Determination of lamb wave dispersion data in lossy anisotropic plates using time domain finite element analysis. Part II: application to 2-2 and 1-3 piezoelectric composite transducer arrays

The use of finite element modeling, combined with optical generation and detection of Lamb waves in plate structures, was extended to encompass periodic ceramic-polymer materials typical of those encountered in 1-3 and 2-2 piezoelectric composite array transducers. The resultant dispersion data was employed to predict the occurrence of Lamb wave-induced cross talk in composite monolithic arrays. The finite element modeling method was then used to simulate the dispersion behavior of two array structures that were subsequently manufactured: a 1-D 45% volume fraction linear array coupon and a 2-D 35% volume fraction array coupon. Excellent agreement between theory and experiment was obtained using impedance measurements and laser scans of the surface displacement profile at selected frequencies. Regions of strong inter-element cross-coupling were identified and these are shown to correlate very well with the dispersion data obtained for the dual-phase plate material. This work is considered to provide a useful basis for the design of wideband monolithic composite arrays and minimization of guided wave propagation along the array substrate.     

基于谱元法的复合材料裂纹梁Lamb波传播特性研究

基于谱元法提出了一种弹簧元来模拟复合材料梁由于横向裂纹导致的轴弯耦合效应,分析复合材料裂纹梁中Lamb波的传播特性。由断裂力学的相关知识求得弹簧元的刚度,建立复合材料裂纹梁的损伤谱元模型。通过模拟复合材料裂纹梁内Lamb波传播,并和传统的有限元结果进行比较,验证了所提出模型的可行性和有效性。推导了频域内Lamb波各模态的能量计算公式,裂纹处的能量守恒证明了所提出模型的正确性,同时计算表明复合材料梁中裂纹处反射与透射的Lamb波各模态能量随着裂纹深度的变化规律具有单调性,结论可以为定量识别复合材料梁裂纹提供实用依据。     

Assessment of debonding in sandwich CF/EP composite beams using A0 Lamb wave at low frequency

The aim of this study is to quantitatively assess debonding in sandwich CF/EP composite structures with a honeycomb core using acoustic waves activated and captured by surface-mounted PZT elements. For experimental investigation, debonding was introduced at different locations in sandwich CF/EP composite beams. The fundamental anti-symmetric A₀ Lamb mode was excited at a low frequency. The transmitted and reflected wave signals in both surface panels were captured by PZT elements after interacting with the debonding damage and specimen boundaries. Aided by finite element analysis (FEA), the differences in wave propagation characteristics in sandwich composite beams and composite laminate (e.g. skin panel only) were investigated. The debonding location was assessed using the time-of-flight (ToF) of damage-reflected waves, and the severity of debonding was evaluated using both the magnitude of the reflected wave signal and the delay in the ToF of Lamb wave signals. Good correlation between the experimental and FEA simulation results was observed. The results demonstrate the effectiveness of Lamb waves activated and captured by surface-mounted PZT elements on either surface of sandwich composite structures in assessing debonding.     

Numerical simulation of the guided Lamb wave propagation in particle reinforced composites

This paper deals with the investigation of the Lamb wave propagation in particle reinforced composites excited by piezoelectric patch actuators. A three-dimensional finite element method (FEM) modeling approach is set up to perform parameter studies in order to better understand how the Lamb wave propagation in particle reinforced composite plates is affected by change of central frequency of excitation signal, volume fraction of particles, size of particles and stiffness to density ratio of particles. Furthermore, the influence of different arrangements is investigated. Finally, the results of simplified models using material data obtained from numerical homogenization are compared to the results of models with heterogeneous build-up. The results show that the Lamb wave propagation properties are mainly affected by the volume fraction and ratio of stiffness to density of particles, whereas the particle size does not affect the Lamb wave propagation in the considered range. As the contribution of the stiffer material increases, the group velocity and the wave length also increase while the energy transmission reduces. Simplified models based on homogenization technique enabled a tremendous drop in computational costs and show reasonable agreement in terms of group velocity and wave length.     

Lamb波在复合材料板中传播的谱有限元建模和仿真

基于谱有限元对Lamb波在复合材料层合板中的传播进行了模拟。结合Gabor小波分析对谱有限元及传统有限元模拟结果与理论结果进行了对比, 并对相控阵法结构探伤的扫描过程进行了模拟和分析, 给出了Lamb波的传播和扫描图像。结果表明, 在得到更精确模拟结果的同时, 谱有限元较传统有限元法能大大缩短计算时间, 证实了该方法在模拟Lamb波在复合材料板中的传播方面的优越性。同时, 谱有限元法能很好地模拟相控阵法探伤的扫描过程, 模拟结果与实际结果吻合, 证实了本文建模方法的可行性和精确性。      

Influence of damaged area on lamb wave propagation in composite plate

The influence of a specified damage on transient propagation of Lamb wave in a composite laminated plate is studied by finite element analysis. The finite element formulation is developed for the laminated plate with embedded or surface-bonded piezoelectric layers. A higher order laminate model is used to describe the displacement field of both composite laminate and piezoelectric layer. The damaged area is modeled by a localized loss of stiffness and quantified by a degradation coefficient . Piezoelectric materials act as both actuators and sensors for generating and receiving Lamb waves. Numerical results show that the waveform, wave peaks and the arrival time of the transmitted Lamb wave are distinctly correlated with quantified degradation coefficient of the damaged area, which are helpful to damage detection for a composite laminated plate in a new way.Tel (Res).: 86-29-88242204, Tel (Off).: 86-29-88213623-8026     

Generation and reception of ultrasonic guided waves in composite plates using conformable piezoelectric transmitters and optical-fiber detectors

A condition monitoring nondestructive evaluation (NDE) system, combining the generation of ultrasonic Lamb waves in thin composite plates and their subsequent detection using an embedded optical fiber system is described. The acoustic source is of low profile with respect to the composite plate thickness, surface conformable, and able to efficiently launch a known Lamb wave mode, at operating frequencies between 100 and 500 kHz, over typical propagation distances of 100 to 500 mm. It incorporates both piezocomposite technology and interdigital design techniques to generate the fundamental symmetrical Lamb wave mode in both metallic and carbon-fiber composite plates. Linear systems and finite element modeling techniques have been used to evaluate the operation of the transducer structure, and this is supplemented by experimental verification of the simulated data. An optical fiber, either bonded to the surface or embedded across the length of the composite plate samples, is used to detect the propagating ultrasonic Lamb waves. Single mode silica fiber has been used in conjunction with a portable 633 nm Mach-Zehnder interferometer for signal demodulation and subsequent data acquisition. This hybrid system is shown to generate and detect the fundamental symmetrical Lamb wave (s(0)) in both carbon-fiber and glass-fiber reinforced composite plates. Importantly, the system signal-to-noise ratio (SNR) associated with the acoustic source compares favorably with s(0) Lamb wave generation using a conventional transducer and angled perspex wedge arrangement.     

识别薄板中兰姆波和体波的阶梯板方法

斜探头在某些频率下激励出的兰姆波,其群速度与体波的传播速度相近,所以通过判断传播速度不易区分出兰姆波和体波。通过数值模拟和实验,分别研究了激励频率为2 MHz的纵波和S0模态兰姆波在阶梯板上的反射特性,发现:在阶梯板上入射S0模态兰姆波时,有反射回波;而入射纵波时,无反射回波。基于这种反射特性的差别,提出了一种利用阶梯板区别薄板中兰姆波和体波的方法,该方法可用于确认探头的激励特性。     

Laser-Generated Lamb Waves Propagation in Multilayered Plates Composed of Viscoelastic Fiber-reinforced Composite Materials

The propagation characteristics of laser-generated Lamb waves in multilayered fiber-reinforced composite plates with different fiber orientations and number of layers have been investigated quantitatively. Considering the viscoelasticity of the composite materials, we have set up finite element models for simulating the laser-generated Lamb waves in two types of the multilayered composite plates. In the first type, different fiber orientations are adopted. In the second one, different number of layers are considered. The results illustrate the occurrence of attenuation and dispersion, which is induced by the viscoelasticity and multilayer structure, respectively.     

基于Lamb波的薄壁槽状结构损伤检测研究

研究复杂工程结构的结构健康监测技术具有现实意义。使用基于Lamb波的仿真和实验方法,对“U”形截面的铝合金构件中的损伤检测问题进行了研究。建立了构件的三维有限元模型并实现了Lamb波传播过程的动态仿真;实验中使用锆钛酸铅压电晶片（PZT wafer）来激发和接收在构件中传播的Lamb波。借助于连续小波变换（CWT）和希尔伯特变换（HT）等方法对仿真和实验中采集到的Lamb波信号进行处理,从中提取了与损伤有关的时域特征,建立了损伤位置和损伤反射波包飞行时间（ToF）之间的定量关系。     

Analysis of Laminated and Sandwich Composite Structures Using Solid-like Shell Elements

A new solid-like shell element was formulated which is suitable for analysis of laminated and sandwich composite structures. Then, a multiscale analysis technique was implemented to the shell element formulation so that micro-level stresses and strains (i.e. stresses and strains in reinforcing fibers and the binding matrix) in those structures can be computed. The shell element has three displacement degrees of freedom per node like a 3-D solid element. Therefore, the shell elements can be stacked easily on top of one another like 3-D solid elements in order to represent multiple layers through the thickness of laminated and sandwich structures. The effect of a thin resin or adhesive layer in laminated and sandwich composite structures was investigated on both static and the dynamic responses of the structures using the developed shell elements. The study showed an apparent effect of the resin/adhesive layer even though it is very thin. As a result, the present shell element can be used effectively to include those thin layers in finite element analysis models of laminated and sandwich composite structures.     

Ultrasonic Lamb wave‐based debonding monitoring of advanced honeycomb sandwich composite structures

Honeycomb sandwich composites are extensively used in military shelters, aerospace structures, ground transportation structures, auto‐racing bodies, ship panels, and other special purpose structures requiring lightweight construction materials. But debondings at the face‐sheet‐to‐core junctions frequently occur due to the variable operating and loading conditions, which may menace the safety and overall integrity of the structural assembly. This paper aims to effectively identify such hidden debonding regions in these advanced structures, using Lamb wave‐based monitoring technique. A semianalytical analysis of Lamb wave dispersion in a healthy sandwich structure is carried out to identify various Lamb modes and to study their propagation phenomenon. A combined finite element‐based simulation and experimental analysis of Lamb wave propagation in sandwich panels (healthy and with debonding) are then carried out using piezoelectric transducer networks. It is observed that the presence of debonding significantly reduces the propagating Lamb wave mode amplitudes. A debonding detection algorithm, which uses the differential changes in Lamb mode amplitudes, is applied to efficiently identify single and multiple debonding regions in the structure.     

基于谱元法的裂Lamb纹梁波传播特性研究

首次提出用一种无质量弹簧元来模拟含横向裂纹梁的轴弯耦合效应,并结合谱元法分析含裂纹梁内Lamb波的传播特性.由卡氏定理和断裂力学方法推导弹簧元的刚度,以此构建裂纹处的平衡条件和位移协调条件,建立损伤谱元模型.通过和传统的有限元模型进行比较,表明在显著提高计算效率的同时,所提出模型在分析结构固有特性和Lamb波传播特性上都具有较高的精度.在所提出模型的基础上又推导出基于谱元法的能量计算公式,通过裂纹处的能量守恒再次验证损伤模型的正确性和有效性,同时研究结果表明裂纹处转化生成的Lamb 波各模态能量随裂纹深度的变化具有单调性,该结论可以为结构健康监测中定量识别裂纹提供实用依据.     

Numerical analysis on the interaction of guided Lamb waves with a local elastic stiffness reduction in quasi-isotropic composite plate structures

This paper investigates how Lamb waves respond to the presence of material degradation in a plate-like structure using a series of finite element analyses. To facilitate this study, the propagation of these guided waves was interpreted with the dispersion characteristics and displacement profiles were analysed in the frequency and wave number domain. The results show that the material degradation simulated by a local stiffness reduction which leads to changes in the dispersive characteristic of the propagating waves has made the Lamb waves technique become an effective tool to assess the material degradation.     

Modeling dynamic crack propagation in fiber reinforced composites including frictional effects

Dynamic crack propagation in a unidirectional carbon/epoxy composite is studied through finite element analyses of asymmetric impact (shear loading) of a rod against a rectangular plate. A finite deformation anisotropic visco-plastic model is used to describe the constitutive response of the composite. Crack propagation is simulated by embedding zero thickness interface element along the crack path. An irreversible mixed-mode cohesive law is used to describe the evolution of interface tractions as a function of displacement jumps. Contact and friction behind the crack tip are accounted for in the simulations. The failure of the first interface element at the pre-notch tip models onset of crack extension. Crack propagation is modeled through consecutive failure of interface elements. The dynamic crack propagation phenomenon is studied in terms of crack initiation time, crack speed, mode I and mode II displacement jumps and tractions associated with the failure of interface elements, effective plastic strain at the crack tip and path independent integral J^′. Analyses are carried out at impact velocities of 5, 10, 20, 30 and 40 m/s, assuming the crack wake is frictionless. Moreover, analyses at impact velocities of 30 and 40 m/s are also carried out with a friction coefficient of 0.5, 1, 5 and 10 along the crack surfaces. The analyses show that steady-state intersonic crack propagation in fiber reinforced composite materials occurs when the impact velocity exceeds a given threshold. A steady-state crack speed of 3.9 times the shear wave speed and 83% of the longitudinal wave speed is predicted in the cases in which the impact velocity is above 10 m/s. Detailed discussion is given on the features of sub-sonic and intersonic crack propagation. It is shown that friction effects, behind the crack tip, do not have a significant effect on maximum crack speed; however, they do on characteristics of the shock wave trailing the crack tip. The analyses also show that the contour integral J^′, computed at contours near the crack tip, is indeed path independent and can serve as a parameter for characterizing intersonic crack propagation.     

Rayleigh Wave Propagation for the Detection of Near Surface Discontinuities: Finite Element Modeling

The paper presents a finite element study designed to gain physical insight into the effect of surface discontinuities on Rayleigh wave propagation in structural elements. In particular, a series of array measurements at various locations within a plate are simulated and compared with experimental measurements. Conversion of array measurements into the frequency-wavenumber domain reveals propagating Lamb modes, which are used to define Rayleigh wave motion. Numerical results show that Rayleigh waves measured after passing a fracture are composed of long wavelength Rayleigh wave energy propagating past the slot and short wavelength Rayleigh wave energy formed behind the slot.     

Air-Coupled Nondestructive Evaluation Dissected

This work develops a two-dimensional theoretical model to simulate the behavior of a fully non-contact air-coupled nondestructive evaluation system for a thin isotropic plate. The model is divided into transmission, guided wave propagation and reception phase. The validation of the complete model was carried out by modeling the same system by means of finite element method using a Multiphysics software. In addition, the dependency of the generated Lamb waves on different transmitter’s parameters and incidence angle is thoroughly investigated. The results of the acoustic pressure excited by the transducer, the out-of-plane velocity amplitudes for the generated first antisymmetric Lamb wave mode, and the radiated pressure from the plate caused by the leaky Lamb wavefield were all compared between the two models and a reasonable degree of similarity was found.     

Laser generation of Lamb waves for defect detection: experimental methods and finite element modeling

The propagation of Lamb waves generated by a pulsed laser beam in an aluminum sheet is modeled using finite element analysis, and the interaction with defects is studied and compared to experimental results. The ultrasonic Lamb waves are detected by an electromagnetic acoustic transducer (EMAT). The frequency content of the received wave is shown to be enhanced when the generation point is situated directly over the defect in both the modeled and experimental cases. Time-frequency analysis using a Wigner transform has enabled individual modes to be identified.     

基于三维弹性理论的碳纤维板中Lamb波建模

基于主动Lamb波的结构健康监测是目前复合材料结构损伤监测技术研究的热点之一,了解Lamb波的传播特性对进行可靠的损伤监测非常重要.本文结合经典三维弹性理论与Lamb波的运动位移方程,对碳纤维复合材料板中传播的Lamb波传播特性进行了建模研究,在此基础上推导了碳纤维板的相速度频散曲线,并讨论了Lamb波传播方向与坐标轴之间的夹角及碳纤维铺层方向对频散曲线的影响,建模结果证明了这种建模方法的正确性.     

A dynamic infinite element for three-dimensional infinite-domain wave problems

A three-dimensional dynamic infinite element which satisfies the following requirements: (1) displacement compatibility on the interface between finite and infinite elements; (2) definition of the wave propagation and amplitude attenuation behaviours in the infinite element using wave propagation functions; (3) convergence of the generalized integrals related to mass and stiffness matrices of the infinite element: and (4) displacement continuity along the common boundary of neighbouring infinite elements in the case of simulating multiple material layers or multiple wave numbers within the foundation, is presented in this paper. Since P-waves, S-waves and R-waves in the foundation can be simulated Simultaneously in the present infinite element, the seismic response of an arch-dam-foundation system, especially a thin double-curvature arch-dam-foundation system where the boundary element loses its competitive capacity with the finite element, can be economically calculated by coupling this infinite element with conventional finite elements. The good accuracy obtained using the present infinite element and finite element coupling model to simulate foundation wave problems has been proven by comparing the current numerical results with previous analytical results.