A0 Lamb Wave Research Articles

Numerical simulation and investigation of the spatial focusing of time reversal A0 Lamb wave mode using circular piezoelectric transducers collocated on a rectangular plate

This paper numerically simulates and investigates the spatial focusing of time reversal A0 Lamb wave mode using a pair of circular piezoelectric (PZT) transducers collocated on a rectangular plate. The poling directionalities of the collocated PZTs enable the selective sensing and actuating of A0 Lamb wave mode during a time reversal process. First, the reciprocity of elasto-dynamics is demonstrated between two distinct displacement fields induced by a point loading and an actuating PZT. Then, a numerical analysis scheme based on a virtual sensor model and the Mindlin plate theory is implemented to reduce huge computing time for simulating the time reversal process. The validity of the implemented numerical scheme is verified through comparison to the conventional finite element analysis in both forward and backward propagation of A0 Lamb wave mode. The performance of the spatial focusing of time reversal A0 Lamb mode is investigated through a parameter study with respect to truncation time and driving frequency of an input source. Finally, the implication of the parameter study is discussed.

Crack Detection in Single-Crystalline Silicon Wafer Using Laser Generated Lamb Wave

In the semiconductor industry, with increasing requirements for high performance, high capacity, high reliability, and compact components, the crack has been one of the most critical issues in accordance with the growing requirement of the wafer-thinning in recent years. Previous researchers presented the crack detection on the silicon wafers with the air-coupled ultrasonic method successfully. However, the high impedance mismatching will be the problem in the industrial field. In this paper, in order to detect the crack, we propose a laser generated Lamb wave method which is not only noncontact, but also reliable for the measurement. The laser-ultrasonic generator and the laser-interferometer are used as a transmitter and a receiver, respectively. We firstly verified the identification of S0 and A0 lamb wave modes and then conducted the crack detection under the thermoelastic regime. The experimental results showed that S0 and A0 modes of lamb wave were clearly generated and detected, and in the case of the crack detection, the estimated crack size by 6 dB drop method was almost equal to the actual crack size. So, the proposed method is expected to make it possible to detect the crack in the silicon wafer in the industrial fields.

Analytical and finite element prediction of Lamb wave scattering at delaminations in quasi-isotropic composite laminates

This paper presents a theoretical and finite element (FE) investigation of the scattering characteristics of the fundamental anti-symmetric (A0) Lamb wave at delaminations in a quasi-isotropic (QI) composite laminate. Analytical models based on the Mindlin plate theory and Born approximation are presented to predict the A0 Lamb wave scattering at a delamination, which is modelled as an inhomogeneity, in an equivalent isotropic model of the QI composite laminate. The results are compared with FE predictions, in which the delamination is modelled as a volume split. The equivalent isotropic model and QI composite laminate are used to investigate the feasibility of the common theoretical approach of modelling the delamination as the inhomogeneity. A good correlation is observed between the theoretical solutions and FE results in the forward scattering amplitudes, but there exists a larger discrepancy in the backward scattering amplitudes. The FE results also show that the fibre direction of the outer laminae has a pronounced influence on the forward and backward scattering amplitudes, which is not predicted by the analytical models.

Scattering characteristics of Lamb waves from debondings at structural features in composite laminates

This article investigates the scattering characteristics of Lamb waves from a debonding at a structural feature in a composite laminate. This study specifically focuses on the use of the low frequency fundamental antisymmetric (A(0)) Lamb wave as the incident wave for debonding detection. Three-dimensional finite element (FE) simulations and experimental measurements are used to investigate the scattering phenomena. Good agreement is obtained between the FE simulations and experimental results. Detailed parameter studies are carried out to further investigate the relationship between the scattering amplitudes and debonding sizes. The results show that the amplitude of the scattered A(0) Lamb wave is sensitive to the debonding size, which indicates the potential of using the low frequency A(0) Lamb wave as the interrogating wave for debonding detection and monitoring. The findings of the study provide improved physical insights into the scattering phenomena, which are important to further advance damage detection techniques and optimize transducer networks.

Improvement of Accuracy in Damage Localization Using Frequency Slice Wavelet Transform

Damage localization is a primary objective of damage identification. This paper presents damage localization in beam structure using impact-induced Lamb wave and Frequency Slice Wavelet Transform (FSWT). FSWT is a new time-frequency analysis method and has the adaptive resolution feature. The time-frequency resolution is a vital factor affecting the accuracy of damage localization. In FSWT there is a unique parameter controlling the time-frequency resolution. To improve the accuracy of damage localization, a generalized criterion is proposed to determine the parameter value for achieving a suitable time-frequency resolution. For damage localization, the group velocity dispersion curve (GVDC) of A0 Lamb waves in beam is first accurately estimated using FSWT, and then the arrival times of reflection wave from the crack for some individual frequency components are determined. An average operation on the calculated propagation distance is then performed to further improve the accuracy of damage localization.

Design of Low Frequency Piezoelectricity Transducer for Excitation of Pure A0 Lamb Wave and Its Application in Nondestructive Testing

Design of Low Frequency Piezoelectricity Transducer for Excitation of Pure A0 Lamb Wave and Its Application in Nondestructive Testing

Improvement of Accuracy in Damage Localization Using Frequency Slice Wavelet Transform

Damage localization is a primary objective of damage identification. This paper presents damage localization in beam structure using impact-induced Lamb wave and Frequency Slice Wavelet Transform (FSWT). FSWT is a new time-frequency analysis method and has the adaptive resolution feature. The time-frequency resolution is a vital factor affecting the accuracy of damage localization. In FSWT there is a unique parameter controlling the time-frequency resolution. To improve the accuracy of damage localization, a generalized criterion is proposed to determine the parameter value for achieving a suitable time-frequency resolution. For damage localization, the group velocity dispersion curve (GVDC) of A0Lamb waves in beam is first accurately estimated using FSWT, and then the arrival times of reflection wave from the crack for some individual frequency components are determined. An average operation on the calculated propagation distance is then performed to further improve the accuracy of damage localization.

Time Reversal Health Monitoring of Composite Plates using Lamb waves

In this work, the use of time reversal technique along with Lamb wave active sensing is investigated for health monitoring of composite plate structures. Piezoelectric wafer active sensors (PWAS) were used for the actuation and reception of the Lamb wave modes in the composite plates. Experiments were conducted on glass-epoxy composite plates with different lay-up sequences to study the time reversal behavior of A0 and S0 Lamb wave modes. Damage in the form of delamination was simulated by inserting a Teflon release film between the sixth and seventh layer of the glass-epoxy composite plate. The change in the shape of the broad band Gaussian pulse under time reversal in the presence of delamination was studied experimentally. Time reversal experiments were further carried out on carbon-epoxy composite t-pull specimen and the specimenwas subjected to a tensile loading in a universal testing machine. PWAS measurements were carried out for healthy and also during different stages of delamination due to tensi...

Design and fabrication of a MEMS Lamb wave device based on ZnO thin film

This paper presents the design and fabrication of a Lamb wave device based on ZnO piezoelectric film. The Lamb waves were respectively launched and received by both Al interdigital transducers. In order to reduce the stress of the thin membrane, the ZnO/Al/LTO/Si3N4/Si multilayered thin plate was designed and fabricated. A novel method to obtain the piezoelectric constant of the ZnO film was used. The experimental results for characterizing the wave propagation modes and their frequencies of the Lamb wave device indicated that the measured center frequency of antisymmetric A0 and symmetric S0 modes Lamb wave agree with the theoretical predictions. The mass sensitivity of the MEMS Lamb wave device was also characterized for gravimetric sensing application.

Directivity of guided ultrasonic wave scattering at notches and cracks

Localized and distributed guided ultrasonic waves array systems offer an efficient way for the long-term monitoring of the structural integrity for large structures. The use of permanently attached sensor arrays has been shown to be applicable to detect simulated corrosion damage. However, the detection sensitivity for fatigue cracks depends on the location and orientation of the crack relative to the transducer elements. Crack-like defects have a directivity pattern of the scattered wave field depending on the angle of the incident wave relative to the defect orientation and on the ratio of the characteristic defect size to wavelength. From FE simulations it has been shown that for cracks and notches almost no energy is scattered in certain directions from the defect, i.e., the data processing algorithm must take into account that for some transducer combinations no change in the signal even for a significant defect will be detected. The directivity pattern of the scattered field for the A0 Lamb wave mode is predicted from 3D Finite Element simulations and verified from experimental measurements at machined part-through and through-thickness notches using a laser interferometer. Good agreement was found and the directivity pattern can be predicted accurately. The amplitude of the scattered wave is quantified for a variation of the angle of the incident wave relative to the defect orientation, the defect depth, and the ratio of the characteristic defect size to wavelength. These results provide the basis for the quantification of the detection sensitivity for defects in plate structures using guided wave array sensors. A hybrid model has been developed, taking the different propagation distances and scattering characteristics into account, in order to predict the relative amplitudes of received pulses for given sensor locations. From a comparison with the signal to noise ratio of the array system, detection capabilities can be predicted for given defect size and orientation.

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.

Optimal Excitation Frequency of Lamb Waves for Delamination Detection in CFRP Laminates

To improve the reliability of delamination detection techniques based on Lamb waves for carbon fibre reinforced plastics (CFRP) composite laminates, the influence of excitation frequency of Lamb waves on the intensity of reflected waves from a delamination in cross-ply CFRP delaminated beams was investigated. The A0 Lamb wave mode was chosen although the conclusion in this work is also applicable to S0 mode. A Chebyshev pseudospectral Mindlin plate element proposed by authors was employed to simulate the A 0 mode propagation and the interaction of the A0 mode with the delamination. Numerical results show that the sensitivity of A0 mode to the delamination at different frequencies is remarkably different. Each delamination with different lengths or different locations along the through-thickness direction of the laminates generally has at least one or more optimal excitation frequencies which can generate the strongest reflected wave signals from the delamination. The reason for this phenomenon was also investigated by analyzing the natural vibration of the local upper- and lower-delaminated regions. The optimal excitation frequencies were identified to be close to the resonant frequencies of the local delaminated regions with pure flexural vibration modes similar to the deformation pattern of A0 mode.

A Multi-Touch Plate Based on Lamb Wave Absorption

In this paper, the A0 Lamb wave propagating in a thin finite copper plate is investigated to design a new multi-touch tactile instrument, which could localize one or several fingers. The position of index is localized by identifying the absorption signals of Lamb waves when it is in contact with the plate. Statistic models are used to improve the robustness of this interface. An artificial silicone finger is fabricated in the calibration procedure. The multi-touch (two fingers or more) applications using this plate is also presented.

Experimental study of the A0 and S0 Lamb waves interaction with symmetrical notches

The aim of this work is to study the fundamental Lamb modes interaction with defects in isotropic plates. For these experimental investigations, symmetrical notches with various depths milled in aluminum plates are considered. Moreover, the incident Lamb wave of a specific mode is generated by means of two identical thin piezoceramic transducers placed at the opposite sides of the plate. The waves scattered by the notch are recorded with conventional transducers located on the plate surface in front and behind the defect. The selection of the A 0 or the S 0 modes is obtained by exciting the transducers with anti-phased or in-phased signals, respectively. Furthermore, a calibration process is investigated to correct errors caused by the presence of the receiver between the emitters and the defects. The power reflection and transmission coefficients are then obtained and the power balance is verified. Finally, these measurements are compared successfully with those obtained by a numerical method using the finite-element modeling described in a previous work.

A fluid level sensor using A0 Lamb wave mode

The aim of this study was to examine the feasibility of creating a fluid level sensor operating in A0 Lamb wave mode. The experimental sensor is composed of a plate of stainless steel 1.3 meters high, in which, an A0 Lamb wave mode is generated. The choices of the material, the plate thickness and the wave vibration mode are all important. We therefore plotted the phase and group velocity curves, and the transversal and longitudinal displacements versus the product frequency x thickness. These curves enabled us to visualize the best target point for the excitation energy on a suitably guided wave mode at an appropriate frequency; this point is referred to as the operating point. When the chosen wave mode is generated, the echo from the reflection at the guide‐water interface is easily detected by the transmitter‐receiver transducer and can be worked efficiently.

A Phased Array-based Method for Damage Detection and Localization in Thin Plates

A method for damage localization based on the phased array idea has been developed. Four arrays of transducers are used to perform a beam-forming procedure. Each array consists of nine transducers placed along a line, which are able to excite and register elastic waves. The A0 Lamb wave mode has been chosen for the localization method. The arrays are placed in such a way that the angular difference between them is 45° and the rotation point is the middle transducer, which is common for all the arrays. The idea has been tested on a square aluminium plate modeled by the Spectral Element Method. Two types of damage were considered, namely distributed damage, which was modeled as stiffness reduction, and cracks, modeled as separation of nodes between selected spectral elements. The plate is excited by a wave packet. The whole array system is placed in the middle of the plate. Each linear phased array in the system acts independently and produces maps of a scanned field based on the beam-forming procedure. These maps are made of time signals (transferred to space domain) that represent the difference between the damaged plate signals and those from the intact plate. An algorithm was developed to join all four maps. The final map is modified by proposed signal processing algorithm to indicate the damaged area of the plate more precisely. The problem for damage localization was investigated and exemplary maps confirming the effectiveness of the proposed system were obtained. It was also shown that the response of the introduced configuration removes the ambiguity of damage localization normally present when a linear phased array is utilized. The investigation is based exclusively on numerical data.

On the propagation of Lamb Waves in Viscoelastic Composites for SHM Applications

This paper presents a theoretical model for anisotropic wave attenuation in composites. The model has been implemented in a software called FIBREWAVE in order to predict dispersion and attenuation of A0 Lamb wave modes. The required input data are the complex stiffness matrix coefficients of the unidirectional plies of the composites, which have been measured by an immersion technique. Good agreement has been observed between predicted and experimental group velocities and wave attenuations.

A mode interaction with a plate free edge: Theory and experiments at very low frequency by thickness product

When a plane acoustic wave reaches a medium with an impedance infinite or null, it experiences a phase shift of zero or pi and its amplitude on the edge is maximum or vanishes. The case of a flexion wave (A0 Lamb wave) at a free end is also simple; its amplitude is multiplied by a factor 2 square root 2 and the phase shift is pi/2. The evanescent wave at the origin of these phenomena, perfectly described by the classical flexural plate theory, is identified as the imaginary A1 mode of the exact Rayleigh-Lamb theory. The experiences confirm the theoretical predictions.

Lamb Wave-Mode Tuning of Piezoelectric Wafer Active Sensors for Structural Health Monitoring

An analytical and experimental investigation of the Lamb wave-mode tuning with piezoelectric wafer active sensors (PWASs) is presented. The analytical investigation assumes a PWAS transducer bonded to the upper surface of an isotropic flat plate. Shear lag transfer of tractions and strains is assumed, and an analytical solution using the spacewise Fourier transform is reviewed, closed-form solutions are presented for the case of ideal bonding (i.e., load transfer mechanism localized at the PWAS boundary). The analytical solutions are used to derive Lamb wave-mode tuning curves, which indicate that frequencies exist at which the A0 mode or the S0 mode can be either suppressed or enhanced. Extensive experimental tests that verify these tuning curves are reported. The concept of “effective PWAS dimension” is introduced to account for the discrepancies between the ideal bonding hypothesis and the actual shear-lag load transfer mechanism. The paper further shows that the capability to excite only one desired Lamb wave mode is critical for practical structural health monitoring (SHM) applications such as PWAS phased array technique (e.g., the embedded ultrasonics structural radar (EUSR)) and the time reversal process (TRP). In PWAS phased array EUSR applications, the basic assumption of the presence of a single low-dispersion Lamb wave mode (S0) is invoked since several Lamb wave modes traveling at different speeds would disturb the damage imaging results. Examples are given of correctly tuned EUSR images versus detuned cases, which illustrate the paramount importance of Lamb wave-mode tuning for the success of the EUSR method. In the TRP study, an input wave packet is reconstructed at a transmission PWAS when the signal recorded at the receiving PWAS is reversed in the time domain and transmitted back to the original PWAS. Ideally, TRP could be used for damage detection without a prior baseline. However, the application of TRP to Lamb waves SHM is impended by the dispersive and multimodal nature of the Lamb waves. The presence of more then one mode usually produces additional wave packets on both sides of the original wave packet due to the coupling of the Lamb wave modes. The PWAS Lamb wave tuning technique described in this paper is used to resolve the side packets problem. Several tuning cases are illustrated. It is found that the 30kHz tuning of the A0 Lamb wave mode with a 16-count smoothed tone burst leads to the complete elimination of the side wave packets. However, the elimination was less perfect for the 290kHz tuning of the S0 mode due to the frequency sidebands present in the tone-burst wave packet.

Ultrasonic guided wave scattering in a plate overlap

Guided wave scattering in a plate overlap is investigated by numerical calculations and experimental measurements of transmission and reflection factors from the overlap region. In the numerical study, a hybrid boundary element-finite element method is used to calculate the guided wave scattered field from the overlap region. Transmission and reflection factors are calculated for incident A0 and S0 Lamb and n0 shear horizontal waves, including higher modes generated through mode conversion phenomena. In addition, parametric studies of transmission and reflection factors in this problem are performed numerically over various incident modes, frequencies, and overlap lengths. For verification and comparison with numerical results, experiments were conducted to measure the transmission and reflection factors for incident Lamb and shear horizontal waves in steel plates with two different overlap areas. The experimental results agree well with the numerical calculations. The numerical and experimental results show that it is highly feasible to carry out efficient Lamb wave nondestructive evaluation (NDE) in overlapped plates and in multilayer structures with various lap joints by selecting various modes and tuning frequency.