基于群速度失配的超声兰姆波二次谐波的时域测量方法

考虑到发射和接收换能器对超声兰姆波时域二次谐波信号所带来的不可避免的影响,提出一种基于基频与二倍频兰姆波群速度失配的超声兰姆波二次谐波的时域测量方法。当基频与二倍频超声兰姆波的相速度匹配而群速度失配时,在超声兰姆波传播过程中所发生的二次谐波信号,在时域上可与源于斜劈换能器的二次谐波信号相分离。采用仅源自于基频兰姆波的时域二次谐波的积分振幅,定量描述兰姆波二次谐波的发生效率。以铝板中传播的兰姆波为例,给出了时域二次谐波的具体测量过程。本文提出的测量方法放宽了超声兰姆波二次谐波的测量条件,且扣除了换能器对二次谐波信号所带来的影响,所测得的二次谐波信号完全来自于基频兰姆波时域信号的二次谐波发生效应。      

楔块中脉冲声场及相控阵成像自检研究

相控阵横波检测必须在换能器前方加上楔块,对于楔块中的声场进行研究具有重要意义。本文通过数值计算和物理实验研究了超声相控阵楔块中的脉冲声场,分析并解释了超声相控阵系统自检成像过程中各种波形的产生机理和转换过程。首先从固体中超声传播理论出发,采用时域有限差分方法对相控阵楔块中各阵元独立发射条件下的脉冲声场进行仿真计算,给出了超声脉冲在楔块中的传播过程;然后开展了对应边界条件下相控阵楔块的B模式成像实验。数值模拟和物理实验的结果基本一致。本文的研究初步展示了楔块中的脉冲声场,其结果可为超声相控阵系统自检和楔块设计提供参考。     

复合材料表面缺陷的超声扩散场定位

传统超声检测多使用直达波进行检测,但在各向异性、非均匀的复杂结构检测中存在诸多限制。将超声波在此类多重散射介质中的传播近似为扩散过程,探索采用超声扩散场信号进行复合材料表面缺陷的检测定位。在此过程中形成的扩散场能对介质密集采样,对缺陷的出现高度敏感。针对铺层结构为[0°/90°]₁₂的碳纤维增强环氧树脂基复合材料板,基于Locadiff方法建立表面缺陷定位的理论模型,开展缺陷出现前后波形的理论不相关性计算。结合实验求解扩散系数,开展检测信号的不相关性分析。最后利用反演计算的模型给出缺陷的定位结果。结果表明,当缺陷直径为10 mm时,定位误差为6.99%;当缺陷直径为5 mm时,定位误差为9.29%,可以实现复合材料表面缺陷的定位。      

一维非线性声波传播特性

针对一维非线性声波的传播问题进行了有限元仿真和实验研究. 首先推导了一维非线性声波方程的有限元形式, 含有高阶矩阵的非线性项导致声波具有波形畸变、谐波滋生、基频信号能量向高次谐波传递等非线性特性. 编制有限元程序对一维非线性声波进行了计算并对仿真得到的畸变非线性声波信号进行处理, 分析其传播性质和物理意义. 为验证有限元计算结果, 开展了水中的非线性声波传播的实验研究, 得到了不同输入信号幅度激励下和不同传播距离的畸变非线性声波信号. 然后对基波和二次谐波的传播性质进行详细讨论, 分析了二次谐波幅度与传播距离和输入信号幅度的变化关系及其意义, 拟合出二次谐波幅度随传播距离变化的方程并阐述了拟合方程的物理意义. 结果表明, 数值仿真信号及其频谱均与实验结果有较好的一致性, 证实计算方法和结果的正确性, 并提出了具有一定物理意义的二次谐波随传播距离变化的简单数学关系. 最后还对固体中的非线性声波传播性质进行了初步探讨. 本研究工作可为流体介质中的非线性声传播问题提供理论和实验依据.     

The influence of magnetic field swept rate on the ultrasonic propagation velocity of magnetorheological fluids

Structure of magnetorheological (MR) fluids depends on the strength of the magnetic field applied and on the mode of its application. The ultrasonic wave propagation velocity changes under the effect of an external magnetic field as a result of formation of clusters arranged along the direction of the field in the MR fluids. Therefore, we propose a qualitative analysis of these clustering structures by measuring properties of ultrasonic propagation. Since the MR fluids are opaque, the non-contact inspection using this ultrasonic technique can be very useful. In this study, we measured ultrasonic propagation velocity in MR fluid influenced by an external magnetic field for different swept rate precisely. With increasing magnetic field intensity, the changes of the ultrasonic wave velocity are more pronounced. Sedimentation effect takes place in certain time for different swept rate due to magnetic particle size and it follows linear relationship in log scale. Significant differences of the ultrasonic wave velocity are established between the case when the field is swept at a constant rate and the case when it is stepped up.     

Modeling of ray paths of head waves on irregular interfaces in TOFD inspection for NDE

The TOFD (Time of Flight Diffraction) technique is a classical ultrasonic inspection method used in ultrasonic non-destructive evaluation (NDE). This inspection technique is based on an arrangement of two probes of opposite beam directions and allows a precise positioning and a quantitative evaluation of the size of cracks contained in the inspected material thanks to their edges diffraction echoes. Among the typical phenomena arising for such an arrangement, head waves, which propagate along the specimen surface and are chronologically the first waves reaching the receiver, are notably observed. Head wave propagation on planar surfaces in TOFD configurations is well known. However, realistic inspection configurations often involve components with irregular surfaces, like steel excavated specimens.     

Reconciliation of the forward scattering and wave theories of electric-field-gradient-induced birefringence

We consider propagation of a linearly polarized, harmonic, plane electromagnetic wave incident on a dilute gas subject to a non-uniform electrostatic field. We work to electric quadrupole–magnetic dipole order. In general, the wave is distorted to include a perpendicular component induced by the electrostatic field gradient, and the resultant is not a plane wave. Although the induced component is small, its contribution to the polarization-dependent refractive index of the gas in Buckingham's quadrupole experiment is significant. We show that distortion of the incident wave accounts exactly for the present discrepancy between wave theory and forward scattering theory of electric-field-gradient-induced birefringence in a gas: both theories yield the result obtained originally by Buckingham and Longuet-Higgins.     

高频聚焦超声声场和温度场的仿真研究*

为探究临床常用的7 MHz高频聚焦超声在多层生物组织中的声传播以及毫秒级时间内的生物传热规律问题,基于Westervelt方程和Pennes传热方程,使用有限元方法建立高频聚焦超声辐照多层组织的非线性热黏性声传播及传热模型。首先分析了线性模型和非线性模型之间的差异,然后在非线性模型下探究换能器的参数对声场和温度场的影响。仿真结果显示：在7 MHz频率下,当换能器输出声功率超过5 W时,声波传播的非线性效应不可忽视(p <0.05);当声功率从5 W增大到15 W时,非线性模型与线性模型预测的温度偏差从20%增加到34.703%;高频聚焦超声波的非线性行为比低频更加显著,基频能量向高次谐波转移的程度增大,声功率为10 W和15 W时4次谐波与基波之比分别达到7.33%和12.12%;高频换能器参数的改变对组织中声场和温度场分布的影响较大,换能器焦距从12 mm减小到11.2 mm,焦点处最高温度增加了77%。结果表明,7 MHz聚焦超声的非线性声传播需要考虑到4次谐波的影响。该文提出的多层组织非线性仿真模型可为高频聚焦超声换能器参数优化及制定安全、有效的术前治疗方案提供理论参考。     

A large ultrasonic bounded acoustic pulse transducer for acoustic transmission goniometry: modeling and calibration

A large, flat ultrasonic transmitter and a small receiver are developed for studies of material properties in acoustic transmission goniometry. While the character of the wave field produced by the transmitter can be considered as a plane wave as observed by the receiver, diffraction effects are noticeable near critical angles and result in the appearance of weak but detectable arrivals. Transmitted ultrasonic waveforms are acquired in one elastic silicate glass and two visco-elastic acrylic glass sample plates as a function of the angle of incidence. Phase velocities are determined from modeling of the shape of curves of the observed arrival times versus angle of incidence. The waveform observations are modeled using a phase propagation technique that incorporates full wave behavior including attenuation. Subtle diffraction effects are captured in addition to the main bounded pulse propagation. The full propagation modeling allows for various arrivals to be unambiguously interpreted. The results of the plane wave solution are close to the full wave propagation modeling without any corrections to the observed wave field. This is an advantage as it places confidence that later analyses can use simpler plane wave solutions without the need for additional diffraction corrections. A further advantage is that the uniform bounded acoustic pulse allows for the detection of weak arrivals such as a low energy edge diffraction observed in our experiments.     

Laser ultrasonic anomalous wave propagation imaging method with adjacent wave subtraction: Application to actual damages in composite wing

Laser ultrasonic wave propagation imaging methods have great potential for integrated structural health management and non-destructive evaluation. However, application of these techniques to complex structures in the field is difficult because they give rise to complicated wave propagation patterns. We developed an anomalous wave propagation imaging method with adjacent wave subtraction using laser ultrasonic scanning to solve this problem. The proposed method is suitable for non-destructive evaluation of complex structures because it highlights the propagation of anomalous waves related to structural discontinuities, and suppresses complex incident waves without the need of pre-stored reference data. In this study, the method was applied to a real composite wing subjected to bending and impact tests. The method enhanced the visibility of the anomalous waves related to damages such as stringer tip debonding, skin-spar debonding, and invisible impact damage. Based on these anomalous waves, variable time window amplitude mapping was performed to show the damage location, size, and shape resemble to the actual damage. Comparisons showed that the methods performed better than the ultrasonic A-scan in terms of damage detection and sizing accuracy. The presence of structural elements such as spars, stringers, ribs, and surface-mounted PZT elements did not adversely affect the inspection. The proposed wing test setup with a built-in ultrasonic propagation imaging system for automatic NDE could be easily expanded throughout a hanger for maintenance inspection.     

Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging

In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described.     

Entrainment and stimulated emission of ultrasonic piezoelectric auto-oscillators

Theoretical modeling and laboratory tests are conducted for nonlinear auto-oscillating piezoelectric ultrasonic devices coupled to reverberant elastic bodies. The devices are shown to exhibit behavior familiar from the theory of coupled auto-oscillators. In particular, these spontaneously emitting devices adjust their limit-cycle frequency to the spectrum of the body. It is further shown that the auto-oscillations can be entrained by an applied field; an incident wave at a frequency close to the frequency of the natural limit cycle entrains the oscillator. Special attention is paid to the phase of entrainment. Depending on details, the phase is such that the oscillator can be in a state of stimulated emission: the incident field amplifies the ultrasonic power emitted by the oscillator. These behaviors are essential to eventual design of an ultrasonic system that would consist of a number of such devices all synchronized to their mutual field, a system that would be an analog to a laser. A prototype uaser is constructed.     

Transmission incoherent ultrasonic imaging of planar objects

A method of obtaining an ultrasonic image of a planar object with spatial variable transparency is proposed on the basis of the results of measuring the amplitude of the ultrasonic wave during the transmission ultrasonic probing. The case is considered in which the wave diffraction strongly affects the amplitude of the field behind the object and the phase is not measured. Even in the absence of phase information, this method allows one to restore the transparency masks of the planar object. The proposed mathematical apparatus can be also used in radio wave probing. Numerical simulation and processing of the experimental data demonstrated the comparability of this method and the aperture synthesis method using the phase information.     

Exact solution for second harmonic generation in XFELs

The generation of harmonic radiation via a non-linear mechanism, driven by electron bunching at the fundamental frequency, is an important option in the operation of high-gain Free-Electron Lasers (FELs). By utilizing harmonic generation at a large scale facility, the production of intense radiation at shorter wavelengths for the same electron beam energy is feasible. This paper describes a theory of second harmonic generation in planar undulators with particular attention to X-Ray FELs (XFELs). Our study is based on an exact analytical solution of Maxwell’s equations, derived with the help of a Green’s function method. Up-to-date theoretical understanding of second harmonic generation is limited to the estimation of the total radiation power, which is based on a comparison of the right hand side of the wave equation for the first harmonic with the right hand side of the equation for the second harmonic, the latter being incorrectly modified. The exact solution should be obtained by solving the wave equation itself. Our work yields correct parametric dependencies and specific predictions of additional properties such as polarization, angular distribution of the radiation intensity and total power. The most surprising prediction is the presence of a vertically polarized part of the second harmonic radiation, whereas current knowledge predicts a horizontally polarized field.     

Nonlinear wave propagation in constrained solids subjected to thermal loads

The classical mathematical treatment governing nonlinear wave propagation in solids relies on finite strain theory. In this scenario, a system of nonlinear partial differential equations can be derived to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such “residual” energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. These results suggest the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather.     

The forward and backward projection of acoustic fields from axisymmetric ultrasonic radiators using impulse response and Hankel transform techniques

A generalized impulse response formulation to evaluate the harmonic pressure field of ultrasonic planar vibrators having axisymmetric nonuniform surface velocity distributions is presented. The harmonic pressure is expressed as a Fourier transform of a generalized impulse response which is a function of the spatially nonuniform velocity of the vibrator. A backward projection method is then developed to reconstruct the normal surface velocity of axisymmetric vibrators from harmonic field pressures using an angular spectrum or Hankel transform formulation. The numerical accuracy of the backward projection technique is evaluated using the impulse response formulation to evaluate the pressure fields for several velocity distributions on disk vibrators. Experiments were performed to reconstruct the velocity distributions over the surface of a uniformly driven piezoelectric ceramic disk and ceramic ring using farfield measurements of the complex pressure. The experimental results were in good agreement with theoretical results based on the electrode patterns of the transducers.     

超声平面波经颅成像相位校正方法

超声平面波经颅成像时,由于颅骨对超声传播的影响引起图像质量下降,需要对颅骨造成的超声相位畸变进行校正.为此,该文研究了两种相位补偿方法:基于近似射线声学的理论方法和基于时间反转的数值计算方法,并利用数值仿真对比了两种方法的补偿和成像效果.结果表明:无论使用近似射线法还是时间反转法,都能够有效地校正因颅骨造成的相位畸变;...     

Elastic wave propagation in sinusoidally corrugated waveguides

The ultrasonic wave propagation in sinusoidally corrugated waveguides is studied in this paper. Periodically corrugated waveguides are gaining popularity in the field of vibration control and for designing structures with desired acoustic band gaps. Currently only numerical method (Boundary Element Method or Finite Element Method) based packages (e.g., PZFlex) are in principle capable of modeling ultrasonic fields in complex structures with rapid change of curvatures at the interfaces and boundaries but no analyses have been reported. However, the packages are very CPU intensive; it requires a huge amount of computation memory and time for its execution. In this paper a new semi-analytical technique called Distributed Point Source Method (DPSM) is used to model the ultrasonic field in sinusoidally corrugated waveguides immersed in water where the interface curvature changes rapidly. DPSM results are compared with analytical solutions. It is found that when a narrow ultrasonic beam hits the corrugation peaks at an angle, the wave propagates in the backward direction in waveguides with high corrugation depth. However, in waveguides with small corrugation the wave propagates in the forward direction. The forward and backward propagation phenomenon is found to be independent of the signal frequency and depends on the degree of corrugation.     

Vector solitary optical beam control with mixed type I–type II second-harmonic generation

The four vector equations, appropriate to a mixed type I–type II second-harmonic generation, in a thin planar waveguide, made from a second-order non-linear material, are solved, both approximately and exactly. The solutions are then used to generate possible applications. In this investigation, both the fundamental and the second-harmonic waves have two transverse field components. It is shown that, by controlling the ratio of the components of the fundamental wave, one component of the second-harmonic wave can be rigorously controlled, and even switched off. The ratio of the harmonic field components depends strongly upon the polarization angle of the fundamental wave, with the extinction angle depending strongly upon the phase mismatch parameter. In a second application, an aperture is placed at the output and it is shown that if approximate stationary states are used as an input to a quadratically non-linear medium, then varying the angle of incidence of two input beams produces an excellent output control. A numerical demonstration is given in which a switch from 80% of the input energy arriving at the output port to less than 3% is readily achievable.     

一种全频散波方程的反问题

基于一种全频散波方程研究了对于谐波和波包的反问题。首先根据Mindlin理论建立了描述无耗散微结构线性固体中波传播模型一一一种全频散波方程,并讨论了其频散特性。然后基于该全频散波方程,提出了利用四种不同谐波的频率和相应波数确定波方程四个未知系数的反问题,并用严格的数学理论论证了此反问题。研究证明,通过测量同一种无耗散微结构线性固体中传播的四种不同谐波的频率和相应波数,在正常频散和反常频散情况下可唯一地确定波方程的未知系数,即材料的未知参数。