Location of micro-cracks in plates using time reversed nonlinear Lamb waves

A promising tool to detect micro-cracks in plate-like structures is used for generating higher harmonic Lamb waves. In this paper, a method combining nonlinear S_0 mode Lamb waves with time reversal to locate micro-cracks is presented and verified by numerical simulations. Two different models, the contact acoustic nonlinearity(CAN) model and the Preisach–Mayergoyz(PM) model, are used to simulate a localized damage in a thin plate. Pulse inversion method is employed to extract the second and fourth harmonics from the received signal. Time reversal is performed to compensate the dispersion of S_0 mode Lamb waves. Consequently, the higher harmonics generated from the damaged area can be refocused on their source. By investigating the spatial distribution of harmonic wave packets, the location of micro-cracks will be revealed.The numerical simulations indicate that this method gives accurate locations of the damaged area in a plate. Furthermore,the PM model is proved to be a suitable model to simulate the micro-cracks in plates for generation of higher harmonics.     

Lamb waves in anisotropic plates (review)

Propagation of Lamb waves in elastic anisotropic plates is studied in the framework of the six-dimensional Cauchy formalism. Closed-form secular equations for dispersion curves for Lamb waves propagating in a plate with arbitrary elastic anisotropy are obtained.     

Nonlinear guided waves in plates: A numerical perspective

Harmonic generation from non-cumulative fundamental symmetric (_S0$S_0$) and antisymmetric (_A0$A_0$) modes in plate is studied from a numerical standpoint. The contribution to harmonic generation from material nonlinearity is shown to be larger than that from geometric nonlinearity. Also, increasing the magnitude of the higher order elastic constants increases the amplitude of second harmonics. Second harmonic generation from non-phase-matched modes illustrates that group velocity matching is not a necessary condition for harmonic generation. Additionally, harmonic generation from primary mode is continuous and once generated, higher harmonics propagate independently. Lastly, the phenomenon of mode-interaction to generate sum and difference frequencies is demonstrated.     

Three-dimensional hybrid model for predicting air-coupled generation of guided waves in composite material plates

For contact-less, non-destructive testing (NDT) purposes using air-coupled ultrasonic transducers, it is often required to numerically simulate the propagation of ultrasonic waves in solid media, and their coupling through air with specific transducers. At that point, one could simulate the propagation in the air and then in the solid component, using a Finite Element (FE) model. However, when three-dimensional (3D) modeling becomes necessary, such a solution reveals to be extremely demanding in terms of number of degrees of freedom and computational time. In this paper, to avoid such difficulties, the propagation in air from an ultrasonic transmitter to a tested solid plate is modeled in 3D using a closed-form solution. The knowledge of the transducer characteristics (diameter, frequency bandwidth, efficiency in Pa/V) allows the spatial distribution and actual pressure (in Pa) of the acoustic field produced in the air to be predicted, for a given input voltage. This pressure field is applied in turn as a boundary condition in a 3D FE model, to predict the plate response (displacement and stress guided beams) for a given distance between the transmitter and the plate, and for a given angle of orientation of the transmitter with respect to the plate. The FE model is so restricted to modeling of the solid structure only, thus reducing very significantly the number of degrees of freedom and computational time. The material constituting the plate is considered to be an anisotropic and viscoelastic medium. To validate the whole modeling process, an air-coupled ultrasonic transducer is used and oriented at a specific angle chosen for generating one specific Lamb mode guided along a composite plate sample, and a laser probe measures the normal velocity at different locations on the surface of the plate. In the field of NDT, it is generally suitable to excite a pure Lamb mode in order to ease the interpretation of received signals that would represent waves scattered by defects. After a validation step, the numerical model is then used to investigate the effect of the material anisotropy on the purity of the incident guided mode.     

Frequency dependent directivity of guided waves excited by circular transducers in anisotropic composite plates

Lamb wave propagation in fiber-reinforced composite plates is featured by a pronounced directivity of wave energy transfer along the fibers from a point surface source. In the case of non-point (sized) source, the main lobe of radiation diagram may turn with frequency up to the orthogonal to the fibers direction. This effect has been theoretically studied and physically explained in the context of semi-analytical integral-equation based mathematical model. The present paper gives its experimental verification.     

Laser-generated thermoelastic acoustic sources and Lamb waves in anisotropic plates

The effect of anisotropy and temperature on the dispersive Lamb wave generation and propagation in a transversely isotropic thin plate has been investigated. A quantitative numerical model for the laser-generated transient ultrasonic Lamb waves propagating along arbitrary directions is presented by using a finite-element method. All factors, such as spatial and time distributions of the incident laser beam, optical penetration, thermal diffusivity, thickness of the plate, and source–receiver distance, can be taken into account. The effects on the ultrasound waveform of the size of the optoacoustic source are investigated; in the limit of strong optical absorption, a subsurface thermal source gives rise to both vertical and lateral shear tensions. The lateral shear tension is equivalent to applying a shear dipole at the top face; the amplitude of the dipole is a function of material symmetry, contrary to the isotropic case, and the character and strength of the equivalent surface stress are a function of propagation direction. The specific results for the lower anti-symmetric and symmetric mode propagation in all planar directions are presented in the thermoelastic regime; the spatial dispersion (variation of the velocity with the direction of propagation) as well as the frequency dispersion is analyzed. PACS 43.35.+d; 02.70.Dh; 42.62.-b; 78.20.Nv; 81.70.Cv     

Prolonged acousto-optic interaction with Lamb waves in crystalline plates

The propagation and acousto-optic interaction of Lamb modes in an anisotropic plate of tellurium dioxide (TeO2) are studied numerically and analytically. In the case of a Y-cut X-propagating TeO2 plate, the very high elastic anisotropy of the crystal greatly modifies the dispersion curves, giving rise to their multiple oscillations. The existence ranges of backward Lamb modes increase with the mode order contrary to the case of isotropic plates. The quasi-collinear light scattering by Lamb waves is considered. Owing to the structure of Lamb wave field, a simultaneous light diffraction at two different optical frequencies can take place while Lamb waves are excited only at the single frequency. It is demonstrated with the Z-cut (110)-propagating plate that a small change in the acoustic frequency can result in a significant shift in the frequency of the scattered light.     

Focusing and waveguiding of Lamb waves in micro-fabricated piezoelectric phononic plates

This paper presents results on the numerical and experimental studies of focusing and waveguiding of the lowest anti-symmetric Lamb wave in micro-fabricated piezoelectric phononic plates. The phononic structure was based on an AT-cut quartz plate and consisted of a gradient-index phononic crystal (GRIN PC) lens and a linear phononic plate waveguide. The band structures of the square-latticed AT-cut quartz phononic crystal plates with different filling ratios were analyzed using the finite element method. The design of a GRIN PC plate lens which is attached with a linear phononic plate waveguide is proposed. In designing the waveguide, propagation modes in square-latticed PC plates with different waveguide widths were studied and the results were served for the experimental design. In the micro-fabrication, deep reactive ion etching (Deep-RIE) process with a laboratory-made etcher was utilized to fabricate both the GRIN PC plate lens and the linear phononic waveguide on an 80 μm thick AT-cut quartz plate. Interdigital transducers were fabricated directly on the quartz plate to generate the lowest anti-symmetric Lamb waves. A vibro-meter was used to detect the wave fields and the measured results on the focusing and waveguiding of the piezoelectric GRIN PC lens and waveguide are in good accordance with the numerical predictions. The results of this study may serve as a basis for developing an active micro plate lens and related devices.     

Thickness measurement in composite materials using Lamb waves

Pulse propagation in plate elements is investigated with the identification of Lamb modes in the range 40–150 kHz. The possibilities of the application of this technique in the measurement of thickness in composites and coarse materials are evaluated, particularly in ferrocement materials.     

Calculation of electromechanical coupling coefficient of Lamb waves in multilayered plates

Two methods have been always used to calculate the electromechanical coupling coefficient of a Lamb wave in a multilayered plate: one is an approximate method using the acoustic velocity difference under different electric boundary conditions and the other is the Green's function method. The Green's function method is more accurate but more complicated, because an 8N-order matrix is used for calculating the electromechanical coupling coefficient of the Lamb wave in an N-layered plate, which induces great computation loads and some calculation deviations. In this paper, a transfer matrix method is used for calculating the electromechanical coupling coefficient of Lamb waves in a multilayered plate, in which only an 8-order matrix is needed regardless of the number of layers of the plate. The results show that the transfer matrix method can obtain the same accuracy as those by the Green's function method, but the computation load and deviation are greatly decreased by avoiding the use of a high order matrix used in the Green's function method.     

分层固体板中导波的激发与频散特性

针对无限大弹性分层固体板,研究了结构中导波的频散和激发特性。首先使用传递矩阵法推导分层板模型中导波的频散方程,然后用二分法求取导波各模式的频散曲线,进而分析结构中导波的频散特性。结果表明:在速度递增或递减的分层板中,基阶模式和高阶模式的高频极限分别等于低速层的瑞利波速和横波波速。对于含低速夹层的分层板,所有模式的高频极限都等于低速层的横波速度。在导波激发特性方面,研究了在具有一定宽度的法向力源作用下的分层板中导波各模式在结构中的法向位移谱。发现在速度递增的分层板结构中基阶模式是主导模式,而对于速度递减和含低速夹层模型,主导模式在不同的频段范围内对应不同的导波模式。     

Research on the propagation of guided waves in multi-layered plates

The dispersion characteristics and excitation mechanisms of the guided waves in multilayered plates are studied in this paper. Firstly, the dispersion equation is obtained by the propagator matrix method. Then, the bisection technique is employed to find all the roots of the dispersion equation. The dispersion characteristics of the guided waves are investigated and analyzed. For the multilayered plates in which the S-wave velocity increases or decreases from top to bottom, it is found that the velocity limits in high frequency of the first and high modes are equal to the Rayleigh wave and S-wave velocities of the low-velocity layer, respectively. It is also found that the velocity limits in the high frequency of all modes are equal to the S-wave velocity of the low-velocity layer for the plate with a low-velocity middle layer. The normal displacement spectrum of all the modes excited by the normal force source with a definite width on the surface of the plate is also investigated. It is proved that the dominant mode is the first mode when the S-wave velocity increases from top to bottom layer and the dominant mode is different in different frequency range for the plate with a low-velocity middle layer.     

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.     

Multi-splitting of Lamb waves band gap in one-dimensional quasi-periodic plates of cantor series

We study numerically the propagation of Lamb waves in one-dimensional (1D) quasi-periodic composite thin plates consisting of a row of air holes embedded in the matrix material silicon according to a Cantor sequence; the surfaces of the plate are parallel to the axis of quasi-periodicity. The phenomenon of multi-splitting in the band gap structures is demonstrated. A semi-quantitative explanation is proposed in which the inherent cavity-like structure is proven to play the essential role in the phenomenon of multi-splitting, which gives a reliable way to predict where and how the band gap is splitting in the quasi-periodic systems. Possible applications are discussed.     

Combined spectral estimator for phase velocities of multimode Lamb waves in multilayer plates

A novel combined spectral estimate (CSE) method for differentiation and estimation the phase velocities of multimode Lamb waves whose wave numbers are much close or overlap one another in multiplayer plates is presented in this paper, which based on auto-regressive (AR) model and 2-D FFT. Simulated signals in brass plate were processed by 2-D FFT and CSE. And experiments are performed by using two conventional angle probes as emitter and receiver on the same surface of three-layered aluminum/xpoxy/aluminum plates, which include symmetrical and unsymmetrical plates. The multimode Lamb waves are excited in these laminates, and the received signal is processed by 2-D FFT and CSE, respectively. The results showed that the phase velocities of multimode signals whose wave numbers are much closed cannot be differentiated by 2-D FFT, but CSE has strong spatial resolution. Compared the measured phase velocities with the theoretical values, the error is smaller than 2% on the whole. It promises to be a useful method in experimental signals processing of multimode Lamb waves.     

Normal mode expansion method for laser-generated ultrasonic Lamb waves in orthotropic thin plates

A quantitative theory for modeling the laser-generated transient ultrasonic Lamb waves, which propagates along arbitrary directions in orthotropic plates, is presented by employing an expansion method of generalized Lamb wave modes. The displacement field is expressed by a summation of the symmetric and antisymmetric modes in the surface stress-free orthotropic plate, and therefore the theory is particularly appropriate for waveform analyses of Lamb waves in thin plates because one needs only to evaluate several lower modes. The transient waveforms excited by the thermoelastic expansion and the oil-coating evaporation are analyzed for a transversely isotropic thin plate. The results show that the theory provides a quantitative analysis to characterize anisotropic elastic stiffness properties of orthotropic plates by laser-generated Lamb wave detection.     

Lamb and torsional waves and their use in flaw detection in tubes

Five separate issues concerning Lamb wave propagation are discussed: (1) the actual motion of the particles in sheet material; (2) the mechanism of the initiation of Lamb waves in plates; (3) the effect of pulse propagation as opposed to continuous waves; (4) wave propagation on the inner and outer surfaces of tubes; and (5) the propagation of waves in tubes at large angles of incidence, beyond the Lamb wave regime.     

超声Lamb波二次谐波发生效率分析与模式选择

在导波模式展开分析方法的基础上,提出激发效率参量来定量表征超声Lamb波积累二次谐波的发生效率。以P92钢板为例,理论计算得到了与频散曲线对应的理论激发效率参量分布图谱,从图谱中选择理论激发效率参量大小不同的两种基频Lamb波模式:纵波型S1模式和交点型A2/S2模式,分别测量这两种基频Lamb波模式在钢板中传播时产生的二次谐波信号。理论计算和实验测量结果表明,这两种基频Lamb波模式的理论和实验激发效率参量的比值基本一致,且激发效率参量较大的纵波型S1模式能激发出效率更高的二次谐波信号。研究结果表明激发效率参量可以有效的用于Lamb波二次谐波发生效率的表征及模式选择。     

3D analysis of interaction of Lamb waves with defects in loaded steel plates

The objective of the research presented here is the investigation of the interaction of guided waves with welds, defects and other non-uniformities in steel plates loaded by liquid. The investigation has been performed using numerical simulation for 2D and 3D cases by the finite differences method, finite element method and measurement of 3D distributions of acoustic fields. Propagation of the S(0) mode in a steel plate and its interaction with non-uniformities was investigated. It was shown that using the measured leaky wave signals in the water loading of the steel plate and by application of signal processing, the 3D ultrasonic field structure inside and outside of the plate can be reconstructed. The presence of leaky wave signals over the defect caused by the mode conversion of Lamb waves has been proved using the numerical modelling and experimental investigations. The developed signal and data processing enables to visualise dynamics of ultrasonic fields over the plate, and also to estimate spatial positions of defects inside the steel plates.