轨道板中超声兰姆波传播的有限元计算和实验*

该文针对我国高速铁路轨道板缺陷的非接触动态检测问题,研究了空气耦合超声兰姆波在轨道板中的传播规律。首先,给出了轨道板中超声兰姆波的相速度和群速度频散曲线,结果表明:随着频厚积的增加,频散现象越明显,并且A0相速度收敛于Rayleigh波的波速。然后,建立轨道板中波传播的有限元模型,计算得到兰姆波传播的群速度为2220 m/s,且二维傅里叶变换系数的较大值沿Rayleigh波的频散曲线分布。最后,在沪杭高铁嘉兴南站进行了现场测试,以8.8°倾斜角向轨道板激励产生超声兰姆波,激发产生的兰姆波模态群速度为2325 m/s,且二维傅里叶变换分析其系数的较大值沿Rayleigh波的频散曲线分布。有限元计算结果和实验结果均与理论计算结果一致。该研究为后续轨道板缺陷的非接触动态检测提供了理论依据和实验方法。     

激光激发黏弹表面波有限元数值模拟

研究黏弹性材料中激光激发的Rayleigh波的传播特征. 考虑到黏弹性材料的黏性特征,在频域内建立黏弹性材料中激光激发Rayleigh波的有限元数值模型. 在验证有限元频域数值模型正确性的基础上,模拟脉冲激光作用在黏弹性材料上激发出Rayleigh波,进而讨论激光激发的黏弹Rayleigh波的传播特征,并比较黏弹性材料与弹性材料中激光激发的Rayleigh波差异,同时分析了材料的黏性劲度参量变化对Rayleigh波特征的影响. 关键词： 表面波 激光超声 有限元方法 黏弹性     

Acoustic field excited by a pulsed laser line source in a cylinder

The excitation and propagation of the acoustic waves in an elastic cylinder are studied by laser ultrasonics both theoretically and experimentally. The theoretical analysis of the two-dimensional acoustic field excited by a pulsed laser line source impacting on the generatrix of an elastic cylinder is presented. The dispersive properties for both cylindrical Rayleigh wave and the higher modes--whispering gallery (WG) modes are analyzed in detail. The numerical transient displacement waveforms for a detecting point located another terminal of the cylinder diameter opposite the source are calculated. The experimental excitation and detection of the acoustic waves in an aluminum cylinder are carried out on a laser ultrasonic system, which mainly consists of a Q-switched Nd:YAG laser and a laser interferometer. The wave components of bulk waves and surface waves (cylindrical Rayleigh waves and WG modes) are analyzed by comparing the numerical and experimental waveforms. The results are in good agreement.     

The acoustoelastic effect on Rayleigh waves in elastic--plastic deformed layered rocks

On the basis of the acoustoelastic theory for elastic--plastic materials, the influence of statically deformed states including both the elastic and plastic deformations induced by applied uniaxial stresses on the Rayleigh wave in layered rocks is investigated by using a transfer matrix method. The acoustoelastic effects of elastic--plastic strains in rocks caused by static deformations, are discussed in detail. The Rayleigh-type and Sezawa modes exhibit similar trends in acoustoelastic effect: the acoustoelastic effect increasing rapidly with the frequency-thickness product and the phase velocity change approaching a constant value for thick layer and high frequency limit. Elastic--plastic deformations in the Castlegate layered rock obviously modify the phase velocity of the Rayleigh wave and the cutoff points for the Sezawa modes. The investigation may be useful for seismic exploration, geotechnical engineering and ultrasonic detection.     

Measurement of cylindrical Rayleigh surface waves using line-focused PVDF transducers and defocusing measurement method

Line-focused PVDF transducers and defocusing measurement method are applied in this work to determine the dispersion curve of the Rayleigh-like surface waves propagating along the circumferential direction of a solid cylinder. Conventional waveform processing method has been modified to cope with the non-linear relationship between phase angle of wave interference and defocusing distance induced by a cylindrically curved surface. A cross correlation method is proposed to accurately extract the cylindrical Rayleigh wave velocity from measured data. Experiments have been carried out on one stainless steel and one glass cylinders. The experimentally obtained dispersion curves are in very good agreement with their theoretical counterparts. Variation of cylindrical Rayleigh wave velocity due to the cylindrical curvature is quantitatively verified using this new method. Other potential applications of this measurement method for cylindrical samples will be addressed.     

激光超声检测带过渡圆角平板表面缺陷的数值研究

为了研究激光激发出的超声波在带过渡圆角的金属平板上的传播规律和检测表面缺陷的方法，采用有限元法模拟了该类平板中的激光超声现象，分析了表面波在圆角区域的传播规律和与表面缺陷的作用过程。数值结果表明:激光激发出纵波、横波和Rayleigh波等，其中Rayleigh波主要存在于表面mm量级，并且在过渡圆角处发生模式转换生成了直达波R′和模式转换波R_R等多种表面波；经过过渡区域后的声波在表面缺陷处发生了反射和透射现象，通过B扫图可以检测缺陷的位置。随着缺陷深度的增加，表面波的透射系数不断减小，且透射波R_t和R_st存在0.5 μs左右的到达时间差，该时间差与缺陷深度近似成线性正相关。数值结果为激光超声检测带过渡圆角的平板表面缺陷提供了有价值的参考。     

DISPERSION OF WAVES IN IMMERSED LAMINATED COMPOSITE HOLLOW CYLINDERS

A layer element method (LEM) is presented for analyzing frequency and group velocity dispersive behaviours of waves in a laminated composite cylinder surrounded by a fluid. The LEM applies finite elements to model the radial displacement of the cylinder and the radial pressure of the fluid, and complex exponentials to express the axial and circumferential displacements of the cylinder as well as the axial and tangential pressures of the fluid. The dispersive equation for the fluid-loaded cylinder follows from variational techniques. The frequency and group velocity dispersive relationships of the fluid-coupling cylinder are obtained by means of the Rayleigh quotient. Numerical results are given for hybrid laminated composite cylinders and cylindrical shells submerged in water. The addition of the fluid is proven to have considerable impact on the group velocity spectra of waves in laminated composite cylinders.     

Propagations of Rayleigh and Love waves in ZnO films/glass substrates analyzed by three-dimensional finite element method

Propagation characteristics of surface acoustic waves(SAWs) in ZnO films/glass substrates are theoretically investigated by the three-dimensional(3D) finite element method. At first, for(11ˉ20) ZnO films/glass substrates, the simulation results confirm that the Rayleigh waves along the [0001] direction and Love waves along the [1ˉ100] direction are successfully excited in the multilayered structures. Next, the crystal orientations of the ZnO films are rotated, and the influences of ZnO films with different crystal orientations on SAW characterizations, including the phase velocity, electromechanical coupling coefficient, and temperature coefficient of frequency, are investigated. The results show that at appropriate h/λ, Rayleigh wave has a maximum k~2 of 2.4% in(90°, 56.5°, 0°) ZnO film/glass substrate structure; Love wave has a maximum k~2 of 3.81% in(56°, 90°, 0°) ZnO film/glass substrate structure. Meantime, for Rayleigh wave and Love wave devices, zero temperature coefficient of frequency(TCF) can be achieved at appropriate ratio of film thickness to SAW wavelength. These results show that SAW devices with higher k~2 or lower TCF can be fabricated by flexibly selecting the crystal orientations of ZnO films on glass substrates.     

激光在管道中激发周向导波的有限元模拟

以超声的热弹激发机理为基础，建立了模拟激光在管道中激发周向导波的有限元模型.为了验证模型的正确性，根据Gao等人报道的实验条件［J. Appl. Phys. 91, 6114 (2002)］进行了模拟，理论模拟结果与Gao等人的实验结果符合很好，说明本数值模型的正确性.在此基础上，模拟激光在不同厚度、不同曲率半径的管道内激发的周向导波波形，同时分析了激光在管道中激发的周向导波波形与平板中激发Lamb波的差异，以及管道厚度和曲率半径对激光激发周向导波的影响.     

Numerical analysis of immersed finite cylindrical shells using a coupled BEM/FEM and spatial spectrum approach

This study numerically analyzes submerged cylindrical shells using a coupled boundary element method (BEM) with finite element method (FEM) in conjunction with the wave number theory, in which the spatial Fourier transform of surface velocity for cylinders is directly related to pressure in a far field. The acoustic loading is formulated using a symmetric complex matrix derived from a boundary integral equation where the symmetry is based on an acoustic reciprocal principle for surface acoustics. In this formulation the acoustic loading matrix is a large acoustic element whose degree of freedom is connected to the normal displacement of the vibrating structures. The coupled BEM/FEM equation is a banded, symmetric matrix, and thus its bandwidth can be minimized using a proper algorithm. This formulation significantly increases numerical efficiency. The computed normal velocity is thus transformed to wave number representation to examine acoustic radiation. A finite plane cylindrical shell, without attached stiffeners, and a shell with internal ring stiffeners are chosen to demonstrate the present analysis procedure. The far field pressure computed directly from the integral equation and predicted by wave number theory correlates closely with increasing vibrating frequency. Meanwhile, the influences of the internal ring structures on acoustic radiation are examined using the wave number theory, which helps in understanding how internal structures influence radiated noise.     

Laser-induced circumferential waves on hollow cylinder and their interaction with defects by finite element method

A three dimensional (3-D) finite element model for simulating laser induced circumferential wave on a hollow cylinder is developed based on the thermoelastical mechanism, which can take any laser source into account and simulate the interactions between circumferential wave and defects in the hollow cylinder. The model is verified by a control calculation. The results show that the waveforms of circumferential wave are in very good agreement with those available in literature, not only on the arrival time and shape but also on the amplitudes of A ₀, S ₀ and A₁ modes. Using the model, circumferential waves on the surfaces of two series hollow cylinders are simulated, one with same thickness but different outer radius, and the other with the same outer radius but different thickness. The results show that a new mode appears in circumferential wave, compared with Lamb wave in plate. With increase of thickness or radius, the amplitude of the new mode reduces. Another conclusion is that with increase of the thickness of the hollow cylinder, the circumferential wave evolves gradually to the cylindrical Rayleigh waveform, which results from the attenuation of the coupling effect between the outer and inner surface. Moreover, the circumferential waves generated on a hollow cylinder with a surface defect are also simulated, and the results indicate that in the circumferential waves obtained at the point beyond the defect, the amplitude of A ₀ mode decreases and its dispersion enhances. More importantly, a new bipolar waveform corresponding to the interaction of S ₀ mode with the defect appears, its amplitude is larger than three times of that of S ₀ mode. As a result, we consider that the new bipolar waveform will be the optimal feature to nondestructively detect the surface defect on the hollow cylinder.     

Analysis of laser-generated ultrasonic force source at specimen surface and display of bulk wave in transversely isotropic plate by numerical method

Taking into account the effects of thermal diffusion and optical penetration, as well as the finite width and duration of the laser source, the laser-generated ultrasonic force source at surface vicinity is presented. The full acoustic fields of laser-generated ultrasonic bulk wave are obtained and displayed in transversely isotropic plate. The features of laser-generated ultrasound bulk waves are analyzed. The features of laser-generated ultrasonic bulk wave are in good agreement with the theoretical results (the phase velocity surfaces), demonstrating the validity of this simulation. The numerical results indicate that the features of laser-generated ultrasound waveforms in anisotropic specimen, different from the case in isotropic materials, have a close relation with the propagating plane and propagation direction. This method can provide insight to the generation and propagation of laser-generated ultrasonic bulk wave in transversely isotropic material.     

激光在近表面弹性性质梯度变化的材料中激发超声波的数值分析

激光激发超声波为评价材料近表面弹性性质提供了有效的手段. 考虑到由于冲击硬化、表面热处理、表面氧化等引起的金属材料近表面层弹性性质的变化，建立了一种激光在基底上的梯度材料中激发超声波的理论模型. 用有限元方法模拟了热弹条件下脉冲激光作用于材料上表面激发出的超声波及其传播过程，研究了近表面层离散的层数对超声波的产生和传播的影响，并分别讨论了表面层“变硬”和“变软”两种情况下声表面波的模式变化及用二维傅里叶变换得到各模式的色散曲线. 为进一步研究近表面层的弹性性质建立合理的计算模型及材料性质的反演提供了理论依 关键词： 超声波 有限元法 近表面弹性性质 色散     

Elastic constants of a plate from impact-echo resonance and Rayleigh wave velocity

A new method is proposed for calculating the dynamic elastic constants of an isotropic plate from measurements of the impact-echo resonance and Rayleigh wave velocity. Poisson's ratio is shown to be a single-valued function of the ratio between thickness frequency and Rayleigh wave velocity. This dependence is derived theoretically from the condition of resonance at the minimum frequency of the first-order symmetric Lamb mode. A finite element model is developed to determine how this frequency varies with Poisson's ratio. The results obtained by modal analysis and the power-spectral density technique are in good agreement with those calculated as the solution of the S1 Lamb mode equation. The method is verified by impact-echo tests on concrete and methacrylate plates. A laser interferometer is used to detect the vibration. Thickness frequencies are accurately identified by applying the multicross-spectral density to the signals detected at several points close to the impact point. In a separate experiment, Rayleigh waves are generated by the mediator technique. The wave velocities are determined from the arrival times of the surface wave at several points. Finally, the main sources of uncertainty are evaluated.     

Numerical simulation of laser-generated ultrasound in non-metallic material by the finite element method

The use of a pulsed laser for the generation of the elastic waves in non-metallic materials in the thermoelastic regime is investigated by using finite element method (FEM), taking into account not only thermal diffusion and the finite spatial and temporal shape of the laser pulse, but also optical penetration and the temperature dependence of material properties. The optimum finite element model is established based on analysis of two important parameters, meshing size and time step, and the stability of solution. Temperature distributions and temperature gradient fields in non-metallic material for different time steps are obtained, this temperature field is equivalent to a bulk force source to generate ultrasonic wave. The laser-generated ultrasound waveforms at the epicenter and surface acoustic waveforms (SAWs) are obtained and the influence of optical penetration into the material on the temperature field and the ultrasound waveforms are analyzed. The numerical results indicate that the heat penetration into non-metallic material is caused mainly by the optical penetration, and the ultrasound waveforms, especially the shape of the precursor, are strongly dependent on the optical penetration depth into non-metallic material.     

Theoretical and experimental research on a disk-type non-contact ultrasonic motor

We developed a disk-type non-contact ultrasonic motor based on B22 vibration mode. The rotors of SU-8 photoresist are fabricated by the UV-LIGA process to control their shapes and thicknesses. So the structures of them are optimized by the experiments. It is found that the revolution speed of disk-type non-contact ultrasonic motor not only depends on the vibration amplitude of the stator, but also the weight and construction of the rotors. The maximum revolution speed of the optimal rotor is 3569 rpm at the input voltage of 20 V and the driving frequency of 45.6 kHz. The exciting principle of traveling wave is presented with theoretical equations. The electric signals applied to the piezoelectric ceramic are designed by the principle. The natural frequency and corresponding vibration mode are calculated and analyzed using finite element method. It is shown that experimental results are in good agreement with simulation, which verifies the effectiveness of the finite element model. Moreover, the levitation distance between the stator and rotor is measured by a CCD laser displacement transducer.     

激光激发瑞利波检测表面倾斜缺陷的研究

研究激光激发瑞利波检测样品的表面倾斜缺陷。基于频域热弹耦合方程,采用有限元方法建立激光激发瑞利波检测倾斜缺陷的数值模型,研究倾斜缺陷的检测机理。数值计算含不同的长度及倾斜角度缺陷的样品中瞬态位移波形,分析瑞利波在倾斜缺陷处模式转换的过程,研究各种瑞利波的传播路径。在此基础上,研究缺陷宽度与材料黏性对瑞利波传播及缺陷检测的影响。结果表明:瑞利波在缺陷处产生的反射及透射瑞利波的到达观测点的时间可以检测缺陷位置和长度,瑞利波在缺陷的底部发生模式转换产生的切变波可以检测缺陷倾斜角度。数值结果和已有的实验结果一致,从而为表面倾斜缺陷的检测提供有效的理论依据。      

Coating thickness affects surface stress measurement of brush electro-plating nickel coating using Rayleigh wave approach

A surface ultrasonic wave approach was presented for measuring surface stress of brush electro-plating nickel coating specimen, and the influence of coating thickness on surface stress measurement was discussed. In this research, two Rayleigh wave transducers with 5 MHz frequency were employed to collect Rayleigh wave signals of coating specimen with different static tensile stresses and different coating thickness. The difference in time of flight between two Rayleigh wave signals was determined based on normalized cross correlation function. The influence of stress on propagation velocity of Rayleigh wave and the relationship between the difference in time of flight and tensile stress that corresponded to different coating thickness were discussed. Results indicate that inhomogeneous deformation of coating affects the relationship between the difference in time of flight and tensile stress, velocity of Rayleigh wave propagating in coating specimen increases with coating thickness increasing, and the variation rate reduces of difference in time of flight with tensile stress increasing as coating thickness increases.     

Experimental study on the surface stress measurement with Rayleigh wave detection technique

In this paper, experimental study on the surface stress measurement of a metallic material based on the Rayleigh wave acoustoelastic theory is introduced. A Rayleigh wave acoustoelastic formula deduced by Husson is optimized to estimate the surface stress of the material. Two micro Rayleigh wave transducers with 5 MHz frequency one of which is used for acoustic pulse emitter and another for receiver are used to determine the time of flight of Rayleigh wave propagating in a certain distance along the surface of the material. The difference in time of flight between two ultrasonic signals obtained in stressed and unstressed object surface is identified by the digital correlation method. A specimen made of Q235 steel and applied with tensile load is used for calibration to obtain the acoustoelastic coefficients of Q235 steel. Furthermore, some principal factors which may result in errors in the experiment are discussed and some measurements are proposed to prevent these errors. Finally the surface stress of a cantilever beam is detected by the Rayleigh wave acoustoelastic technique and the experimental result is well compared with the theoretical value.     

Numerical simulation and experimental detection of leaky Lamb waves induced by pulse laser at air-solid interfaces

Based on the thermoelastic mechanism of laser ultrasonic, the problems of the thermal conduction and the coupling between the motion of solid and fluid are solved by using the finite element method. And then the transient waveforms of leaky Lamb waves induced by pulse laser action on the air-aluminum interface are obtained. Experimental signals of laser-induced leaky Lamb waves at the air-aluminum interface are detected by applying an our-developed detector, based on the light deflection principle. The dispersion and attenuation properties of leaky Lamb waves are analyzed through the phase spectral analysis.