Lamb Wave Dispersion Curves Research Articles

Damage detection by means of broadband local wavenumber estimation in plate-like structures

This short communication evinces the ability of the CFAT methodology [Q. Leclère, JSV, 2015] to detect and characterize thickness-loss defects on homogeneous flat panels. A contactless measurement of the velocity field of an aluminium plate is performed by scanning laser vibrometry, from which the equivalent rigidity (apparent bending stiffness) is locally estimated within a wide frequency band in the ultrasonic domain. The method allows imaging thickness-reduction defects on the hidden face of an aluminium plate up to several hundreds of kilohertz. The first part details the experimental protocol, followed by a second enhancing the identification of the wavenumbers of symmetric S_0 and antisymmetric A_0 modes. The comparison with theoretical Lamb waves dispersion curves reveals the precision of the method. Finally, the methodology validates the possibility to precisely estimate the local material thickness and as a consequence the location, size and depth of a reference defect in the shape of a flat bottom hole (assuming homogeneous material properties of the plate).

Study on Time-frequency Imaging of Ultrasonic Detection with Phase Shifted Fiber Bragg Grating Sensing

Abstract The influence of the wavelength difference between the laser source and the phase-shifted fiber Bragg grating (PS-FBG) on the intensity of the power demodulation system based on an adjustable laser source was studied experimentally, and the optimum of the output laser wavelength was determined. Then, the research on time-frequency imaging damage identification based on smooth pseudo-Wigner-Ville distribution was carried out. The Time of Flight of the acoustic wave signal was calculated and time compensation was made according to the Wigner-Ville distribution and the Lamb wave dispersion curve. The ultrasonic waves before and after damage were measured with spatially arranged PS-FBGs. The difference signals were processed in a window, and then the time-frequency energy of the normalized difference signal was imaged to assess the damage detection and location. Although the mode and group velocity of ultrasound measured by each fiber grating were different, the accurate location and identification of artificial damage in an aluminum alloy plate was realized by using only three PS-FBGs and a smooth Wigner time-frequency imaging method.

Lead Zirconate Titanate Transducers Embedded in Composite Laminates: The Influence of the Integration Method on Ultrasound Transduction.

In the context of an embedded structural health monitoring (SHM) system, two methods of transducer integration into the core of a laminate carbon fiber-reinforced polymer (CFRP) are tested: cut-out and between two plies. This study focuses on the effect of integration methods on Lamb wave generation. For this purpose, plates with an embedded lead zirconate titanate (PZT) transducer are cured in an autoclave. The embedded PZT insulation, integrity, and ability to generate Lamb waves are checked with electromechanical impedance, X-rays, and laser Doppler vibrometry (LDV) measurements. Lamb wave dispersion curves are computed by LDV using two-dimensional fast Fourier transform (Bi-FFT) to study the quasi-antisymmetric mode (qA0) excitability in generation with the embedded PZT in the frequency range of 30 to 200 kHz. The embedded PZT is able to generate Lamb waves, which validate the integration procedure. The first minimum frequency of the embedded PZT shifts to lower frequencies and its amplitude is reduced compared to a surface-mounted PZT.

Comparative Study of Dispersion Curves for LAMB Waves Using Analytical Solutions and Semi-Analytical Methods

Lamb wave dispersion curves are useful for optimizing the inspection scanning distance that can be covered with good sensitivity in many current applications. However, one of the main problems concerning this calculation lies in selecting a numerical method that is computationally accurate and efficient. In this paper, Lamb waves dispersion curves are generated by the Scaled Boundary Finite Element Method, and by the Rayleigh–Lamb equation. For the semi-analytical case, waveguide cross-section discretization was performed using isoparametric elements and high-order spectral elements. The semi-analytical formulations lead to an eigenvalue problem that can be solved efficiently by calculating the couples of wavenumbers and frequencies that guarantee the wave mode propagation, the basis for generating the dispersion curves. These are compared with those obtained from the analytical solution for the symmetric and antisymmetric modes; in both cases, homogeneous plates of constant thickness are considered. The numerical results show good agreement when using a low number of isoparametric elements, or a single spectral element with shape functions of the order of six for computing the dispersion curves and wave structure. The calculation is given with low computational effort, and the relative variation with respect to the analytical reference values is less than 2%.

Non-destructive measurements of thickness and elastic constants of plate structures based on Lamb waves and particle swarm optimization

Lamb wave has become an important non-destructive measurement method due to its advantages of small attenuation, easy excitation, and simultaneous inversion of multiple parameters. According to its propagation properties, we proposed an improved particle swarm optimization method for the inversion of the thickness and elastic constants of plates in the study. Numerical simulations and validation experiments further confirmed that the Young's modulus, Poisson’s ratio, and thickness of plates could be accurately obtained from the measured zero-order modal Lamb wave dispersion curves. Then, through a series of orthogonal experiments, the influences of the error sources of measurement points on inversion parameters were explored. In addition, the statistical significance of the above influences on each inversion parameter is discussed in detail. This study provides a basis for the accurate and efficient non-destructive measurements based on Lamb waves.

Detecting the interfacial bonding of concrete-filled steel tube columns after fire by two stress wave-based methods – A case study

For concrete-filled steel tubes (CFST), the steel tube can increase the stiffness of the member, while the filled concrete prevents column buckling and allows the steel tube to withstand high temperatures for longer periods of time. The bonding between the steel tube and the concrete is difficult to evaluate from the appearance. In this paper, the bonding conditions of the CFST columns of a high-rise building under construction after a fire was evaluated by two stress wave-based non-destructive test (NDT) methods in-situ. They are the Lamb wave-based method and the normalized impact-echo method. Among them, the Lamb wave dispersion curve, which is obtained by a single tapping of a steel ball and a receiver 0.4 m away, can quickly evaluate the interface bonding conditions under the measuring line. The normalized impact-echo can pin-point the precise location of interfacial debonding. The test results show that both NDT methods can accurately classify good bonding conditions in the region without fire damage. Combining the results of the two methods, we found that high temperature was likely to cause some damage, such as microcracks on the concrete surface or intermittent separation of steel from concrete, but there is no continuous gap at the steel–column interface.

Lamb Waves Propagation Characteristics in Functionally Graded Sandwich Plates.

Functionally graded materials (FGM) have received extensive attention in recent years due to their excellent mechanical properties. In this research, the theoretical process of calculating the propagation characteristics of Lamb waves in FGM sandwich plates is deduced by combining the FGM volume fraction curve and Legendre polynomial series expansion method. In this proposed method, the FGM plate does not have to be sliced into multiple layers. Numerical results are given in detail, and the Lamb wave dispersion curves are extracted. For comparison, the Lamb wave dispersion curve of the sliced layer model for the FGM sandwich plate is obtained by the global matrix method. Meanwhile, the FGM sandwich plate was subjected to finite element simulation, also based on the layered-plate model. The acoustic characteristics detection experiment was performed by simulation through a defocusing measurement. Thus, the Lamb wave dispersion curves were obtained by V(f, z) analysis. Finally, the influence of the change in the gradient function on the Lamb wave dispersion curves will be discussed.

Experimental Method for Simultaneous Determination of the Lamb Wave A0 Modes Group and Phase Velocities.

Determining Lamb wave dispersion curves when measuring phase and group velocity values at a fixed frequency is now a common and relevant task. In most cases, in order to solve such a problem, it is necessary to know the exact properties of the material, particularly its thickness. In experimental methods, Lamb wave parameters are evaluated directly from the test materials. This paper proposes a new and simple experimental algorithm for A0 mode group and phase velocity determination based on signal filtering and zero-crossing estimating. The main idea is to capture the zero-crossing instances of the signals closest to the signal envelope peaks and use these time instances to determine the phase and group velocities. The reliability of the proposed method was evaluated using simulated and experimental signals propagating in an aluminum plate. Theoretical modeling has shown that the proposed method enables the calculation of the A0 mode group and phase velocities with a mean relative error of less than 0.7%. An accuracy of 0.8% was observed during the experimental measurements.

Error analysis and reliability of zero-order Lamb mode inversion for waveguide characterization

In recent years, several fitting techniques have been presented to reconstruct the parameters of a plate from its Lamb wave dispersion curves. Published studies show that these techniques can yield high accuracy results and have the potential of reconstructing several parameters at once. The precision with which parameters can be reconstructed by inverting Lamb wave dispersion curves, however, remains an open question of fundamental importance to many applications. In this work, we introduce a method of analyzing dispersion curves that yields quantitative information on the precision with which the parameters can be extracted. In our method, rather than employing error minimization algorithms, we compare a target dispersion curve to a database of theoretical ones that covers a given parameter space. By calculating a measure of dissimilarity (error) for every point in the parameter space, we reconstruct the distribution of the error in that space, beside the location of its minimum. We then introduce dimensionless quantities that describe the distribution of this error, thus yielding information about the spread of similar curves in the parameter space. We demonstrate our approach by considering both idealized and realistic scenarios, analyzing the dispersion curves obtained numerically for a plate and experimentally for a pipe. Our results show that the precision with which each parameter is reconstructed depends on the mode used, as well as the frequency range in which it is considered.

Semi-Analytical Finite Element (SAFE) method for plotting Lamb waves dispersion curves of an aluminum plate and comparison with Disperse software

Investigation into ultrasonic Non-destructive evaluation (NDE) methods for assessing complex designs depends firmly on displaying apparatuses that calculate dispersion curves. These expectations are vital for empowering the best assessment methodologies to be distinguished and their aversions to being assessed. This study, the main purpose of this work is to do a quantitative evaluation of the SAFE technique by calculating dispersion curves (wavenumber, phase velocity, and group velocity) and comparing them to those generated by Disperse Software.

Plotting Lamb waves dispersion curves of an aluminum plate by the Semi-Analytical Finite Element (SAFE) method and comparison with analytical curves

It is well known that the propagation of Lamb waves in elastic solid medias depends on the frequency and on the material properties, but it does not depend on the propagation direction in isotropic medias and gives rise to two basic types of modes, symmetric and antisymmetric ones. This paper presents an application of the semi-analytical finite element (SAFE) method on an isotropic aluminum plate of thickness e = 2mm. The main goal of this paper is to make a quantitative evaluation of the SAFE method by carrying out the following tasks: a) calculation of the dispersion curves (wavenumber, phase velocity, group velocity, b) calculation of the relative error and validation of the proposed algorithm, c) comparison between the curves obtained by SAFE method on those obtained by Bisection method. It should be noted here that our study is restricted on the propagative modes.

Third harmonic approximate phase velocity matching nonlinear early fatigue damage detection

The phase velocity matching Lamb waves are considered as an effective solution to excitation in the detection of nonlinear ultrasound early fatigue damage. In general, it is difficult to meet the phase velocity matching in real-world measurement. In this paper an approach to approximate phase velocity matching early fatigue damage detection is proposed. With the third harmonic approximate phase velocity matching modes treated as excitation frequencies by the Lamb wave dispersion curve, an analysis is conducted with regard to the time–frequency diagrams of the response signals at different frequencies. The change in the third harmonic amplitude with crack growth is analyzed by Fast Fourier Transform (FFT), which leads to the results suggesting that the third harmonic amplitude declines with crack growth. Moreover, a comparison is performed in the normalized relative third-order nonlinear parameters (NRTNP) of phase velocity matching and approximate phase velocity matching, with the relative deviation falling within 0.12.

Reconstruction of Lamb Wave Dispersion Curves in Different Objects Using Signals Measured at Two Different Distances.

The possibilities of an effective method of two adjacent signals are investigated for the evaluation of Lamb waves phase velocity dispersion in objects of different types, namely polyvinyl chloride (PVC) film and wind turbine blade (WTB). A new algorithm based on peaks of spectrum magnitude is presented and used for the comparison of the results. To use the presented method, the wavelength-dependent parameter is proposed to determine the optimal distance range, which is necessary in selecting two signals for analysis. It is determined that, in the range of 0.17–0.5 wavelength where is not higher than 5%, it is appropriate to use in the case of an A0 mode in PVC film sample. The smallest error of 1.2%, in the distance greater than 1.5 wavelengths, is obtained in the case of the S0 mode. Using the method of two signals analysis for PVC sample, the phase velocity dispersion curve of the A0 mode is reconstructed using selected distances x1 = 70 mm and x2 = 70.5 mm between two spatial positions of a receiving transducer with a mean relative error , and for S0 mode, x1 = 61 mm and x2 = 79.7 mm with . In the case of the WTB sample, the range of 0.1–0.39 wavelength, where is not higher than 3%, is determined as the optimal distance range between two adjacent signals. The phase velocity dispersion curve of the A0 mode is reconstructed in two frequency ranges: first, using selected distances x1 = 225 mm and x2 = 231 mm with mean relative error ; and second, x1 = 225 mm and x2 = 237 mm with .

Airborne acoustic characterisation of cultural heritage paintings: A preliminary study

In order to assess the health of cultural heritage paintings, for example prior to their restoration, visual inspections as well as techniques such as X-ray imaging are commonly used. Non-contact acoustic methods could become another exploration modality thanks to their non-destructive character and the fact that they are expected to be more sensitive to certain defects, such as a delamination, than other techniques. A setup has been designed for such applications, based on airborne ultrasonic transducers operating in the several hundred kHz to over 1 MHz range, specific transmit/receive electronics and automated scanning stages allowing 2D through-transmission scans to be performed on areas up to 80 × 80 square centimeters. Measurements on well-known thin plates made of plastic, wood and gesso on wood were first performed to evaluate the possibilities of the technique, then simple paintings on canvas were tested and finally a real ancient painting was scanned. A method where the transmission amplitude is plotted versus the angle between the propagation axis and the normal to the painting surface is developed for local characterization of the elastic constants of the sample under test, thanks to comparison with simulated Lamb wave dispersion curves using a fitting procedure. These promising results open the way towards comparison between acoustic, radiological and other imaging results on paintings with severe defects that require restoration.

Comparison between elastic and porous elastic material models for sediment acoustical behavior in an aluminum-sediment double layer

In this paper, Lamb waves dispersion curves are extracted for a double layer aluminum-sediment (gypsum) plate, both numerically and experimentally. For this purpose, the gypsum elastic properties are approximately calculated using ultrasonic bulk waves method. Then, by using the porous elastic behavior model for the gypsum, as well as the elastic model, available in ABAQUS commercial software, the dispersion curves are calculated numerically in the frequency range of 100–200 kHz for the sedimentary plate. In order to validate the numerical dispersion curves, an experimental setup consists of a 1-mm-thick aluminum plate covered by a 1.5 mm thick sediment (gypsum) area, equipped with two piezoelectric disks has been provided. The experimental dispersion curves for two fundamental symmetric and anti-symmetric modes, S0 and A0, have been extracted, using the time of flight method, applied on filtered experimental signals. Results show that the relative error between porous elastic and experimental models is 5.26% and 3.56% while relative error between numerical elastic model and the experimental model is 5.9% and 4.3%, for S0 and A0 modes, respectively. It is concluded that for dry sediments, the elastic mechanical behavior is acceptable. However, in case of wet sediments, dispersion curves should be extracted using a porous elastic model before defect detection in sedimentary structures. The unique capability of the porous elastic model is the possibility of wet sediment consideration, for dispersion curves evaluation.

High-resolution Lamb waves dispersion curves estimation and elastic property inversion

Ultrasonic Lamb waves have been widely used for non-destructive evaluation and testing. However, the inversion from the measured guided signals to the material properties is still a challenging task in terms of multimodal dispersive signal processing and parameter estimation. This paper presents a robust strategy including the high-resolution extraction of the multimodal dispersion curves and model-based elastic property estimation. First, the estimation of signal parameters via rotation invariant technique (ESPRIT) is employed to extract the dispersion curves of the Lamb waves in the plates. Then, the particle swarm optimization (PSO) algorithm is used to retrieve the optimal model parameters by maximizing the objective function built from the dispersion equations. The elastic properties (i.e., two independent constants for the isotropic plate and four constants for the transversely isotropic plate) can thus be determined. Results of the steel, aluminum and composite plates demonstrate that the estimates are in agreement with the references. The root mean squared errors (RMSEs) between the estimated and theoretical dispersion curves calculated by the inversed model parameters for simulation, steel, aluminum and composite experiments are 0.027 rad/mm, 0.032 rad/mm, 0.033 rad/mm and 0.102 rad/mm respectively. The estimated error of thickness is less than 1%. The proposed model-based inversion strategy offers several advantages: (1) the high-resolution estimation of dispersion curves allows the objective function built for the parameter inversion without a peak-finding process. (2) The ESPRIT based dispersion curves extraction strategy offers a sharp objective function in the parameter space. (3) The inverse problem for ultrasonic waveguide characterization is solved using the PSO optimizer which can be implemented with ease and few parameters need to be tuned.

Dispersion characteristics of guided waves in functionally graded anisotropic micro/nano-plates based on the modified couple stress theory

In this paper, the acoustic wave motion characteristics of Lamb and SH waves in functionally graded (FG) anisotropic micro/nano-plates are studied based on the modified couple stress theory. A higher efficient computational approach, the extended Legendre orthogonal polynomial method (LOPM) is utilized to deduce solving process. This polynomial method does not need to solve the FG micro/nano-plates hierarchically, which provides a more realistic analysis model for FG micro/nano-plates and has high computational efficiency. Simultaneously, the solutions based on the global matrix method (GMM) are also deduced to verify the correctness of the polynomial method. Furthermore, the effects of size and material gradient are studied in detail. Numerical results show that the size effect causes wrinkles in Lamb wave dispersion curves, and the material gradient characteristic changes the amplitude and range of wrinkles. For SH waves, the length scale parameter Lx increases the cut-off frequency but does not change the overall trend of the dispersion curve; on the contrary, Lz does not change the cut-off frequency but causes the dispersion curve to show an upward trend.

Monitoring the curing process of epoxy adhesive using ultrasound and Lamb wave dispersion curves

Monitoring the stiffness of adhesives is a crucial issue when considering the durability and strength of adhesive joints. While there are many studies conducted on specimens made only from adhesive, the problem of curing of an adhesive film in real joints is moderately considered. This paper presents the monitoring of stiffening of epoxy adhesive using ultrasound. Ultrasonic pulse velocity method was firstly applied for monitoring of adhesive specimens. Then, a new procedure using dispersion relations and scanning laser vibrometry was proposed for monitoring the curing process of an adhesive joint of steel plates. Both approaches gave comparable results showing the increase of the dynamic elastic modulus of adhesive in time. The study presented that the proposed procedure was capable of real-time monitoring the curing process of an adhesive layer in multi-layer systems.

Parametric Study of Ultrasonic De-Icing Method on a Plate with Coating

Ultrasonic de-icing is a promising method to de-ice structures by using lightweight and simple transducers, with the advantage of low power consumption. A successful ultrasonic de-icing technique requires the understanding of the effects of different parameters on de-icing. This paper presents a thorough parametric study of the ultrasonic de-icing method on a plate with coating. First, the dispersion equations of shear horizontal (SH) and Lamb waves were derived based on the global matrix method. Meanwhile, interface shear concentration coefficients (ISCC) were introduced to represent the ability of ultrasonic de-icing, which was further integrated into Lamb wave and SH waves dispersion curves for the selection of optimal frequencies. Second, a three-layer plate model (host plate-coating-ice) was used to demonstrate the effect of different parameters of coating and the thickness of ice on ultrasonic de-icing. The theoretical model provided the design principle of coating and ultrasonic parameters required for efficient de-icing. Finally, an experiment was conducted on an ultrasonic de-icing platform to validate the proposed ultrasonic de-icing method. In this process, material parameters including the Young’s modulus, thickness of coating, and thickness of the ice layer were analyzed. The trends of power consumption and optimal frequency of experiments are in good agreement with the analytical calculated results.

Evaluation of the thermal aging of aeronautical composite materials using Lamb waves

This work aims to demonstrate the ability to evaluate bulk thermal aging of aeronautical composite materials using Lamb waves. These composite materials are bi-dimensional woven composite structures with polymers matrix. More than 20 different thermal aging profiles are obtained by modulating the temperature and curing duration. The impact on material properties is evaluated using normalized destructive characterization and x-ray computed tomography. Lamb waves are generated and detected using a single 3 MHz phased array transducer in contact with the composite structure. In that way, a spatio-temporal image of elastic wave propagation in the composite material is obtained. The dispersion curves are calculated by using a bi-dimensional discrete Fourier transform or singular value decomposition to project the experimental data into the wavenumber-frequency domain. Both methods allow for accurate estimation of the Lamb wave dispersion curves. Thermal aging is then evaluated by comparing experimental data with a set of dispersion curves that correspond to different controlled thermal aging profiles. Our promising results open the door toward quantitative evaluation of composite material thermal aging on the runway.