations forced by the modelled source terms. Computations of the acoustic field based on the approximated Lighthill’s stress tensor are shown to be in good agreement with those computed from the surface dipole sources obtained using Curle’s solution to the acoustic analogy. It is shown in this paper that the stress tensor source term in the streamwise direction makes a comparable, but slightly larger contribution to the overall radiated field, compared with that due to the stress tensor in the direction normal to the mean flow. In addition, it is shown that shear sources, which arise due to the interaction between the fluctuating velocity and the background steady mean velocity, make the greatest contribution to the acoustic field, while the self-noise sources, which represents the interaction between the fluctuating velocities, is shown to be comparably negligible.     

Three-dimensional analysis of scattering by pressure-release plane surfaces and the validity of the image solution

Because of the complexity of the scattering integrals in three dimensions, numerous approximations are used to obtain closed-form solutions. By considering the scattering by an infinite, pressure-release plane surface, the effects of various phase approximations and source directivity approximations can be examined independently of the surface roughness. Calculations are carried out using the Fraunhofer and Fresnel phase approximations, and two directivity approximations. It has been shown experimentally that the image solution is valid for the reflection of an acoustic beam by an infinite, pressure-release plane surface if the plane is in the farfield of the source. Consequently, the image solution is used to compare analytical solutions obtained using various phase and directivity approximations, and it is found that both the Fresnel phase approximation and a realistic directivity approximation are required to achieve a good fit. The solution produced by the Fraunhofer phase approximation is obtained as an asymptotic limit of the modified Fresnel solution. Criteria for the validity of the Fraunhofer and Fresnel phase approximations are developed. The Fresnel phase approximation is valid under fairly broad conditions, but the Fraunhofer phase approximation is never valid for an infinite plane surface that must be in the farfield of the source.     

Features of the acoustic field of angle surface-wave transducers

The influence of process features in the fabrication of angle transducers (deviation from uniform distribution of mechanical stresses/strains over their transmitting/receiving surface) on the acoustic field of excited surface waves has been investigated. Calculation was carried out within the parabolic approximation by replacing a real angle transducer of surface waves with a linear source located on the surface of a waveguide (control object) with a nonuniform (cosine) distribution of stress amplitudes. The expressions for the stress (strains) at an arbitrary observation point for a point receiver (reflector) and for the stress averaged over the receiver plane are obtained in complex form. The coordinate dependences of the stress amplitudes and phases have been calculated for typical technological modes; the calculation results are presented as plots. It is shown that the effect of deviations from uniform distribution is strongest in the transition (from the near-to far-field) zone, where nonuniformity of displacements of 10–15% at the edges of a piezoelectric cell causes a change in their amplitude by 15–30% in comparison with uniform distribution; this must be taken into account when estimating diffraction corrections. The possibilities of experimentally verifying the degree of nonuniformity of the stress distribution over the angle-transducer surface are discussed.