基于快速多极子基本解方法(FMM-MFS)的弹性波二维散射模拟研究

针对弹性波二维散射问题,发展一种新的快速多极子基本解方法（FMM-MFS）。方法基于单层位势理论,通过在虚边界上设置膨胀波线源和剪切波线源以构造散射波场,从而避免了奇异性的处理和边界单元离散;结合快速多极子展开技术（FMM）,大幅度降低了计算量和存储量,突破了传统方法难以处理大规模散射问题的瓶颈。以全空间孔洞对P、SV波的二维散射为例,给出了具体求解步骤,并在个人计算机上实现了上百万自由度问题的快速精确计算。在方法效率和精度检验基础上,分别以单孔洞和随机孔洞群对平面波（P、SV波）的散射为例进行计算模拟,揭示了孔洞（群）周围弹性波散射的若干重要规律。     

Numerical modelling of the scattering of elastic waves in plates

This paper describes the application of finite difference methods to the calculation of the scattering of elastic waves. The emphasis is on cracklike defects in plates, and it is shown that a common numerical technique can span a range of wavelengths from Lamb waves to ultrasonic waves with many reflections from the surfaces of the plate. Quantitative results are given for the scattering of Lamb waves and ultrasonic shear waves from surface-breaking cracks.     

带形介质内SH型导波对圆柱孔洞的动力分析

弹性板壳的反平面运动中由缺陷引起的应力集中问题可以按照带形介质中圆柱孔洞对SH型导波的散射问题来分析。首先,构造带形介质中相容导波的形式,即其满足上、下边界应力自由条件。之后,由波函数展开法给出圆柱孔洞散射波的级数表示,根据累次镜像叠加的方法构造由上、下边界反射所形成的相容的散射导波。最后,给定入射导波,由圆柱孔洞边界应力自由的条件来定解波函数级数的系数。数值算例求解了特定导波对圆柱孔洞的散射,给出了圆柱孔洞边沿的动应力分布,讨论了导波阶数、频率以及孔洞位置的影响。     

多排任意排列的弹性桩屏障对平面P波或SV波多重散射

提出可计算任意排列、任意圆截面多排弹性桩屏障对平面P波或SV波的多重散射理论方法,可弥补单重散射假定只在散射体截面尺寸相对入射波长可忽略情况下成立的不足,并考虑桩与桩间互相干涉现象。散射过程定义任意一弹性桩对入射P波或SV波的散射为第一重,第二重散射可将第一重散射波作为次生波源,继而对所有散射体皆遵循此过程;每一重散射均在桩土边界满足应力及位移连续条件,从而获得前一重与后一重散射的波函数迭代关系;总散射波场可由所有散射体各重散射叠加获得。数值计算考查相同截面多排桩屏障的散射重数、桩距、排距、桩土模量比等参数对屏障隔离效果影响。该方法可作为实际工程隔振设计理论参考依据。     

Three‐dimensional BEM for scattering of elastic waves in general anisotropic media

Based on the full‐space Green's functions, a three‐dimensional time‐harmonic boundary element method is presented for the scattering of elastic waves in a triclinic full space. The boundary integral equations for incident, scattered and total wave fields are given. An efficient numerical method is proposed to calculate the free terms for any geometry. The discretization of the boundary integral equation is achieved by using a linear triangular element. Applications are discussed for scattering of elastic waves by a spherical cavity in a 3D triclinic medium. The method has been tested by comparing the numerical results with the existing analytical solutions for an isotropic problem. The results show that, in addition to the frequency of the incident waves, the scattered waves strongly depend on the anisotropy of the media. Copyright © 2003 John Wiley & Sons, Ltd.     

A scattering problem by means of the spectral representation of Green's function for a layered acoustic half-space

 The problem in this paper is for scattering waves caused by an object and a plane wave in a layered acoustic half space. The boundary integral equation method as well as the spectral representation of Green's function for a layered acoustic half space are introduced to the present analyses. The spectral form of Green's function developed here is expressed in terms of the eigenfunctions for the point and the continuous spectra, that is the extension form of Green's function expressed by Ewing, Jardetsky and Press (1957). The advantage of the spectral representation of Green's function is that it enables us to decompose the scattering waves into eigenfunctions for the layered medium. Several numerical calculations are carried out to examine the efficiency of the present method as well as the properties of the scattering waves. According to the numerical results, the spectral form of Green's function provides accurate values and is applicable to the boundary element analysis for a layered medium. The spectral structures of the scattering waves are also found to be able to explain their properties. Received 2 November 1999     

Wave forces on arrays of floating bodies

Summary Previous work on the scattering of an incident wave field by an array of fixed vertical cylinders is extended to calculate the added-mass and damping coefficients for an array of floating axisymmetric bodies. The method is based upon a large spacing approximation where diverging waves are replaced by plane waves. It is shown that, given the scattering and radiation properties of a single body, the interaction effects within an array can be calculated both simply and accurately.     

Scattering of antiplane shear waves in a fiber-reinforced composite medium with interfacial layers

Summary This paper deals with the scattering of antiplane shear waves in a metal matrix composite reinforced by fibers with interfacial layers. We assume same-size cylindrical inclusions and same-thickness interface layers with nonhomogeneous elastic properties. The effective complex wave numbers follow from the coherent wave equation which depends only upon the scattering amplitude of the single scattering problem. Effective elastic constants can be obtained from phase velocities of coherent waves. Numerical calculations for an SiC-fiber-reinforced Al composite are carried out, and the effect of interface properties on scattering cross section, phase velocity, attenuation of coherent plane wave, and effective elastic constant is shown graphically.     

Scattering by a dense finite layer of infinite cylinders at oblique incidence

This paper presents the scattering solution for a finite dense layer of cylinders irradiated by an arbitrarily polarized plane wave at a general incident direction. The theoretical formulation utilizes the effective field approach and quasi-crystalline approximation to derive the governing equations for the propagation constant and amplitudes of the effective waves. The finite layer thickness gives rise to effective waves propagating in both the forward and backward directions inside the dense medium. Formulas are developed for the far-field coherent and incoherent scattered intensities, as well as the extinction and scattering cross sections of the dense layer. The forward peak of the incoherent scattered intensity is shown to be shifted to the propagating direction of the effective waves. The influence of incident direction, layer thickness, and solid volume fraction on the scattering properties is illustrated by means of a numerical example.     

Scattering of elastic waves by spherical inclusions with applications to low frequency wave propagation in composites

Scattering of plane elastic waves by a spherical inclusion is considered. A unified method of solution is presented which treats compressional and shear incidence on a similar basis. Explicit results are given for Rayleigh scattering. We apply the results of the single scattering problem to the propagation of low frequency waves in a composite containing a dilute concentration of spherical inclusions. Explicit formulae are given for the effective wave speeds and attenuations when the inclusions are voids. Both the compressional and shear wave speeds decrease initially as a function of frequency.     

Cross sections for surface plasmon polariton scattering from a nanoparticle in the dipole approximation

The differential and total cross sections for the scattering of surface electromagnetic waves in the optical frequency range (surface plasmon polaritons, SPPs) from a small particle into waves in the near-field zone (SPPs) and into waves propagating from the surface to the far-field zone have been calculated within the framework of the dipole approximation. The efficiencies of these scattering channels are compared as dependent on the main parameters of the system. An increase in the wavelength of the radiation exciting SPPs at a plane dielectric-metal interface (air-gold) may lead to a change in the most effective scattering channel.     

Laser Generation and Detection of Ultrasound in Concrete

Laser ultrasonic techniques are used to examine the propagation of ultrasonic waves in concrete. This optical methodology provides a repeatable, broad band generation source and an absolute detection system that does not interfere with the process being monitored. The presence of aggregate, in addition to voids and flaws, can cause wave scattering in concrete. Fast Fourier Transform techniques are used to determine the effect of aggregate size and propagation distance on the frequency content of both surface and body waves. This paper examines the scattering of ultrasonic waves in undamaged concrete and establishes the fundamentals for the application of laser ultrasonics for the material characterization and nondestructive evaluation of concrete.     

Effects of sensor locations on air-coupled surface wave transmission measurements across a surface-breaking crack

Previous studies show that the surface wave transmission (SWT) method is effective to determine the depth of a surface-breaking crack in solid materials. However, nearfield wave scattering caused by the crack affects the reliability and consistency of surface wave transmission measurements. Prior studies on near-field scattering have focused on the case where crack depth h is greater than wavelength λ of surface waves (i.e., h/λ > 1). Near-field scattering of surface waves remains not completely understood in the range of h/λ for the SWT method (i.e., 0 ≤ h/λ ≤ 1/3), where the transmission coefficient is sensitive to crack depth change and monotonically decreases with increasing h/λ. In this study, the authors thoroughly investigated the near-field scattering of surface waves caused by a surface-breaking crack using experimental tests and numerical simulations for 0 ≤ h/λ ≤ 1/3. First, the effects of sensor locations on surface wave transmission coefficients across a surface-breaking crack are studied experimentally. Data are collected from Plexiglas and concrete specimens using air-coupled sensors. As a result, the variation of transmission coefficients is expressed in terms of the normalized crack depth (h/λ) as well as the normalized sensor location (x/λ). The validity of finite element models is also verified by comparing experimental results with numerical simulations (finite element method). Second, a series of parametric studies is performed using the verified finite element model to obtain more complete understanding of near-field scattering of surface waves propagating in various solid materials with different mechanical properties and geometric conditions. Finally, a guideline for selecting appropriate sensor arrangements to reliably obtain the crack depth using the SWT method is suggested.     

Propagation of Rayleigh, Scholte and Stoneley waves along random boundaries

The effect of boundary roughness on the propagation of Rayleigh, Scholte and Stoneley waves is analysed under the assumption of the wavelength being much larger than the roughness scale of the interface. The scattering of the fundamental interface waves is represented by systems of plane waves in both neighbouring half-spaces; the formulas for amplitudes of these waves are determined using the perturbation method. The phase velocity of the interface waves is analysed by an approximate technique and is found to increase with the growing boundary roughness for all three types of interface waves.     

Scattering of elastic waves by a crack with spring-mass contact

The scattering problem of elastic waves by a crack with spring-mass contact is investigated. Such a crack may be regarded as a simplified model of a thin elastic inclusion. Boundary integral equations are formulated for both displacement and traction on crack faces and are solved numerically. Numerical results are presented for stress intensity factors, crack-opening displacements and scattering cross-sections. Our results are in good agreement with other published solutions. It is also found that the effect of a mass can not be neglected in evaluation of scattering cross-sections, even if the mass is small.     

Global identities for water-wave scattering potentials

Within the context of the linearised theory of time-harmonic water waves in three dimensions, a number of identities are obtained that are satisfied throughout the fluid domain by the velocity potential in scattering problems. This is done for both incident plane waves and for incident cylindrical waves. The implications of these results for the solution of time-domain scattering problems by the method of expansion in generalised eigenfunctions are discussed. In particular, it is demonstrated explicitly, for both two and three dimensions, that two different formulations of the generalised eigenfunction method are equivalent. Further, a new representation is given for the time-domain solution as an integral over the angles of incidence for particular generalised eigenfunctions.     

Physical optics theory for the diffraction of waves by impedance surfaces

The solution of the scattering problem of waves by a half-screen with equal face impedances, which was introduced by Malyughinetz, is transformed into a physical optics integral by using the inverse edge point method. The obtained integral is applied to the diffraction problem of plane waves by an impedance truncated circular cylinder and the scattered waves are derived asymptotically. The results are examined numerically.     

Diffraction of evanescent plane waves by a resistive half-plane

Diffraction of evanescent plane waves by a resistive half-plane is examined. The scattering integrals are constructed with the modified theory of physical optics. These integrals are evaluated uniformly by using an unusual method. The scattered fields of evanescent waves are obtained by giving the angle of incidence a complex value. The diffracted waves are plotted numerically for different parameters of the incident field.     

Scattering of ultrasound in solids as visualized by the photoelastic technique

Our efforts in the past few years to visualize the scattering of ultrasound in solids by the photoelastic technique are briefly reviewed. Photoelastic photographs are presented showing the dynamic processes of scattering in glass of plane longitudinal or transverse waves by a cylindrical cavity or cavities as well as by two-dimensional surface-breaking or internal cracks. Phenomena like creeping and multiple scattering are clearly seen, in addition to some details which are not predicted by known theories.     

Time-domain analysis of ultrasonic reflection from imperfect interfaces

The specular reflection of ultrasound from defect covered bond planes is analyzed in the time-domain using the independent scattering model for incident plane waves. We hypothesize that the early-time asymptotics of the reflected wave are given exactly by the independent scattering model for waves that are normally incident on the bond plane. For non-normal incidence, a more restricted result is available for reflected longitudinal waves. We present theoretical arguments for the plausibility of the hypothesis. Experimental measurements made on two sets of model bond planes test and support the hypothesis. Our motivations are as follows. An effort is underway to develop nondestructive methods for estimating the integrity of metal-metal bonds. These methods primarily focus on the reflection of ultrasound in the long wavelength limit, where one can estimate an effective elastic constant. People have characterized the overall quality of the bond in terms of this elastic constant. However, one cannot in this way infer more detailed information such as the average size of the defects or their area fraction. Higher frequency probes, which do provide more detailed information, have been studied in the independent scattering model. Consequently, we have (1) extended the independent scattering model to the time-domain, and (2) shown that it is asymptotically correct for early-time reflections from a defect covered plane (the bond plane). We expect that time-domain methods, based on the analysis presented in this paper, will form the basis for a more rigorous technique for determining the area fraction and the average defect size.