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.     

板材厚度变化对Lamb波透射系数的影响

对Lamb波与厚度变化的板材之间的相互作用进行了分析。针对S0模式Lamb波入射情况,利用混合边界元模型计算了台阶状散射体的透射系数与厚度变化的关系,并进行了实验验证。结果表明S0模式的透射系数能够很好的反映板材的厚度变化,从而为该类材料的定量无损检测提供一定的理论支撑,在实际工业中具有重要的应用意义。     

Acoustic microscopy and dispersion of leaky Rayleigh waves onrandomly rough surfaces: a theoretical study

A theoretical investigation of the dispersion of leaky Rayleigh waves propagating along one-dimensional (1-D) rough fluid-solid interfaces was carried out by simulating the measurement process of a line-focus beam acoustic microscope. The interface profiles were described in terms of their rms, also known as the roughness of the profile, autocorrelation length, and autocorrelation function. The reflectivity of the interfaces was calculated by using a second-order perturbation approach in the profile roughness. Theoretical V(z) curves were generated and analyzed to yield values of the phase velocity of the Rayleigh waves. The dependence of the Rayleigh wave velocity on the profile and material parameters was examined. Significant variations of the phase velocity were found for values of the roughness which are small compared to the shortest of the wavelengths involved in the scattering. The dispersion relations also showed considerable sensitivity to changes in mechanical properties typical of materials of engineering interest. In the low-frequency range, simulations indicated the dispersion of Rayleigh waves to be rather insensitive to the spectral content of the profile     

Scattering of s-polarized electromagnetic plane waves from a film with a shallow random rough surface on a perfect conductor

Scattering of s-polarized electromagnetic planes waves from a film, with a shallow random rough one-dimensional surface, bounded by vacuum and a perfect conductor is calculated. An integral equation that relates the amplitude of the scattered field to the incident wave is found by use of the Rayleigh hypothesis. The integral equation is solved numerically and by use of the perturbation theory, up to the fourth order in the surface profile function. In the angular dependence of the incoherent part of the differential reflection coefficient, the backscattering peak and two additional satellite peaks are observed, owing to two guided waves supported by the film. Analysis of the perturbation solution reveals that the background scattering exhibits minima and maxima as functions of the thickness. By studying the behavior of the scattering as a function of the absorption index of the film, it is shown that the amplitudes of the peaks are low when k ~ 10(-2) and high when k ~ 10(-4).     

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.     

Rayleigh waves in magneto-electro-elastic half planes

This paper investigates Rayleigh waves in magneto-electro-elastic half planes. The magneto-electro-elastic materials are assumed to possess hexagonal (6 mm) symmetry. Sixteen sets of boundary conditions are considered and the corresponding frequency equations are derived. It is found that for any of the 16 sets of boundary conditions, the Rayleigh waves, if exist, are always non-dispersive. Numerical results show that both the material coefficients and boundary conditions can significantly influence the Rayleigh wave properties in magneto-electro-elastic half planes.     

Rayleigh波作用下地下结构地震反应影响分析

采用基于时域粘弹性人工边界的Rayleigh波输入方法,进行了土-地下结构相互作用体系在Rayleigh波作用下的动力时程反应分析,对Rayleigh波作用下地下结构的地震反应特性进行研究。重点讨论了地下结构材料强度、结构厚度以及土层刚度等因素对Rayleigh波作用下地下结构地震反应的影响。结果表明Rayleigh波对浅埋地下结构的地震动力反应影响显著,将使结构产生较大的内力与变形,在地下结构抗震设计尤其是浅埋地下结构的抗震设计时应予以足够的重视。     

Periodic Green's functions analysis of SAW and leaky SAWpropagation in a periodic system of electrodes on a piezoelectriccrystal

A method of periodic Green's functions with a propagation factor exp(iβx), unknown in advance, is used to calculate dispersion curves and attenuation coefficients for Rayleigh- and leaky- waves propagating in a periodic system of thin electrodes on a piezoelectric surface. To describe the charge distribution on the electrodes both a step approximation and Chebyshev polynomials are used, the last being more adequate in most cases. Numerically determined values of the Green's function are used and interpolated either linearly or using a modified variant of Ingebrigtsen's formula. Such basic parameters as stopband width, stopband center frequency, wave velocity and attenuation in the stopband are found. These parameters can be used in the coupling-of-modes (COM) analysis and design of SAW devices. The analysis includes bulk wave radiation and scattering. The dependence of the corresponding attenuation coefficient on frequency is determined. Results obtained allow the determination directly and properly of the COM parameters and the design of SAW devices having large number of electrodes most precisely and rapidly. Numerical results for Rayleigh waves on YZ-LiNbO₃ and leaky waves on 36°YX-LiTaO₃ substrates are presented     

Grazing angle scattering of electromagnetic waves in gratings with varying mean parameters

Abstract

Highly unusual sensitivity of wave scattering in thick periodic gratings to small step-like variations of mean structural parameters at the grating boundaries is predicted and described for the case when the scattered wave (the +1 diffracted order) propagates almost parallel to the front grating boundary (the geometry of GAS — grazing-angle scattering). The analysis is carried out for GAS of bulk TE electromagnetic waves in holographic gratings with varying mean permittivity, and GAS of optical modes guided by a slab with a periodic groove array and varying mean thickness. In particular, it is shown that variations of the mean permittivity by ～0.007% may result in several times variations in the scattered wave amplitude in the grating. At the same time, it is also demonstrated that near the main GAS resonance, the scattered wave amplitudes are only weakly dependent on small variations of mean structural parameters. Physical explanations of the predicted effects are presented. Possible ways of enhancing and, vice versa, reducing (compensating for) the unusual sensitivity of GAS are indicated. Feasible applications of the predicted effects for the design of new highly sensitive sensors and measurement techniques are discussed.     

Subsurface atomic force microscopy: towards a quantitative understanding

Recent experiments in the field of subsurface atomic force microscopy have demonstrated that it is possible to nondestructively image micro- and even nanoparticles that are embedded significantly deep within the bulk of a sample. In order to get insights into the contrast formation mechanism, we performed a finite element analysis and an analytical study, in which we calculated the amplitude and phase variation on the surface of an ultrasound wave that has traveled through the sample. Our calculations were performed as closely as possible to the situation in the experiments to enable a (future) comparison based on our predictions. We show that Rayleigh scattering of acoustic waves accounts for the measured contrast and we verify the characteristic Rayleigh dependences. The numerical results show that the contrast is independent of the depth at which a particle is buried, whereas the analytical study reveals a 1/depth dependence. In addition, we find a large deviation in the width of the particle in the contrast at the surface when applying the numerical or the analytical calculation respectively. These results indicate the importance of both the reflections of sound waves at the sample interfaces and bulk damping, as both are treated differently in our two models.     

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。     

Fundamental solutions for SH-waves in a continuum with large randomness

Fundamental solutions for horizontally polarized shear (SH) waves propagating in continuous medium with an arbitrarily large random wave number are derived herein. These fundamental solutions, or Green's functions, besides being useful in their own right, also serve as kernel functions for integral equation formulations that can be used in the numerical solution of elastic wave scattering problems of practical importance. Thus, the present work serves as an extension of earlier derivations of boundary integral equation statements based on the perturbation approach by removing the assumption of small fluctuations of key medium properties about their mean values. The methodology developed here is based on a series expansion of the fundamental solutions of the SH wave equation under time harmonic conditions using an orthogonal polynomial basis (polynomial chaos) for the randomness. The position-dependent coefficients of this expansion are subsequently found from the resulting vector wave equation, which is uncoupled through use of the eigensolution of its system matrix. Finally, some representative cases are solved and the results are contrasted with those obtained by the perturbation method. At the same time, the accuracy of the solution to the number of terms used in the polynomial expansion is investigated.     

Propagation of boundary acoustic waves along a ZnO layer between two materials

Theoretical and experimental results on boundary acoustic waves propagated along a ZnO layer sandwiched between two materials are presented. It is shown that boundary acoustic waves can exist only when the material constants of the three materials satisfy the particular conditions obtained here. Experiments on SiO(2)/ZnO/SiO(2 ) were performed to verify the theoretical prediction of the existence of boundary waves. Boundary waves were excited and received by interdigital transducers and propagated along the ZnO layer. Propagation loss was practically the same as for Rayleigh waves, indicating a proper mode of the system. The results suggest that future SAW (surface acoustic wave) devices can be made without any package.     

Boundary element method calculation for coherent electromagnetic scattering from two and three dielectric spheres

A quadratic, isoparametric boundary element formulation has been used to calculate the multiple scattering of electromagnetic waves from systems of two and three dielectric spheres. Extinction efficiency results for the scattering of a plane wave are presented for variations of the separation of the two spheres in three kinds of orientations of the system with respect to the incident wave. These have been verified against analytical calculations based on Mie's theory and calculations by other authors. The results demonstrate a large side scattering resonance (the so-called specular resonance). Agreement between the results establishes the boundary element method as a very powerful tool for solving multiple scattering problems because the method applies to arbitrarily shaped objects having a homogeneous dielectric constant in any configuration. To illustrate the versatility of the method, scattering from three spheres is calculated.     

An Efficient and Stable Spectral-Element Method for Acoustic Scattering by an Obstacle

A spectral-element method is developed to solve the scattering problem for time-harmonic sound waves due to an obstacle in an homogeneous compressible fluid. The method is based on a boundary perturbation technique coupled with an efficient spectral-element solver. Extensive numerical results are presented, in order to show the accuracy and stability of the method.     

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     

Influence of metal thickness on phase velocity and thermal sensitivity of SAW devices

Most surface acoustic wave (SAW) devices exhibit a very small sensitivity to thermal effects. However, even on intrinsically compensated crystal cuts, the deposition of metal strips at the surface (transducers or reflectors) induces important changes in the thermoelastic properties of the device. A theoretical approach based on the Sinha-Tiersten perturbation method is proposed to model the influence of metallization on SAW properties on (ST, X) quartz, namely the temperature stability of the phase velocity of Rayleigh waves. Because this perturbation method only gives access to the first-order temperature coefficient of frequency (TCF), it is combined with a conventional calculation of the second-order TCF to predict the evolution of the turnover temperature. The proposed calculation also requires temperature derivatives of the elastic constants of the metal, which can be calculated for different materials. Finally, theoretical results are compared with experimental data measured on SAW devices on (ST, X) quartz, using aluminum gratings     

Lagrangian finite element treatment of transient vibration/acoustics of biosolids immersed in fluids

Superposition principle is used to separate the incident acoustic wave from the scattered and radiated waves in a displacement‐based finite element model. An absorbing boundary condition is applied to the perturbation part of the displacement. Linear constitutive equation allows for inhomogeneous, anisotropic materials, both fluids and solids. Displacement‐based finite elements are used for all materials in the computational volume. Robust performance for materials with limited compressibility is achieved using assumed‐strain nodally integrated simplex elements or incompatible‐mode brick elements. A centered‐difference time‐stepping algorithm is formulated to handle general damping accurately and efficiently. Verification problems (response of empty steel cylinder immersed in water to a step plane wave, and scattering of harmonic plane waves from an elastic sphere) are discussed for assumed‐strain simplex and for voxel‐based brick finite element models. A voxel‐based modeling scheme for complex biological geometries is described, and two illustrative results are presented from the bioacoustics application domain: reception of sound by the human ear and simulation of biosonar in beaked whales. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

半圆柱型沉积盆地对SH波散射的数值分析

该文实现了一种半无限域SH波散射问题的数值分析方法。采用传递矩阵法得到SH波斜入射时的自由场,将其作为输入;采用集中质量显式有限元方法计算区域内节点的位移;采用透射人工边界计算人工边界点的位移;通过编写的FORTRAN程序实现计算过程。运用该方法对均匀半空间内半圆柱型沉积盆地在SH波入射下的散射进行了分析,与Trifunac M D的解析解进行了对比,验证了该文方法的有效性,分析了不同入射角对地表位移和位移谱放大系数的影响。最后,对成层半空间内半圆柱型沉积盆地在SH波入射下的散射进行了分析。相对于解析方法而言,该方法可以考虑更为复杂地形情况。