Search Results (39)

A signal-processing algorithm for the detailed determination of delamination in multilayer structures is proposed in this work. The algorithm is based on calculating the phase velocity of the Lamb wave A₀ mode and estimating this velocity dispersion. Both simulation and experimental studies were conducted to validate the proposed technique. The delamination having a diameter of 81 mm on the segment of a wind turbine blade (WTB) was used for verification of the proposed technique. Four cases were used in the simulation study: defect-free, delamination between the first and second layers, delamination between the second and third layers, and defect (hole). The calculated phase velocity variation in the A₀ mode was used to determine the location and edge coordinates of the delaminations and defects. It has been found that in order to estimate the depth at which the delamination is, it is appropriate to calculate the phase velocity dispersion curves. The difference in the reconstructed phase velocity dispersion curves between the layers simulated at different depths is estimated to be about 60 m/s. The phase velocity values were compared with the delamination of the second and third layers and a hole drilled at the corresponding depth. The obtained simulation results confirmed that the drilled hole can be used as a defect corresponding to delamination. The WTB sample with a drilled hole of 81 mm was used in the experimental study. Using the proposed algorithm, detailed defect parameters were obtained. The results obtained using simulated and experimental signals indicated that the proposed new algorithm is suitable for the determination of delamination parameters in a multilayer structure. Full article

Periodic permanent magnet(PPM) electromagnetic acoustic transducers (EMATs) are commonly employed for axial defect inspection in pipelines. However, the lowest-order shear horizontal waves (SH0) guided waves have difficulties in distinctly differentiating internal and external defects. To enhance the signal-to-noise ratio and resolution, a unidirectional electromagnetic acoustic transducer (EMAT) based on Circumferential Lamb waves (CLamb waves) is developed. Through structural parameter optimization and excitation frequency adjustment, high-amplitude and low-dispersion CLamb waves are successfully generated in the high-frequency-thickness product region of the dispersion curve. Finite element simulations and experimental validation confirm the capability of this EMAT in exciting CLamb waves for the detection of crack-like defects. Experimental results demonstrate that the excitation efficiency of the CLamb EMAT exceeds that of the periodic permanent magnet electromagnetic acoustic transducer by more than tenfold. The defect reflection signal of the CLamb EMAT exhibits higher resolution and more significant amplitude compared to the PPM EMAT. The integration of this method with SH0 mode detection allows for the inspection of both internal and external defects in pipelines, offering a new avenue for EMAT applications in pipeline inspection. Full article

Lateral modes are responsible for the in-band spurious resonances that appear on BAW resonators, degrading the in-band filter response. In this work, a fast computational method based on the transmission line matrix (TLM) method is employed to model the lateral resonances of BAW resonators. Using the precomputed dispersion curves of Lamb waves and an equivalent characteristic impedance for the TE₁ mode, a network of transmission lines is used to calculate the magnitude of field distributions on the electrodes. These characteristics are specific to the stack layer configuration. The model’s implementation is based on nodal Y matrices, from which particle displacement profiles are coupled to the electric domain via piezoelectric constitutive relations. Consequently, the input impedance of the resonator is obtained. The model exhibits strong agreement with FEM simulations of FBARs and SMRs, and with measurements of several SMRs. The proposed model can provide accurate predictions of resonator input impedance, which is around 200 times faster than conventional FEM. Full article

In this paper, a radial gradient seismic metamaterial (RGSM) is proposed. The structural unit cell is composed of an external square soil embedded with a triangular-cross-sectioned steel ring, which is filled at different angles of multiple steel rings to form a supercell. The dispersion curve and attenuation spectrum of the unit cell are calculated by the finite element method, and the opening mechanism of the band gap is explained by analyzing the modes at the band gap boundary. The influence of geometric parameters and material parameters on the band gap is further studied, and the optimized supercell radial gradient seismic metamaterial (OS-RGSM) structure is designed through structure and parameter optimization. The ultra-low broadband excellent band gap in the range of 2.35–20 Hz for seismic Lamb waves is realized, and its three-dimensional frequency response and displacement field diagram are calculated. In addition, the attenuation characteristics of the optimized supercell seismic metamaterial on the seismic surface wave are calculated and analyzed. It is found that the attenuation can reach more than 50% in the ultra-low frequency range of 3.5–9 Hz. The seismic wave barrier is verified by the vibration transmission characteristics of RGSM under finite period and dynamic time history analysis. The results show that RGSM can effectively shield from seismic Lamb waves in the ultra-wideband with the starting frequency of 2.35 Hz and can also effectively attenuate the seismic surface wave in semi-infinite space. Full article

The application of non-stationary Lamb wave signals is a promising tool in various industrial applications where information about changes inside a structure is required. Phase velocity is one of the Lamb wave parameters that can be used for inhomogeneities detection. The possibility of reconstructing the segment of the phase velocity in a strong dispersion range using only two signals is proposed. The theoretical study is performed using signals of the A₀ mode propagating in an aluminium plate at a frequency of 150 kHz, 300 kHz, 500 kHz and 900 kHz. The experiment was carried out at a value of 300 kHz. The studies conducted indicated that the maximum distance between two signals, at which the time-of-flight can be measured between the same phase points, is the main parameter for the two signals technique application. Theoretical and experimental studies were performed, and the mean relative error was calculated by comparing the obtained results with those calculated via the SAFE method. In the theoretical study, the mean relative error of 0.33% was obtained at 150 kHz, 0.22% at 300 kHz, 0.23% at 500 kHz and 0.11% at 900 kHz. The calculated mean relative errors ${\delta }_{c_{ph}}=0.91\%$ and ${\delta }_{c_{ph}}=1.36\%$ were obtained at different distances in the experimental study. The results obtained show that the estimation of the phase velocity in dispersion ranges using only two received signals was a useful tool that saved time and effort. Full article

Traditional Lamb wave inspection and imaging methods heavily rely on prior knowledge of dispersion curves and baseline recordings, which may not be feasible in the majority of real cases due to production uncertainties and environmental variations. In order to solve this problem, a two-step Lamb wave strategy utilizing adaptive multiple signal classification (MUSIC) and sparse reconstruction of dispersion reconstruction is proposed. The multimodal Lamb waves are initially reconstructed in the f-k domain using random measurements, allowing for the identification and characterization of multimodal Lamb waves. Then, using local polynomial expansion and derivation, the phase and group velocities for each Lamb wave mode could be computed. Thus, the steering vectors of all potential scattering Lamb waves for each grid in the scanning area can be established, thereby allowing for the formulation of the MUSIC algorithm. To increase the precision and adaptability of the MUSIC method, the local wave components resulting from potential scatters are extracted with an adaptive window, which is governed by the group velocities and distances of Lamb wave propagation. As a result, the reconstructed dispersion relations and windowed wave components can be used to highlight the scattering features. For the method investigation, both a simulation and experiment are carried out, and both the dispersion curves and damage locations can be detected. The results demonstrate that damage localization is possible without theoretical dispersion data and baseline recordings while exhibiting a considerable accuracy and resolution. Full article

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. Full article

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%. Full article

Ultrasonic guided waves offer a convenient and practical approach to structural health monitoring and non-destructive evaluation. A key property of guided waves is the fully defined relationship between central frequency and propagation characteristics (phase velocity, group velocity and wavenumber)—which is described using dispersion curves. For many guided wave-based strategies, accurate dispersion curve information is invaluable, such as group velocity for localisation. From experimental observations of dispersion curves, a system identification procedure can be used to determine the governing material properties. As well as returning an estimated value, it is useful to determine the distribution of these properties based on measured data. A method of simulating samples from these distributions is to use the iterative Markov-Chain Monte Carlo (MCMC) procedure, which allows for freedom in the shape of the posterior. In this work, a scanning-laser Doppler vibrometer is used to record the propagation of Lamb waves in a unidirectional-glass-fibre composite plate, and dispersion curve data for various propagation angles are extracted. Using these measured dispersion curve data, the MCMC sampling procedure is performed to provide a Bayesian approach to determining the dispersion curve information for an arbitrary plate. The distribution of the material properties at each angle is discussed, including the inferred confidence in the predicted parameters. The percentage errors of the estimated values for the parameters were 10–15 points larger when using the most likely estimates, as opposed to calculating from the posterior distributions, highlighting the advantages of using a probabilistic approach. Full article

The 2D-FFT is described as a traditional method for signal processing and analysis. Due to the possibility to determine the time and frequency (t,f) domains, such a method has a wide application in various industrial fields. Using that method, the obtained results are presented in images only; thus, for the extraction of quantitative values of phase velocities, additional algorithms should be used. In this work, the 2D-FFT method is presented, which is based on peak detection of the spectrum magnitude at particular frequencies for obtaining the quantitative expressions. The radiofrequency signals of ULWs (ultrasonic Lamb waves) were used for the accuracy evaluation of the method. An uncertainty evaluation was conducted to guarantee the metrological traceability of measurement results and ensure that they are accurate and reliable. Mathematical and experimental verifications were conducted by using signals of Lamb waves propagating in the aluminum plate. The obtained mean relative error of 0.12% for the A₀ mode (160 kHz) and 0.05% for the S₀ mode (700 kHz) during the mathematical verification indicated that the proposed method is particularly suitable for evaluating the phase-velocity dispersion in clearly expressed dispersion zones. The uncertainty analysis showed that the plate thickness, the mathematical modeling, and the step of the scanner have a significant impact on the estimated uncertainty of the phase velocity for the A₀ mode. Those components of uncertainty prevail and make about ~92% of the total standard uncertainty in a clearly expressed dispersion range. The S₀ mode analysis in the non-dispersion zone indicates that the repeatability of velocity variations, fluctuations of the frequency of Lamb waves, and the scanning step of the scanner influence significantly the combined uncertainty and represent 98% of the total uncertainty. Full article

The ultrasonic Lamb wave detection principle can realize the noncontact measurement of liquid level in closed containers. When designing an ultrasonic Lamb wave sensor, it is vital to thoroughly study and select the optimal wedge size at the front of the sensor. In this paper, firstly, we select the best working mode of Lamb waves according to their propagation dispersion curve in aluminum alloy, and we obtain the best angle of wedge through experiments. Secondly, we study the impact of the size of the wedge block on the results, and we obtain the selection method of wedge block parameters. The evaluations show that, when the frequency–thickness product is 3 MHz·mm, the Lamb waves work in the A1 mode, and the experimental effect is the best. At this time, the incident angle of the ultrasonic wave is 27.39°. The wedge thickness should be designed to avoid the near-field area of the ultrasonic field, and we should choose the length as odd multiples of 1/4 wavelength. The rules obtained from the experiment can effectively select the best working mode for ultrasonic Lamb waves, while also providing a basis for the design of the wedge block size in a Lamb wave sensor. Full article

This work determined the attenuation coefficients of Lamb waves of ten engineering materials and compared the results with calculated Lamb-wave attenuation coefficients, α–S and α–A. The Disperse program and a parametric method based on Disperse results were used for calculations. Bulk-wave attenuation coefficients, α_L and α_T, were required as input parameters to the Disperse calculations. The calculated α–S and α–A values were found to be dominated by the α_T contribution. Often α–A_o coincided with α_T. The values of α_L and α_T were previously obtained or newly measured. Attenuation measurement relied on Lamb-wave generation by pulsed excitation of ultrasonic transducers and on surface-displacement detection with point contact receivers. The frequency used ranged from 10 kHz to 1 MHz. A total of 14 sheet and plate samples were evaluated. Sample materials ranged from steel, Al, and silicate glass with low attenuation to polymers and a fiber composite with much higher attenuation. Experimentally obtained Lamb-wave attenuation coefficients, α–S and α–A, for symmetric and asymmetric modes, were mostly for the zeroth mode. Plots of α–S_o and α–A_o values against frequency were found to coincide reasonably well to theoretically calculated curves. This study confirmed that the Disperse program predicts Lamb-wave attenuation coefficients for elastically isotropic materials within the limitation of the contact ultrasonic techniques used. Further refinements in experimental methods are needed, as large deviations often occurred, especially at low and high frequencies. Methods of refinement are suggested. Displacement measurements were quantified using Rayleigh wave calibration. For signals below 300 kHz, 1-mV receiver output corresponded to 1-pm displacement. Peak displacements after 200-mm propagation were found to range from 10 pm to 1.5 nm. With the use of signal averaging, the point-contact sensor was capable of detecting 1-pm displacement with 40 dB signal-to-noise ratio and had equivalent noise of 4.3 fm/√Hz. Approximate expressions for α–S_o and α–A_o were obtained, and an empirical correlation was found between bulk-wave attenuation coefficients, i.e., α_T = 2.79 α_L, for over 150 materials. Full article

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. Full article

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. Full article

The aim of this work is to propose a numerical methodology based on the finite element (FE) method to investigate the dispersive behavior of guided waves transmitted, converted, and reflected by reinforced aluminum and composite structures, highlighting their differences. The dispersion curves of such modes can help designers in improving the damage detection sensitivity of Lamb wave based structural health monitoring (SHM) systems. A preliminary phase has been carried out to assess the reliability of the modelling technique. The accuracy of the results has been demonstrated for aluminum and composite flat panels by comparing them against experimental tests and semi-analytical data, respectively. Since the good agreement, the FE method has been used to analyze the phenomena of dispersion, scattering, and mode conversion in aluminum and composite panels characterized by a structural discontinuity, as a stiffener. The research activity allowed emphasizing modes conversion at the stiffener, offering new observations with respect to state of the art. Converted modes propagate with a slightly slower speed than the incident ones. Reflected waves, instead, have been found to travel with the same velocity of the incident ones. Moreover, waves reflected in the composite stiffened plate appeared different from those that occurred in the aluminum one for the aspects herein discussed. Full article