Calculation of leaky Lamb waves with a semi-analytical finite element method

A semi-analytical finite element method (SAFE) has been widely used for calculating dispersion curves and mode shapes of guided waves as well as transient waves in a bar like structures. Although guided wave inspection is often conducted for water-loaded plates and pipes, most of the SAFE techniques have not been extended to a plate with leaky media. This study describes leaky Lamb wave calculation with the SAFE. We formulated a new solution using a feature that a single Lamb wave mode generates a harmonic plane wave in leaky media. Dispersion curves obtained with the SAFE agreed well with the previous theoretical studies, which represents that the SAFE calculation was conducted with sufficient accuracy. Moreover, we discussed dispersion curves, attenuation curves, and displacement distributions for total transmission modes and leaky plate modes in a single side and both two side water-loaded plate.     

A combined finite element and modal decomposition method to study the interaction of Lamb modes with micro-defects

This paper presents a combined finite element and modal decomposition method to study the interaction of Lamb waves with damaged area. The finite element mesh is used to describe the region around the defects. On the contrary to other hybrid models already developed, the interaction between Lamb waves and defects is computed in the temporal domain. Then, the modal decomposition method permits to determine the wave reflected and transmitted by the damaged area. Modal analysis allows also identifying the mode conversions induced by the defects. These numerical results agree with previous finite element results concerning the interaction of Lamb modes with a notch. Experiments, carried out with gauged defects on an aluminum plate, are also compared to numerical predictions to validate the simulation. Compared to classical techniques of simulation, this new method allows us to investigate the interaction of Lamb modes generated at high frequency-thickness product with micro-defects as corrosion pitting.     

基于空耦超声Lamb波的金属板状结构内部缺陷检测方法

针对接触式超声检测方法在金属板结构内部缺陷实际工程检测中存在的环境要求高、效率低、操作难度高等问题,提出了空耦超声Lamb波检测方法,该方法能更好地适应现场应用环境,提高检测效率,减少传感器数量。通过有限元仿真和实验分析比较了空耦超声检测与接触式超声检测两种方法接收到的信号和成像效果。结果表明:有限元仿真和实验中,空耦超声检测方法对缺陷位置的定位误差分别为2 mm和3.6 mm,接触式检测方法对缺陷位置的定位误差分别为2 mm和11.3 mm,空耦检测具有较高的定位精度;单侧激励条件下,适合采用A0模态Lamb波对板内缺陷进行检测;空耦超声检测可以通过调整信号接收角度接收单一模态Lamb波,避免伪像产生。该方法为后续金属板状结构内部缺陷的空耦超声检测提供参考。     

Semi-analytical solution for three-dimensional transient response of functionally graded annular plate on a two parameter viscoelastic foundation

The three-dimensional transient analysis of functionally graded annular plates with arbitrary boundary conditions is carried out in this paper. The material properties of the FGM plate are assumed to vary smoothly in an exponential law along the thickness direction. The plate is assumed to rest on a two parameter viscoelastic foundation. A semi-analytical method, which integrates the state space method (SSM), Laplace transform and its inversion, as well as the one-dimensional differential quadrature method (DQM), is proposed to obtain the transient response of the plate. The state space method is used to obtain the analytical solution in the thickness direction. The differential quadrature method is employed to approximate the solution in the radial direction. The Laplace transform and the numerical inversion are used to obtain the solution in time domain. Numerical results show a good agreement between the response histories obtained by the present method and finite element method. The effects of the boundary conditions at the edges, the material graded index, the Winkler and shearing layer elastic coefficients, and the damping coefficient are studied. Numerical examples show that the peak response decreases as the material graded index, the Winkler and shearing layer elastic coefficients, and the damping coefficient increase. The results obtained in this paper can serve as benchmark data in further research.     

Prediction and measurement of nonpropagating Lamb modes at the free end of a plate when the fundamental antisymmetric mode A0 is incident

Reflection of Lamb waves when the fundamental mode A0 is incident at the free end of a plate is studied, in order to identify the extent to which the generation of nonpropagating modes influences the field local to the end of the plate. Semi-analytical predictions, finite element simulations, and experimental measurements are presented for frequencies below the A2 cutoff. First it is shown, for frequencies below the A1 cutoff, that reflection of the A0 mode is accompanied by a delay in phase, and that there is significant additional motion due to nonpropagating modes within about five plate thicknesses of the end. The extend of this additional motion in the vicinity of the end of the plate is demonstrated by subtracting the contribution of the propagating modes from the displacement field. The wave field at frequencies above the A1 cutoff is more complex because the A1 as well as the A0 propagating modes are present at the end of the plate. Nevertheless, it has still been possible, using semi-analytical predictions and finite element simulations, to demonstrate the additional motion due to the nonpropagating modes.     

Piezoelectric transducer parameter selection for exciting a single mode from multiple modes of Lamb waves

Excitation and propagation of Lamb waves by using rectangular and circular piezoelectric transducers surface-bonded to an isotropic plate are investigated in this work. Analytical stain wave solutions are derived for the two transducer shapes, giving the responses of these transducers in Lamb wave fields. The analytical study is supported by a numerical simulation using the finite element method. Symmetric and antisymmetric components in the wave propagation responses are inspected in detail with respect to test parameters such as the transducer geometry, the length and the excitation frequency. By placing only one piezoelectric transducer on the top or the bottom surface of the plate and weakening the strength of one mode while enhancing the strength of the other modes to find the centre frequency, with which the peak wave amplitude ratio between the S0 and A0 modes is maximum, a single mode excitation from the multiple modes of the Lamb waves can be achieved approximately. Experimental data are presented to show the validity of the analyses. The results are used to optimize the Lamb wave detection system.     

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。     

Lamb wave topological imaging for blind hole defects in isotropic plates

The research aims at validating the ability of topological imaging to blind holes in isotropic plates using Lamb waves. Due to the defect is not symmetric around the midplane of the plate, the effect of Lamb mode conversion will have to be taken into account.The imaging method is based on two computations of ultrasonic fields, one forward and one adjoint, performed for the defect-free reference medium. The excited signal and scattered Lamb waves caused by the blind hole, are used as emitting sources to compute the forward problem and the adjoint problem, respectively. With the help of the finite element simulations,the natural refocusing process of the multimode Lamb waves at the defect location is visually demonstrated by the transient acoustic field snapshots at the different moments to strengthen the physical mechanism of the topological imaging method. The numerical results demonstrate that topological imaging has relatively stronger applicability to the blind hole in contrast to classical Delay And Sum(DAS) method and Time Reversal(TR) method. The topological imaging could handle complex Lamb wave signals containing mode conversions without the imaging quality being affected. The proposed imaging method presents a certain developing potential for detecting and imaging asymmetric defects in plate-like configurations using Lamb waves.     

Multiple reflections of Lamb waves at a delamination

Wave propagation in laminated plates with delaminations was calculated using the semi-analytical finite element method. The visualization results and deeper numerical analyses revealed the following phenomena on the fundamental Lamb modes at delamination regions of laminated plates. First, Lamb wave propagates toward the delamination, and then splits into two independent waves at the "Entrance" of the delamination with no significant reflections. These two waves reach the "Exit" of the delamination with the different phases and arrival time. Thus reflected and transmitted waves are excited at the Exit. The repetition of such reflections at the Exit causes the multiple reflections at regular intervals corresponding to the delamination size.     

板状结构Lamb波频散补偿与聚焦接收成像检测

对板状结构中Lamb波的频散和多模现象进行了理论分析,采用有限元仿真方法获取了Lamb波与缺陷作用后的回波信号,对信号进行聚焦接收处理,即在一定距离范围内利用导波频散特性对各个模式信号进行频散补偿,提取补偿后信号的幅值,结果表明当所得信号幅值最大时,所对应的补偿距离等于缺陷与换能器之间的实际距离.利用这一结论,提出了以...     

Investigation of a silicon-based one-dimensional phononic crystal plate via the super-cell plane wave expansion method

The super-cell plane wave expansion method is employed to calculate band structures for the design of a silicon-based one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.     

The band gaps of Lamb waves in a ribbed plate: A semi-analytical calculation approach

In this paper a semi-analytical method is proposed to investigate the transmission band gaps of Lamb waves through repetitive structures in a waveguide. For a unit cell the scattering matrix is obtained by the Lamb mode matching technique at each artificially sliced interface and then substituted into the Bloch theorem to solve the eigenproblem incurred by cell repetition. The method is implemented on a ribbed plate. The band gaps in the dispersion curves are confirmed by the dips of Lamb wave transmission coefficients, and attributed to the coupled vibrations of Lamb modes in different sliced sections of the unit cell.     

基于波传播法的周期复合板振动带隙衰减特性研究

运用波传播法对有限和无限周期对边简支复合板的振动带隙衰减特性进行了研究.在建立相邻板结构边界连续方程的基础上, 分别运用传递矩阵和Bloch定理建立了有限和无限周期复合板的耦合运动方程, 并详细对比分析了有限和无限周期复合板带隙衰减特性的关联关系.研究表明: 周期板结构的振动带隙频率范围与激励方式和激励位置是相关的, 若周期复合板在宽度方向按某阶模态进行线激励, 则该激励下的振动带隙与无限周期复合板在该阶模态下的振动带隙是一致的; 若周期板在点激励作用, 则该点激励下的振动带隙是参与振动的各阶模态振动带隙的交集. 此外, 还进一步研究了结构阻尼对振动衰减带隙的影响. 关键词： 周期复合板 带隙衰减特性 波传播法 结构阻尼     

Analysis of Second-Harmonic Generation of Low-Frequency Dilatational Lamb Waves in a Two-Layered Composite Plate

We analyze the effect of second-harmonic generation(SHG) of primary Lamb wave propagation in a two-layered composite plate, and then investigate the influence of interfacial properties on the said effect at low frequency. It is found that changes in the interfacial properties essentially affect the dispersion relation and then the maximum cumulative distance of the double-frequency Lamb wave generated. This will remarkably influence the efficiency of SHG. To overcome the complications arising from the inherent dispersion and multimode natures in analyzing the SHG effect of Lamb waves, the present work focuses on the analysis of the SHG effect of low-frequency dilatational Lamb wave propagation. Both the numerical analysis and finite element simulation indicate that the SHG effect of low-frequency dilatational Lamb wave propagation is found to be much more sensitive to changes in the interfacial properties than primary Lamb waves. The potential of using the SHG effect of low-frequency dilatational Lamb waves to characterize a minor change in the interfacial properties is analyzed.     

Laser-ultrasonic generation of Lamb waves in the reaction force range

The Laser-ultrasonic generation of Lamb waves in an elastic plate is investigated theoretically and experimentally for a laser source whose intensity is high enough to create reaction forces (normal tractions) on the illuminated surface of the specimen. The analytical solutions for transient waves are derived using the integral transform method first by considering an arbitrary source shape and time excitation function, and then specifically for circular and line source shapes. The simulation study allows us not only to predict the behavior of individual wave modes but also to construct the overall responses; thus it helps us better understand the wave excitation mechanisms. The dispersive and multi-modal nature of laser-generated Lamb waves is presented by showing the spatiotemporal Fourier transform of displacements obtained by the simulation study. The transform, displayed in the frequency-wave number domain, enunciates the characteristics of the propagating individual Lamb wave modes. The simulation results are then compared with the 2-D Fourier transform of a set of experimental data obtained by scanning an aluminum plate specimen.     

Active fiber composites for the generation of Lamb waves

Active fiber composites (AFC) are thin and conformable transducer elements with orthotropic material properties, since they are made of one layer of piezoelectric ceramic fibers. They are suitable for applications in structural health monitoring systems (SHM) with acoustic non-destructive testing methods (NDT). In the presented work the transfer behavior of an AFC as an emitter of transient elastic waves in plate-like structures is investigated. The wave field emitted by an AFC surface bonded on an isotropic plate was simulated with the finite-difference method. The model includes the piezoelectric element and the plate and allows the simulation of the elastic wave propagation. For comparison with the model experiments using a laser interferometer for non-contact measurements of particle velocities at different points around the AFC on the surface of the plate were performed. Transfer functions defined as the ratio of the electric voltage excitation signal and the resulting surface velocity at a specific point are separately determined for the two fundamental Lamb wave modes. In order to take the orthotropic behavior of the AFC into account the transfer functions are determined for several points around the AFC. Results show that the AFC is capable to excite the fundamental symmetric and antisymmetric Lamb wave mode. The antisymmetric mode is mainly radiated in the direction of the piezoelectric fibers, while the symmetric mode is spread over a larger angle. The amplitudes of the emitted waves depend on the frequency of the excitation as well as on the geometric dimensions of the transducer.     

复合兰姆波声子晶体中超宽部分禁带

兰姆波在声子晶体薄板中的传播特性因其在无损检测、 减振技术和传感器件等领域的潜在应用价值而受到越来越多的关注. 本文采用超原胞平面波展开法和有限元法系统地研究了复合对称结构声子晶体薄板中的兰姆波超宽部分禁带. 结果表明: 对于在薄板侧面对称地嵌入双层矩形空气柱构成的复杂系统, 低阶兰姆波部分带隙结构极为丰富. 将晶格常数(L)和板厚(H) 比值具有匹配关系的兰姆波声子晶体衔接构成复合结构, 低阶兰姆波部分禁带宽度因各组分结构的部分禁带交叠而得到显著拓宽, 可在低频超宽频带内实现对特定低阶兰姆波模式良好的模式选择功能. 该研究结果对兰姆波缺陷无损检测中模式优化选择及兰姆波单向导通器件设计等方面具有重要意义.     

Microcrack localization using a collinear Lamb wave frequency-mixing technique in a thin plate

A novel Lamb wave frequency-mixing technique is proposed for locating microcracks in a thin plate,which does not require the resonance condition of Lamb wave mixing and can accurately locate the microcracks through only one-time sensing.Based on the bilinear stress-strain constitutive model,a two-dimensional finite element(FE)model is built to investigate the frequency-mixing response induced by the interaction between two primary Lamb waves and a microcrack.When two primary Lamb waves of A0 and S0 modes with different frequencies excited on the same side of the plate simultaneously impinge on the examined microcrack,under the modulation of the contact acoustic nonlinearity,the microcrack itself can be deemed as the secondary sound source and it will radiate the Lamb waves of new combined frequencies.Based on the time of flight of the generated A0 mode at difference frequency,an indicator named normalized amplitude index(NAI)is defined to directly locate the multi-microcracks in the given plate.It is found that the number and location of the microcracks can be intuitively visualized by using the NAI based frequency-mixing technique.It is also demonstrated that the proposed frequency mixing technique is a promising approach for the microcrack localization.     

基于时间反转理论的聚焦Lamb波结构损伤成像

从理论和实验上研究了时间反转法在频散和多模式的Lamb波结构健康检测方面的应用.当Lamb波在包含有损伤的板类结构中传播时,损伤的存在表现为一个被动波源.采用分布式传感器网络,基于传递函数的观点,通过推导由损伤这个被动波源产生的时间反转波场幅值的表达式,证实了当观察点位于损伤位置时,时间反转波场的幅值最大.为验证时间反转方法的聚焦效应,提出了一种适合于分布的激励/接收传感器网络的成像方法,该方法可以对损伤定位并近似确定损伤尺寸.结合有限元的实验结果显示了Lamb波检测信号的能量可在损伤处聚焦,表明时间反转     

A time reversal damage imaging method for structure health monitoring using Lamb waves

This paper investigates the Lamb wave imaging method combining time reversal for health monitoring of a metal-lic plate structure.The temporal focusing effect of the time reversal Lamb waves is investigated theoretically.It demonstrates that the focusing effect is related to the frequency dependency of the time reversal operation.Numerical simulations are conducted to study the time reversal behaviour of Lamb wave modes under broadband and narrowband excitations.The results show that the reconstructed time reversed wave exhibits close similarity to the reversed nar-rowband tone burst signal validating the theoretical model.To enhance the similarity,the cycle number of the excited signal should be increased.Experiments combining finite element model are then conducted to study the imaging method in the presence of damage like hole in the plate structure.In this work,the time reversal technique is used for the recompression of Lamb wave signals.Damage imaging results with time reversal using broadband and narrowband excitations are compared to those without time reversal.It suggests that the narrowband excitation combined time reversal can locate and determine the size of structural damage more precisely,but the cycle number of the excited signal should be chosen reasonably.