具有表面效应的压电半空间中的表面波

纳米科技的快速发展使压电纳米结构在纳米机电系统中得到广泛应用,形成了诸如纳米压电电子学等新的研究方向.与传统的宏观压电材料相比,在纳米尺度下压电材料往往呈现出不同的力学特性,而造成这种差异的原因之一便是表面效应.本文基于Stroh公式、Barnett-Lothe积分矩阵及表面阻抗矩阵,研究计入表面效应的任意各向异性压电半空间中的表面波传播问题,导出了频散方程.针对横观各向同性压电材料,假设矢状平面平行于材料各向同性面,发现Rayleigh表面波和B-G波解耦,并得到各自的显式频散方程.结果表明,Rayleigh表面波的波速小于偏振方向垂直于表面的体波,而B-G波的波速小于偏振方向垂直于矢状平面的体波.以PZT-5H材料为例,用数值方法考察表面残余应力和电学边界条件对表面波频散特性的影响发现:表面残余应力只对第一阶Rayleigh波有明显的影响;电学开路情形的B-G波比电学闭路情形的B-G波传播快.本文工作可为纳米表面声波器件的设计或压电纳米结构的无损检测提供理论依据.     

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。     

Using laser ultrasonics for nondestructive residual stress evaluation

A non-contact measuring technique of ultrasonic waves velocity is proposed, in which Rayleigh waves are detected by a laser Doppler velocimeter and the velocity is measured precisely by means of a sing-around unit and a digital oscilloscope. With the proposed technique, the acoustoelastic coefficient of Rayleigh waves in mild steel SS41 is obtained, which is in good agreement with that obtained by the contact method. Furthermore the non-contact technique is applied to evaluate the residual stress in a butt-welded steel plate, the result is reasonable.     

超声纯横波法测试45#钢的内部应力

声各向同性的金属材料在应力作用下,材料表现出声各向异性,这是用声弹性法分析材料内部应力的基础。本文用垂直于应力方向传播的超声纯横波对45#钢进行测试,测试时横波的偏振化方向分别平行和垂直于应力方向。实验结果表明:材料在拉、压应力作用下,相互正交的两超声纯横波的声速都发生了变化,且声各向异性因子与应力成线性关系。利用此关系可测试材料内部应力,提供了一种无损测试材料内部应力的方法,另外本实验方法也可以对材料内部残余应力进行评估。实验中利用回振法测量声速,可测量声速的微小变化,精度高。     

The Potential of Ultrasonic Non-Destructive Measurement of Residual Stresses by Modal Frequency Spacing using Leaky Lamb Waves

This paper investigates the potential of ultrasonic non-destructive measurements of residual stresses using the modal frequency spacing method based on the interference spectrum of leaky Lamb waves as an alternative to the commonly used flight-time approach in ultrasonic methods. Extensive experiments were carried out to verify the viability and robustness of the technique using an instrumented leaky Lamb wave setup with uniaxial stressed samples and welded steel samples. To improve the signal-to-noise ratio, multiple sets of raw signals of specularly reflected and leaky Lamb waves were acquired and then averaged in the time domain. The acquired data in the time domain were then transformed into the frequency domain to form the interference spectrum of leaky Lamb waves with a good repeatability. The acoustoelastic coefficient of carbon steel is then derived from the measured relationship of wave velocity and applied stress. Finally, a welded steel plate was examined and residual stress was evaluated. The current work demonstrates the feasibility and the potential of the proposed method in measuring residual stresses in welded plates and thin-walled structures.     

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.     

A device for measuring the velocity of ultrasonic waves: An application to stress analysis

In this paper we present a device for the practical application of an ultrasonic critical-angle refractometry (UCRfr) technique. UCRfr is a technique for measuring the velocity of longitudinal, shear and Rayleight waves, developed to improve the traditional ultrasonic methods for measuring the stress level in materials by means of acousto-elasticity. The technique consists of relating the variations in wave propagation velocity to variations in the angle of refraction at the interface with a second medium. Variations in the angle of refraction are determined on the basis of delay in receiving of the same wave at two different points. The study deals with the measurements of velocity changes of longitudinal wave due to uniaxial stress. In the present work the effects of stress on aluminum and steel specimens have been studied. Experimentation has show the potential of the technique for stress measurement; on the other hand, when the applied stress is known, it allows the measurement of the acoustoelastic constants of longitudinal waves. As regards measuring variations in velocity induced by stress, using this method it is possible, with a suitable choice of the material the device is made of, to isolate the effects of stress on velocity from the possible effects of temperature.     

基于PVDF复合压电效应的低强度冲击波柔性测量

为探索低强度冲击波的柔性测量技术,对PVDF(polyvinylidene fluoride)压力传感器开展冲击波加载和灵敏度标定实验,评估其低强度冲击波压力测量的可靠性。基于微结构设计改进薄膜传感器,获得适用于低强度冲击波压力测量的高灵敏柔性传感器,结果表明:单一压电工作模式的薄膜传感器测量低强度冲击波时有效输出电荷量和信噪比较低,测量结果容易受压电膜力电响应非线性、结构表面变形振动以及封装因素的影响,灵敏度系数不稳定、个体差异性大。采用周向固支的微结构设计能够将作用于薄膜传感器表面幅值较低的冲击波转换为幅值较高的面内拉应力,产生的复合压电效应可大幅提高传感器名义灵敏度系数、降低个体差异性。研制的柔性传感器在0.2～0.7 MPa压力范围内名义灵敏度约900～1 350 pC/N,相对测量误差不大于±13%。     

Transference of Love-type waves in a bedded structure containing a functionally graded material and a porous piezoelectric medium

The frequency of the Love-type surface waves in a bedded structure consisting of a porous piezoelectric(PP) medium and a functionally graded material(FGM)substrate is approximated. The FGM layer is assumed to have a constant initial stress.The Wentzel-Kramers-Brillouin(WKB) approximation technique is used for the wave solution in the FGM layer, and the method of separation of variables is applied for the solution in the porous piezoelectric medium. The dependence of the wave frequency on the wave number is obtained for both electrically open and short cases. The effects of the gradient coefficient of the FGM layer, the initial stresses(tensile stress and compressive stress), and the width of the FGM layer are marked distinctly and shown graphically. The findings may contribute towards the design and optimization of acoustic wave devices.     

Microstructure Effect on the Lcr Elastic Wave for Welding Residual Stress Measurement

The ultrasonic residual stresses measurement is based on the acoustoelastic effect that refers to the change in velocity of the elastic waves when propagating in a stressed media. The experimental method using the longitudinal critically refracted (Lcr) waves requires an acoustoelastic calibration and an accuracy measurement of the time-of-flight on both stressed and unstressed media. The accuracy of this method is strongly related to that of the calibration parameters, namely the time-of-flight at free stress condition (t₀) and the acoustoelastic coefficient (K). These parameters should be obtained on a free stress sample that has an identical microstructure to that of the stressed media. Our study concerns the ultrasonic evaluation of the welding residual stresses. This assembly process induces three distinct microstructures in the weld seam: the melted zone (MZ), heat affected zone (HAZ) and the parent metal (PM). Previously, the residual stresses evaluation in the steel welded plates, by the use of the Lcr wave method, was only possible in the MZ and in the PM zones. While in the HAZ, the residual stresses were incorrectly evaluated due to its small width impeding the extraction of the calibration sample. In this paper, we propose an original approach to solve this problem, which consists of reproducing the microstructure of this zone using a specific heat treatment. For the experimental part, P355 steel welded plates were used and the three zones were probed. The results compared with those obtained by the hole-drilling reference method show a proven potential of the ultrasonic method using the Lcr waves. The Lcr wave residual stresses measurements were made with sufficient accuracy, such as the variability of repeated measures was estimated on the order of ± 36 MPa.     

MEASUREMENT AND ANALYSIS OF LASER GENERATED RAYLEIGH AND LAMB WAVES CONSIDERING ITS PULSE DURATION

In this article, laser generated Rayleigh and Lamb waves are studied by taking into account its pulse duration. The physical model and theoretical solution are presented to predict the corresponding waveforms for aluminum samples under the ablation generation regime.The waveforms of the excited Rayleigh and Lamb waves by laser with selected pulse duration were measured by laser interferometer and analyzed theoretically, and the agreement between measurement and analysis is demonstrated for the validation of the theoretical model and solution.The broadening of the Rayleigh wave and the disappearing of high order Lamb wave modes can be found with the increase of the pulse duration by the laser ultrasonic technique.     

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.     

Directional Wave Propagation in a Highly Nonlinear Square Packing of Spheres

We studied the dynamic response of a two-dimensional square packing of uncompressed stainless steel spheres excited by impulsive loadings. We developed a new experimental measurement technique, employing miniature tri-axial accelerometers, to determine the stress wave properties in the array resulting from both an in-plane and out-of-plane impact. Results from our numerical simulations, based on a discrete particle model, were in good agreement with the experimental results. We observed that the impulsive excitations were resolved into solitary waves traveling only through initially excited chains. The observed solitary waves were determined to have similar (Hertzian) properties to the extensively studied solitary waves supported by an uncompressed, uniform, one-dimensional chain of spheres. The highly directional response of this system could be used as a basis to design granular crystals with predetermined wave propagation paths capable of mitigating stress wave energy.     

界面凹坑上纵波－瑞利波转换的实验研究

应用超声技术对界面半球形凹坑上的纵波－瑞利波的波型转换进行了实验研究。在一个特制的钢质模型上，频率为ＩＭＨｚ的纵波从６个不同方向依次入射到３个不同直径的表面凹坑上，然后在８个不同的方向上接收瑞利波。所接收的散射信号被数字化后进行了ＦＦＴ运算。根据所得实验数据得知，当纵波垂直入射凹坑时所转换的瑞利波的总能量最大；当凹坑直径与入射波长相等时波型转换率最大等结论。其中一些结果为反卷积运算和已知数值计算所验证。     

The propagation and localization of Rayleigh waves in disordered piezoelectric phononic crystals

In this paper, the propagation and localization of Rayleigh waves in disordered piezoelectric phononic crystals with material 6 mm are studied taking the electromechanical coupling into account. The electric field is approximated as quasi-static. The analytical solutions of Rayleigh waves are obtained. The 6×6 transfer matrix between two consecutive unit cells is obtained by means of the mechanical and electrical continuity conditions. The expression of the localization factor in disordered periodic structures is presented by regarding the variables of the mechanical and electrical fields as the elements of the state vector. The numerical results for a piezoelectric phononic crystal—PVDF-PZT-2 piezocomposite—are presented and analyzed. From the results we can see that the localization is strengthened with the increase of the disorder degree. The characteristics of the passbands and stopbands are influenced by different ratios of the thickness of the polymers to that of the piezoelectric ceramics. Disorder in elastic constant c₁₁ of PZT-2 can also result in the localization phenomenon. The propagation and localization of Rayleigh waves in piezoelectric phononic crystals may be controlled by properly designing some structural parameters.     

Propagation of Love waves in a functionally graded piezoelectric material (FGPM) layered composite system

In this theoretical study, we investigate the propagation of Love waves in a layered structure consisting of two different homogenous piezoelectric materials, an upper layer and a substrate. A functionally graded piezoelectric material (FGPM) buffer layer is in between the upper layer and the substrate. We employ the power series technique to solve the governing differential equations with variable coefficients. The influence of the gradient coefficients of FGPM and the layer thicknesses on the dispersion relations, the electro-mechanical coupling factor, and the stress distributions of Love waves in this structure are investigated. We demonstrate that the low gradient coefficient raises the significant variation of the phase velocity within a certain range of ratios of upper layer thickness to equivalent thickness. The electro-mechanical coupling factor can be increased when the equivalent thickness equals one or two wavelengths, and the discontinuity of the interlaminar stress can be eliminated by the FGPM buffer layer. The theoretical results set guidelines not only for the design of high-performance surface acoustic wave (SAW) devices using the FGPM buffer layer, but also for the measurement of material properties in such FGPM layered structures using Love waves.     

Étude expérimentale des champs turbulents acoustiques à l'immédiat aval d'une onde de choc

An original measurement technique based on Rayleigh scattering (Collective Light Scattering) was used in the flow conditions of a normal Mach 2.85 shock wave/homogeneous turbulence interaction. The experimental investigation was limited to the region just downstream of the shock. A non-dimensional attenuation law for the evanescent acoustic waves was found using CLS measurements. This law is significantly different from the one predicted by the Linear Interaction Analysis. However, it was confirmed by hot-wire measurements for which quite severe assumptions were used.     

Dispersion characteristics of wave propagation in layered piezoelectric structures: Exact and simplified models

This article presents a study of the dispersion characteristics of wave propagation in layered piezoelectric structures under plane strain and open-loop conditions. The exact dispersion relation is first determined based on an electro-elastodynamic analysis. The dispersion equation is complicated and can be solved only by numerical methods. Since the piezoelectric layer is very thin and can be modeled as an electro-elastic film, a simplified model of the piezoelectric layer reduces this complex problem to a non-trivial solution of a series of quadratic equations of wave numbers. The model is simple, yet captures the main phenomena of wave propagation. This model determines the dispersion curves of PZT4-Aluminum layered structures and identifies the two lowest modes of waves: the generalized longitudinal mode and the generalized Rayleigh mode. The model is validated by comparing with exact solutions, indicating that the results are accurate when the thickness of the layer is smaller or comparable to the typical wavelength. The effect of the piezoelectricity is examined, showing a significant influence on the generalized longitudinal wave but a very limited effect on the generalized Rayleigh wave. Typical examples are provided to illustrate the wave modes and the effects of layer thickness in the simplified model and the effects of the material combinations.     

Dynamic photoelasticity as an aid in developing new ultrasonic-test methods

A prerequisite for the development of quantitative ultrasonic-inspection techniques for surface flaws is a thorough understanding of the ways in which elastic waves interact with defects. Analytical and numerical approaches are presently inadequate. Experimental methods are needed for a better understanding of wave interactions with real geometries. This paper describes how dynamic photoelasticity was used to study the interaction between Rayleigh waves and slots. To fully interpret the interactions between an incident Rayleigh wave and a surface slot, the problem was subdivided as follows: first, the reflections and mode conversions of a Rayleigh wave at a corner were studied. This simulated the Rayleigh-wave interaction with a slot opening. Then, the interaction when a Rayleigh wave ran off the tip of a slot was observed, and, finally, the total interaction with slots perpendicular to the surface was studied. The results for these three cases are presented. It is suggested that the most important property of a Rayleigh wave that can be used to size surface and near-surface defects is the subsurface particle motions. These motions persist up to a depth of the order of a wavelength. The shape (that is, the frequency spectrum of the transmitted wave) should, therefore, be affected by the depth of the slot. Spectroscopic analysis is applied to the photoelastic data to develop a simple method for sizing slots. Results from ultrasonic tests on slots in steel confirm the validity of the suggested method. By applying contemporary concepts of signal processing to photoelastic data, a powerful new area of experimental investigation is introduced. It promises to overcome the current inability of scatter theories to predict the interactions between real-life defects and acoustic waves as used in ultrasonic testing. Applications of this approach will improve the quantitative ability of ultrasonic-inspection methods.     

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.