Acoustoelastic determination of residual stress with laser doppler velocimetry

The main object of this study is to develop a new technique for stress nondestructive measurement. A noncontact measurement technique of ultrasonic wave velocity is proposed. In the measurement system, a laser Doppler velocimeter, which is noncontact, is used to detect wave motions due to Rayleigh waves instead of a piezoelectric transducer. The noncontact measurement technique is applied to determine the stress-acoustic coefficient of Rayleigh waves for aluminum 5052 and a structural steel, and the results are in good agreement with those obtained using knife-edge piezoelectric transducers. The technique is also used to evaluate residual stress existing in an H-section rolled beam of the structural steel. The distribution of residual stress is reasonable.     

Modeling nonlinear Rayleigh wave fields generated by angle beam wedge transducers—A theoretical study

Nonlinear Rayleigh wave fields generated by an angle beam wedge transducer are modeled in this study. The calculated area sound sources underneath the wedge are used to model the fundamental Rayleigh sound fields on the specimen surface, which are more accurate than the previously used line sources with uniform or Gaussian amplitude distributions. A general two-dimensional nonlinear Rayleigh wave equation without parabolic approximation is introduced and the solutions are obtained using the quasilinear theory. The second harmonic Rayleigh wave due to material nonlinearity is given in an integral expression with these fundamental Rayleigh waves radiated by the wedge transmitter acting as a forcing function. Multi-Gaussian beam (MGB) models are employed to simplify these integral solutions and to extract the diffraction and attenuation correction terms explicitly. The effect of nonlinearity of generating sources on the second harmonic Rayleigh wave fields is taken into consideration; simulation results show that it will affect the magnitude and diffraction correction of the second harmonic waves in the region close to the Rayleigh wave sound sources. This research provides a theoretical improvement to alleviate the experimental restriction on analyzing the effects of diffraction, attenuation and source nonlinearity when using angle beam wedge transducers as transmitters.     

Scattering of a Rayleigh wave by an elastic wedge whose angle is less than 180°

The steady-state problem of scattering of an incident Rayleigh wave by an elastic wedge whose angle is less than 180° is considered. The problem is reduced to the numerical solution of a pair of Fredholm integral equations of the second kind whose kernels are continuous functions. Numerical results are given for the amplitude and phase of the Rayleigh waves transmitted and reflected by the corner.     

一种求解瑞利波散射问题的修正边界元方法

边界元法的一大优势是用于求解半空间等无限域问题,然而对于弹性波的传播问题,传统边界元法在采用全平面或全空间格林函数时,在截断边界处仍会产生虚假的反射回波,直接影响到散射场的求解准确性。因此,本文在传统边界元法基础上提出一种修正边界元法,用于计算无限大半平面中的弹性波场问题。该方法以瑞利波形式的远端散射场代替原本因截断而舍去的部分,通过互易定理建立单位瑞利波和全平面格林函数的积分方程,求得修正系数,并代入修正边界元矩阵,计算出瑞利波的散射场。为验证本文所提方法,文中将多个算例的结果与解析解对比,并用该方法计算了不同缺陷的散射场。这些对比结果表明,本文所提修正边界元法可准确求解瑞利波散射场,为基于表面波的缺陷反演问题研究提供了有效的正演途径。     

Analysis of comb transducers with sliding teeth

Ultrasonic comb transducer generates surface acoustic waves on an elastic substrate by periodic traction exerted by its vibrating periodic teeth on the substrate surface. In this paper, the comb teeth are actually sliding elastic spacers between an acoustic buffer and the substrate. The incident wave in acoustic buffer scatters on periodic spacers producing interface waves in the system which transform into Rayleigh waves at the transducer edges. The full-wave theory of interface wave generation is presented, concluded by efficiency estimation of transformation of the incident wave into the surface wave in the substrate and of the surface waves back to bulk waves in the acoustic buffer. Numerical examples presented for all aluminum substrate, buffer and teeth show the 11-teeth comb combined efficiency for generation and detection on the level of ?40 dB for optimized teeth height.     

Scattering of a pulsed Rayleigh wave by a spherical cavity in an elastic half space

The time-dependent scattering by a spherical cavity in an elastic half space is considered. The incoming wave is a pulsed Rayleigh wave. The stationary part of the problem is solved by the T-matrix method, and an integration in frequency is performed with a modified gaussian weight function. The displacement components at some points on the surface of the half space are computed and shown in a number of plots.     

Analysis of scattering waves in an elastic layered medium by means of the complete eigenfunction expansion form of the Green’s function

A scattering problem due to an object and a plane incident wave in an elastic layered half space is presented in this paper. The complete eigenfunction expansion form of the Green’s function developed by the author and the boundary integral equation method are introduced into the analysis. First, the complete eigenfunction expansion form of the Green’s function is investigated for its application to the scattering problem. A comprehensive explanation is also given for the fact that the complex Rayleigh wave modes exhibit standing waves. Next, a method for the analysis of scattering waves by means of the Green’s function is presented. The advantage of the present method is that the formulation itself is independent of the number of layers and the scattering waves can be decomposed into the modes for the spectra defined for the layered medium. Several numerical calculations are performed to examine the efficiency of the present method as well as the properties of the scattering waves. According to the numerical results, the complete eigenfunction expansion form of the Green’s function provides accurate values for application to a boundary element analysis. The spectral structure and radiation patterns of the scattering wave are presented and investigated. The differences in directionality can be found from the radiation patterns of the scattering waves decomposed into the modes for the spectra.     

曲面曲率对Rayleigh波传播特性的影响

对任意形状的均匀各向同性线弹性曲面物体,用 WKB～（1）方法求解了沿曲面传播的Rayleigh表面波的运动微分方程,同时考虑了波传播方向及其垂直方向曲面曲率对波的穿透性的影, 所获波动方程的势函数解答表明,在一般情况下垂直波传播方向的曲面曲率对波的穿透深度的影响是不容忽视的.进而以同种介质平面表面情况下的Rayleigh面波的传播特性为基准,给出了曲面曲率引起波数或波速变化的解析表达式.通过理论分析和数值算例,描述了曲面上Rayleigh面波传播行为的一些基本特征.     

Scattering of an obliquely incident Rayleigh wave in an elastic quarterspace

We study the three-dimensional problem of scattering of waves in a homogeneous, isotropic, linearly elastic quarter space. We obtain an equation for the Fourier transform of the normal displacements on the free surfaces. For oblique incidence of a Rayleigh surface wave, we numerically solve this equation. Reflection and tansmission coefficients are plotted versus angle of incidence. For angles of incidence smaller than a critical angle, we observed that no energy is radiated into the solid by body waves. The farfield scattering patterns are also plotted.     

Extinction of elastic wave energy due to scattering in a viscoelastic medium

Forward scattering theorem for elastic longitudinal and shear wave scatterings by an arbitrary-shaped three-dimensional object embedded in a viscoelastic medium is derived. It is shown that the formulae for extinction cross-sections of an object in an energy-absorbing medium are formally the same with those of the object in the lossless elastic medium. Numerical calculations are executed for the longitudinal wave scattering in an epoxy matrix by a spherical inclusion with different material properties. The condition of negative extinction is examined with the causality constraint on the viscoelastic medium taken into account. It is found that the negative extinction occurs in the Rayleigh limit when the attenuation of the medium is sufficiently high and, more restrictedly, the wave speed in the object is larger than that in the medium, while it occurs less likely in the high frequency range considered in this paper (0<ka<100).     

Scattering of elastic waves by an arbitrary small imperfection in the surface of a half-space

T , the first of two articles, is concerned with the scattering of elastic waves by arbitrary surface-breaking or near surface defects in an isotropic half-plane. We present an analytical solution, by the method of matched asymptotic expansions, when the parameter , which is the ratio of a typical length scale of the imperfection to the incident radiation's wavelength, is small. The problem is formulated for a general class of small defects, including cracks, surface bumps and inclusions, and for arbitrary incident waves. As a straightforward example of the asymptotic scheme we specialize the defect to a two-dimensional circular void or protrusion, which breaks the free surface, and assume Rayleigh wave excitation ; this inner problem is exactly solvable by conformal mapping methods. The displacement field is found uniformly to leading order in , and the Rayleigh waves which are scattered by the crack are explicitly determined. In the second article we use the method given here to tackle the important problem of an inclined edge-crack. In that work we show that the scattered field can be found to any asymptotic order in a straightforward manner, and in particular the Rayleigh wave coefficients are given to O(²).     

NUMERICAL ANALYZITION OF NANO-PARTICLE FOLLOWING FEATURES FOR RAYLEIGH SCATTERING VELOCITY MEASUREMENT TEST IN LOW DENSITY WIND TUNNEL

在低密度风洞试验流场中,加入少量纳米粒子,可以增强瑞利散射测速试验的散射光强度.纳米粒子能否适应流场气流速度变化是测量结果准确性的关键.为了研究瑞利散射测速实验中测量到的纳米粒子的速度能否反映流场当地气流速度,采用基于直接模拟蒙特卡罗方法的稀薄两相流双向耦合算法,对低密度风洞流场中纳米粒子在大梯度流场中的跟随性进行了数值研究.仿真了10 nm,50 nm和100 nm TiO₂三种尺寸的纳米粒子分别在M6和M12低密度风洞返回舱高超声速绕流流场中的运动特性.仿真结果显示,不同尺寸的纳米粒子在不同的流场稀薄度条件下的跟随性不同,纳米粒子尺寸越小,跟随性越好.在稀薄度较低的M6流场中,10 nm粒子跟随性很好,与瑞利散射测量结果比较接近,粒径50 nm以上的粒子跟随性较差,而在稀薄度较高的M12流场中,10 nm粒子的跟随性也变差,表明通过瑞利散射测量到的纳米粒子速度和流场中气体速度有一定差距,不能准确反映流场当地速度.     

弹性波绕任意形状界面孔的散射

求解了弹性波绕任意形状界面孔的散射问题．通过入射波、反射波或折射波及孔的散射波场的叠加,得到了界面孔在SH波绕射下的总波场．总波场波函数的级数项待定系数可采用边界配点法来确定,该法不受边界正交性的限制,能够适用于任意形状的边界．最后,对界面椭圆孔进行了实例计算,得到了椭圆孔边的动应力集中系数．     

The coupling between ocean waves and rectangular ice sheets

This paper describes a semi-analytic approach to problems involving rectangular elastic plates of shallow draft floating on water. Specifically, two problems are considered: the scattering of plane monochromatic incident waves by a single elastic plate and the propagation/attenuation of waves through a periodic rectangular arrangement of plates. The approach combines Fourier methods with Rayleigh–Ritz methods for free modes of rectangular plates which reduces each problem to an algebraic system of equations which are numerically accurate and efficient to compute. A selection of results are given to illustrate the work. The approach can be applied to many problems in hydroelasticity including the seakeeping of large flat-bottomed marine vessels, deflections in very large floating structures such as offshore airports and wave propagation through areas of broken sea ice.     

An approach for obtaining approximate formulas for the Rayleigh wave velocity

In this paper, we introduce an approach for finding analytical approximate formulas for the Rayleigh wave velocity for isotropic elastic solids and anisotropic elastic media as well. The approach is based on the least-square principle. To demonstrate its application, we applied it in order to obtain an explanation for Bergmann’s approximation, the earliest known approximation of the Rayleigh wave velocity for isotropic elastic solids, and used it to establish a new approximation. By employing this approach, the best approximate polynomials of the second order of the cubic power and the quartic power in the interval [0, 1] were found. By using the best approximate polynomial of the second order of the cubic power, we derived an approximate formula for the Rayleigh wave speed in isotropic elastic solids which is slightly better than the one given recently by Rahman and Michelitsch by employing Lanczos’s approximation. Also by using this second order polynomial, analytical approximate expressions for orthotropic, incompressible and compressible elastic solids were found. For incompressible case, it is shown that the approximation is comparable with Rahman and Michelitsch’s approximation, while for the compressible case, it is shown that our approximate formulas are more accurate than Mozhaev’s ones. Remarkably, by using the best approximate polynomials of the second order of the cubic power and the quartic power in the interval [0, 1], we derived an approximate formula of the Rayleigh wave velocity in incompressible monoclinic materials, where the explicit exact formulas of the Rayleigh wave velocity so far are not available.     

Scattering of guided waves by circumferential cracks in composite cylinders

A somewhat generalized numerical procedure is used in this paper to study the problem of wave scattering by circumferential cracks in composite pipes. The study is motivated by the need to develop a model for the quantitative, ultrasonic non-destructive evaluation of cracks in pipes. For this purpose, a stiffness-based Rayleigh–Ritz type approach is employed first to obtain the approximate wave numbers and wave modes. Using the wave function expansions of the incident and scattered fields in the axial direction and decomposing the problem into separate symmetric and anti-symmetric problems, a three-dimensional wave scattering problem is reduced to two, independent two-dimensional problems over the circular cross-section. Both these problems can be reduced further to quasi-one-dimensions by discretizing the cross-section into finite elements and using a transfer matrix approach in the circumferential direction. This simplification greatly reduces the computational time. A comparison of the results for an isotropic pipe demonstrates the reliability and accuracy of the modified numerical procedure. Numerical results for the reflection and transmission coefficients of different incident wave modes are also presented for a 2-ply composite pipe with a crack. The crack may have an arbitrary circumferential length and radial depth. Simple extrapolations from one wave to another wave, separately incident on a crack, are demonstrated to be impossible due to different mode conversions by the crack.     

Propagation and scattering of ultrasonic waves in polycrystals with arbitrary crystallite and macroscopic texture symmetries

A general ultrasonic attenuation model for a polycrystal with arbitrary macroscopic texture and triclinic ellipsoidal grains is described with proper accounting for the anisotropic Green’s function for the reference medium. The texture and the ellipsoidal grain frames in the model are independent and the wave propagation direction is arbitrary. The attenuation coefficients are obtained in the Born approximation accompanied by the Rayleigh and stochastic asymptotes. The scattering model displays statistical anisotropy due to two independent factors: (1) shape of the oriented grains and (2) preferred crystallographic orientation of the grains leading to macroscopic anisotropy of the homogenized reference medium. The model is applicable to most single phase polycrystalline materials that may occur as a result of thermomechanical manufacturing processes leading to different macrotextures and elongated-shaped grains. It predicts the strength of ultrasonic scattering and its dependence on frequency and propagation direction as a function of grain shape, grain crystallographic symmetry and macroscopic texture parameters and provides the texture-induced dependence of macroscopic ultrasonic velocity on propagation angle. It considers proper wave polarizations due to macroscopic anisotropy and scattering-induced transformations of waves with different polarizations. Competing effects of grain shape and texture on the attenuation are observed. In contrast to the macroscopically isotropic case, where in the stochastic regime the attenuation is highest in the direction of the longest ellipsoidal axis of the grain, the wave attenuation in the elongation direction may be suppressed or amplified by the texture with different effects on the quasilongitudinal and quasitransverse waves. The frequency behavior is also interestingly affected by texture: a hump in the total attenuation coefficient is found for the fast quasitransverse wave which is purely the result of macroscopic anisotropy and the existence of two quasitransverse waves; this hump is not observed in the macroscopically isotropic case. Striking differences of the texture effect on the directional dependences of the attenuation coefficients are found at low versus high frequencies.     

The transient elastodynamic field excited by trans-Rayleigh trains

The elastic wave field due to a surface load in motion over an elastic half-space is investigated. The model serves as a canonical solution for the modelling of high speed ‘trans-Rayleigh’ trains. The analysis presented leads to closed form expressions for the particle displacement, conical waves and Rayleigh waves as separate contributions. The linearized elastodynamic equations are mapped into a proper form in order to apply the Cagniard-de Hoop technique and find closed form time domain solutions for the particle displacement in the subsonic state, transonic state and supersonic state. A special transformation is used that yields closed form space-time domain expressions for the Conical wave as well as the Rayleigh wave contributions. Attention is focussed on surface source speeds in the neighbourhood of the Rayleigh wave speed and speeds that exceed the wave speed of the shear wave. Numerical results for the conical wave field and Rayleigh wave field are presented at observation points just below the surface showing the enormous effects of the Rayleigh wave at source speeds in the near vicinity of the Rayleigh wave speed.     

初应力对压电层状结构声表面波传播性能的影响

研究了压电层状结构中初应力对广义Ｒａｙｌｅｉｇｈ波传播相速度和机电耦合性能的影响,通过求解含初应力的运动微分方程,对自由界面电学开路和短路两种情况得到了相应的相速度方程。给出了具体的数值算例,所得结果对于提高和改善声表面波器件性能有参考意义。     

Propagation of Rayleigh waves on curved surfaces

The propagation and properties of Rayleigh waves on curved surfaces are investigated theoretically. The Rayleigh wave dispersion equation for propagation on a curved surface is derived as a parabolic equation, and its penetration depth is analyzed using the curved surface boundary. Reciprocity is introduced to model the diffracted Rayleigh wave beams. Simulations of Rayleigh waves on some canonical curved surfaces are carried out, and the results are used to quantify the influence of curvature. It is found that the velocity of the surface wave increases with greater concave surface curvature, and a Rayleigh wave no longer exists once the surface wave velocity exceeds the bulk shear wave velocity. Moreover, the predicted wave penetration depth indicates that the energy in the Rayleigh wave is transferred to other modes and cannot propagate on convex surfaces with large curvature. A strong directional dependence is observed for the propagation of Rayleigh waves in different directions on surfaces with complex curvatures. Thus, it is important to include dispersion effects when considering Rayleigh wave propagation on curved surfaces.