Lamb wave generation and reception with time-delay periodic linear arrays: a BEM simulation and experimental study

Single-mode Lamb wave excitation at high-frequency-thickness products using a conventional linear array transducer

Lamb wave excitation at high-frequency-thickness products offers a potential solution for high-resolution guided wave testing. The method is attractive for crack imaging and corrosion mapping, especially in hidden locations where direct access is limited. However, multiple modes may propagate, complicating signal interpretation, which is undesirable. In this work, a systematic approach is presented, in an effort to determine the influence of the key parameters related to single higher order Lamb wave mode excitation using a conventional linear array transducer. Specifically, a linear time delay law is used to enhance the targeted mode, while the array's length, pitch and apodisation profile remain to be optimally selected. First, an analytical solution is derived based on modal analysis. This provides a natural decomposition of the amplitude of a guided wave mode into the product of the response of a single element and the excitation spectrum. Then, a key observation is made, associating the excitation spectrum to the directivity function for bulk wave phased array steering. This allows the application of well-established phased array analysis tools to guided wave phased array excitation. In light of this fact, minimisation of the spectrum's bandwidth, elimination of the grating lobes and derivation of an apodisation profile are performed, to enhance the purity of the targeted mode. Finally, experiments conducted on an aluminium plate verify the above theoretical results. The Full Matrix is acquired, and all signals are reconstructed synthetically.

One-dimension frequency-wavenumber-domain based model for ultrasonic waves generated by dual-array transducers

Array transducers can allow wavelength and frequency selectivity and can be used to generate different types of waves, such as ultrasonic bulk or guided waves. Dual-array transducers consist of two interlaced arrays, where the elements of each array are electrically connected. Therefore, by driving each array with a pair of phased pulses one can achieve a degree of wave generation control that allows unidirectional generation, unlike single array transducers that generate waves in both 0° and 180° directions with respect to the array's longitudinal axis. In this paper, we present a one-dimensional analytical model to determine the ultrasonic waves generated by dual-array transducers based on the excitability of the array in the frequency-wavenumber domain, the so-called operation region, determined by the joint spatial and temporal spectrum of the dual-array. We further exploited it to analyse the effectiveness of unidirectional generation with time-delayed excitation signals that provide ideal constructive or destructive interferences. The model also provides the time-domain received waveforms, which were compared to experimentally generated shear-horizontal ultrasonic guided waves, with a dual periodic permanent magnet array electromagnetic acoustic transducer, showing very good agreement. The adequate selection of the excitation signal allowed one to obtain up to about 40 dB unidirectionality experimentally.

Excitation of unidirectional SH wave within a frequency range of 50 kHz by piezoelectric transducers without frequency-dependent time delay

Unidirectional generation of a pure guided wave mode is of practical importance in structural health monitoring (SHM). Currently, unidirectional propagation guided waves can only be generated by using transducer array in a phased array form, which is limited within a very narrow frequency range. If a variable-wavelength unidirectional wave source is required, both the transducer spacing and time delay usually need to be changed with frequency, which is against the permanent arrangement demand of transducers in SHM. In this work, inspired by the unique features of bidirectional SH₀ wave (the fundamental shear horizontal mode) piezoelectric face-shear and thickness-shear transducers, a new method was proposed for generating unidirectional SH₀ wave. Two types of transducer configurations (double-side and single-side) were designed to unidirectionally generate SH₀ wave without frequency-dependent time delay. Both finite element simulations and experiments were conducted to validate the unidirectional features of the proposed double-side and single-side transducer configurations. Results shows that the double-side transducer configuration is capable of generating unidirectional propagation SH₀ wave at the frequency range from 100 kHz to 150 kHz, while the corresponding working frequency range for the single-side one is from 100 kHz to 140 kHz. The proposed method provides a cheap way for generation of the unidirectional SH₀ wave within a certain frequency range without adjusting the relative transducer spacing and the time delay with frequency, so it will have great potential applications in SHM.

Unidirectional Shear Horizontal Wave Generation by Periodic Permanent Magnets Electromagnetic Acoustic Transducer With Dual Linear-Coil Array

Shear horizontal (SH) waves are commonly generated by periodic permanent magnet (PPM) electromagnetic acoustic transducers (EMATs) in metallic media. Conventional PPM EMATs generate ultrasonic waves, which simultaneously propagate both forward and backward. This can be an undesirable characteristic, since the backward wave can be eventually reflected, reaching the receiver transducer where it can mix with the signal of interest. This limitation can be overcome using two side-shifted PPM arrays and racetracks coils to generate SH waves in a single direction. That design relies on the EMAT wavefront diffraction to produce constructive and destructive interference, but produces unwanted backward traveling sidelobes. Here, we present a different design, which uses a conventional PPM array and a dual linear-coil array. The concept was numerically simulated, the main design parameters were assessed and the unidirectional EMAT was experimentally evaluated on an aluminum plate, generating the SH0-guided wave mode nominally in a single direction. The amplitude ratio of the generated waves at the enhanced to the weakened side is above 20 dB. Since the wavefronts from the two sources are perfectly aligned, no obvious backward sidelobes are present in the acoustic field, which can significantly reduce the probability of false alarm of an EMAT detection system.

Suppression of Lamb wave excitation via aperture control of a transducer array for ultrasonic clamp-on flow metering

During ultrasonic clamp-on flow metering, Lamb waves propagating in the pipe wall may limit the measurement accuracy by introducing absolute errors in the flow estimates. Upon reception, these waves can interfere with the up and downstream waves refracting from the liquid, and disturb the measurement of the transit time difference that is used to obtain the flow speed. Thus, suppression of the generation of Lamb waves might directly increase the accuracy of a clamp-on flow meter. Existing techniques apply to flow meters with single element transducers. This paper considers the application of transducer arrays and presents a method to achieve a predefined amount of suppression of these spurious Lamb waves based on appropriate amplitude weightings of the transducer elements. Finite element simulations of an ultrasonic clamp-on flow measurement setting will be presented to show the effect of array aperture control on the suppression of the Lamb waves in a 1-mm-thick stainless steel pipe wall. Furthermore, a proof-of-principle experiment will be shown that demonstrates a good agreement with the simulations.

An ultrasonic guided wave excitation method at constant phase velocity using ultrasonic phased array probes

High-order ultrasonic guided wave modes have recently been attracting interest in a variety of nondestructive testing applications, ranging from thickness gauging to bond characterization. Accurate control of the transmitted ultrasonic guided wave mode is paramount when working at frequencies above the cutoff of the first high-order mode. The high number of modes available makes this range of frequency-thickness products difficult to exploit in practice. Many papers and textbooks have showed that multielement probes, such as comb transducers, are able to target a specific wavelength which depends on the elementary pitch. This method can be enhanced by adding an elementary delay law. However, this method of excitation has major drawbacks as the areas of excitation in a dispersion curves depends on the frequency and the technique is not unidirectional. This paper demonstrate that a conventional phased array transducer for which the elementary pitch is small relative to the targeted wavelength is able to excite high order guided wave modes at a constant phase velocity (independently of the frequency). The aim is to excite different regions of the dispersion curves by controlling the input signal bandwidth and the angle of the generated beam. The paper describes the theoretical background and details the differences between the various methods of excitation of ultrasonic guided waves, especially with the comb transducer method. Finite element simulations are presented to verify the analytical predictions and quantify the unidirectional and diffraction properties of the transmitted beam. Experiments conducted on an aluminum plate show striking agreement with finite element simulations, including the possibility of exciting a single mode in a narrow region at high frequency-thickness products. Experiments conducted on a CFRP plate demonstrates that the method can be adapted to other materials.

A Five-Level, 1-MHz, Class-D Ultrasonic Driver for Guided-Wave Transducer Arrays

This paper presents the design, characterization, and testing of an ultrasonic transducer driver capable of arbitrary waveform generation with a bandwidth of up to 1 MHz and an output range of ±96 V. The architecture is derived from bridged class-D switching amplifiers and has a five-level power stage. The proposed device was implemented with eight synchronized channels and an all-digital control circuitry to transmit guided-wave ultrasound signals using custom piezoelectric multi-element array transducers, allowing programmable mode selectivity.

Influence of aperture angles and design focal depths on the performance of point-focusing shear vertical wave electromagnetic acoustic transducers

Electromagnetic acoustic transducers (EMATs) with concentric meander-line (CML) coils possess the capability of producing point-focusing shear vertical (PFSV) waves. For the CML coil, an intercepted circular arc of the concentric circle with a continuously changing spacing, the aperture angle is a key factor effecting the point-focusing performance. Thus, the influence of aperture angles of CML coils on the point-focusing behavior of PFSV-EMATs is analyzed using the established finite element modeling in detail, which also considers the effect of lift-off distance on the signal amplitude. The beam directional pattern is characterized quantitatively by the half-power beam width, indicating the relationship between the aperture angle and beam width. In addition, since the focus offset is sensitive in depth direction, the effect of design focal depths on focal offset is also carefully studied. Three CML coils with an aperture angle of 30°, 90°, and 150° are fabricated by printed circuit board technique and experimentally analyzed; the experimental results are well consistent with the simulation results. These findings can be used to design optimized PFSV-EMATs with good point-focusing performance.

Influence of the Spatial Dimensions of Ultrasonic Transducers on the Frequency Spectrum of Guided Waves

Ultrasonic guided wave (UGW)-based condition monitoring has shown great promise in detecting, localizing, and characterizing damage in complex systems. However, the application of guided waves for damage detection is challenging due to the existence of multiple modes and dispersion. This results in distorted wave packets with limited resolution and the interference of multiple reflected modes. To develop reliable inspection systems, either the transducers have to be optimized to generate a desired single mode of guided waves with known dispersive properties, or the frequency responses of all modes present in the structure must be known to predict wave interaction. Currently, there is a lack of methods to predict the response spectrum of guided wave modes, especially in cases when multiple modes are being excited simultaneously. Such methods are of vital importance for further understanding wave propagation within the structures as well as wave-damage interaction. In this study, a novel method to predict the response spectrum of guided wave modes was proposed based on Fourier analysis of the particle velocity distribution on the excitation area. The method proposed in this study estimates an excitability function based on the spatial dimensions of the transducer, type of vibration, and dispersive properties of the medium. As a result, the response amplitude as a function of frequency for each guided wave mode present in the structure can be separately obtained. The method was validated with numerical simulations on the aluminum and glass fiber composite samples. The key findings showed that it can be applied to estimate the response spectrum of a guided wave mode on any type of material (either isotropic structures, or multi layered anisotropic composites) and under any type of excitation if the phase velocity dispersion curve and the particle velocity distribution of the wave source was known initially. Thus, the proposed method may be a beneficial tool to explain and predict the response spectrum of guided waves throughout the development of any structural health monitoring system.

A Guided Wave Sensor Enabling Simultaneous Wavenumber-Frequency Analysis for Both Lamb and Shear-Horizontal Waves

Guided waves in plate-like structures have been widely investigated for structural health monitoring. Lamb waves and shear horizontal (SH) waves, two commonly used types of waves in plates, provide different benefits for the detection of various types of defects and material degradation. However, there are few sensors that can detect both Lamb and SH waves and also resolve their modal content, namely the wavenumber-frequency spectrum. A sensor that can detect both waves is desirable to take full advantage of both types of waves in order to improve sensitivity to different discontinuity geometries. We demonstrate that polyvinylidene difluoride (PVDF) film provides the basis for a multi-element array sensor that detects both Lamb and SH waves and also measures their modal content, i.e., the wavenumber-frequency spectrum.

An Adaptive Array Excitation Scheme for the Unidirectional Enhancement of Guided Waves

Control over the direction of wave propagation allows an engineer to spatially locate defects. When imaging with longitudinal waves, time delays can be applied to each element of a phased array transducer to steer a beam. Because of the highly dispersive nature of guided waves (GWs), this beamsteering approach is suboptimal. More appropriate time delays can be chosen to direct a GW if the dispersion relation of the material is known. Existing techniques, however, need a priori knowledge of material thickness and acoustic velocity, which change as a function of temperature and strain. The scheme presented here does not require prior knowledge of the dispersion relation or properties of the specimen to direct a GW. Initially, a GW is generated using a single element of an array transducer. The acquired waveforms from the remaining elements are then processed and retransmitted, constructively interfering with the wave as it travels across the spatial influence of the transducer. The scheme intrinsically compensates for the dispersion of the waves, and thus can adapt to changes in material thickness and acoustic velocity. The proposed technique is demonstrated in simulation and experimentally. Dispersion curves from either side of the array are acquired to demonstrate the scheme's ability to direct a GW in an aluminum plate. The results show that unidirectional enhancement is possible without a priori knowledge of the specimen using an arbitrary pitch array transducer. The experimental results show a 34-dB enhancement in one direction compared with the other.

Tailoring the excitation of fundamental flexural guide waves in coated bone by phase-delayed array: two-dimensional simulations

The fundamental flexural guided wave (FFGW) enables ultrasonic assessment of cortical bone thickness. In vivo, it is challenging to detect this mode, as its power ratio with respect to disturbing ultrasound is reduced by soft tissue covering the bone. A phase-delayed ultrasound source is proposed to tailor the FFGW excitation in order to improve its power ratio. This situation is analyzed by 2D finite-element simulations. The soft tissue coating (7-mm thick) was simulated as a fluid covering an elastic plate (bone, 2-6 mm thick). A six-element array of emitters on top of the coating was excited by 50-kHz tone bursts so that each emitter was appropriately delayed from the previous one. Response was recorded by an array of receivers on top of the coating, 20-50 mm away from the closest emitter. Simulations predicted that such tailored/phase-delayed excitations should improve the power ratio of FFGW by 23 ± 5 dB, independent of the number of emitters (N). On the other hand, the FFGW magnitude should increase by 5.8 ± 0.5 dB for each doubling of N. This suggests that mode tailoring based on phase-delayed excitation may play a key role in the development of an in vivo FFGW assessment.

Mode perturbation method for optimal guided wave mode and frequency selection

With a thorough understanding of guided wave mechanics, researchers can predict which guided wave modes will have a high probability of success in a particular nondestructive evaluation application. However, work continues to find optimal mode and frequency selection for a given application. This "optimal" mode could give the highest sensitivity to defects or the greatest penetration power, increasing inspection efficiency. Since material properties used for modeling work may be estimates, in many cases guided wave mode and frequency selection can be adjusted for increased inspection efficiency in the field. In this paper, a novel mode and frequency perturbation method is described and used to identify optimal mode points based on quantifiable wave characteristics. The technique uses an ultrasonic phased array comb transducer to sweep in phase velocity and frequency space. It is demonstrated using guided interface waves for bond evaluation. After searching nearby mode points, an optimal mode and frequency can be selected which has the highest sensitivity to a defect, or gives the greatest penetration power. The optimal mode choice for a given application depends on the requirements of the inspection.

Numerical simulation of nonlinear Lamb waves used in a thin plate for detecting buried micro-cracks

Compared with conventional linear ultrasonic inspection methods, which are sensitive only to severe defects, nonlinear ultrasonic inspection methods are better for revealing micro-cracks in thin plates. However, most nonlinear ultrasonic inspection methods have only been experimentally investigated using bulk or Rayleigh waves. Numerical studies, especially numerical simulations of Lamb ultrasonic waves, have seldom been reported. In this paper, the interaction between nonlinear S0 mode Lamb waves and micro-cracks of various lengths and widths buried in a thin metallic plate was simulated using the finite element method (FEM). The numerical results indicate that after interacting with a micro-crack, a new wave-packet was generated in addition to the S0 mode wave-packet. The second harmonics of the S0 mode Lamb waves and the new wave-packet were caused by nonlinear acoustic effects at the micro-crack. An amplitude ratio indicator is thus proposed for the early detection of buried micro-cracks.

Numerical and experimental analysis of unidirectional meander-line coil electromagnetic acoustic transducers

The elastic waves generated by traditional meander-line coil electromagnetic acoustic transducers (EMATs) propagate in two directions, overlapping the echo signals from defects with the same distances, and the defect echo signal is hard to distinguish from the edge-reflected signal when the EMATs are near the edge of a specimen. In this paper, a unidirectional EMAT with two meander-line coils is proposed. A finite element model is used to simulate the directivity of the Rayleigh and shear vertical waves generated by these EMATs. Six transducers are fabricated using the printed circuit technique. The unidirectional Rayleigh wave and shear vertical wave are tested, and the results agree well with the simulation.

A single probe spatial averaging technique for guided waves and its application to surface wave rail inspection

The nondestructive testing of structures using guided waves requires systems with high mode selectivity. Usually this is achieved with relatively complex probes comprising multiple transducer rings or arrays. For the rapid inspection of very long structures with only partial access to the waveguide, this may not be a viable solution. In this paper we present a very flexible alternative whereby a simple robust probe is scanned along the wave guide, and the acquired scan data is used for customizing the mode selectivity at the postprocessing stage. The characteristics of this spatial averaging method are discussed using a simple analytical model and compared to an existing linear array technique. The mode selectivity is found to be mainly limited by the uncertainty of the phase velocity assumed for the mode of interest. The method was successfully applied to surface wave rail inspection and was found to suppress unwanted modes very efficiently.

Generation and detection of guided waves using PZT wafer transducers

We report here the use of finite element simulation and experiments to further explore the operation of the wafer transducer. We have separately modeled the emission and detection processes. In particular, we have calculated the wave velocities and the received voltage signals due to A0 and S0 modes at an output transducer as a function of pulse center frequency. These calculations include the effects of finite pulse width, pulse dispersion, and the detailed interaction between the piezoelectric element and the transmitting medium. We show that the received signals for A0 and S0 modes have maxima near the frequencies predicted from the previously published point-force model.

Signal processing for damage detection using two different array transducers

This work describes an investigation into the development of a new health monitoring system for aeronautical applications. The health monitoring system is based on the emission and reception of Lamb waves by multi-element piezoelectric transducers (i.e., arrays) bonded to the structure. The emitter array consists of three different elementary bar transducers. These transducers have the same thickness and length but different widths. The receiver array has 32 same elements. This system offers the possibility to understand the nature of the generated waves and to determine the sensitivity of each mode to possible damage. It presents two principal advantages: Firstly, by exciting all elements in phase, it is possible to generate several Lamb modes in the same time. Secondly, the two-dimensional fourier transform (2D-FT) of the received signal can be easily computed. Experimental results concerning an aluminum plate with different hole sizes will be shown. The A0-, S0-, A1-, S1- and S2-modes are generated at the same time. This study shows that the A0 mode seems particularly interesting to detect flaws of this geometrical type.

Omni-directional guided wave transducer arrays for the rapid inspection of large areas of plate structures

Omni-directional guided wave array transducers contain a circular pattern of elements that individually behave as omni-directional point transmitters or receivers. The data set acquired from such an array contains time-domain signals from each permutation of transmitter and receiver. A phased addition algorithm is developed that allows an omni-directional, B-scan image of the surrounding plate to be synthesized from any geometry of array. Numerically simulated data from a single reflector is used to test the performance of the algorithm. The results from an array containing a fully populated circular area of elements (Type I array) are found to be good, but those from an array containing a single ring of elements (Type II array) contain many large side-lobes. An enhancement to the basic-phased addition algorithm is presented that uses deconvolution to suppress these side-lobes. The deconvolution algorithm enables a Type II array to equal the performance of a Type I array of the same overall diameter. The effect of diameter on angular resolution is investigated. Experimental data obtained from a guided wave array containing electromagnetic acoustic transducers (EMAT) elements for exciting and detecting the So Lamb wave mode in a 5-mm thick aluminium plate are processed with both algorithms and the results are discussed.

Design of optimal configuration for generating A0 Lamb mode in a composite plate using piezoceramic transducers

This work concerned a technique for a health monitoring system based on the generation and sensing of Lamb waves in composite structures by thin surface-bonded piezoceramic transducers. The objective was to develop transducers that are adapted for the damage detection in orthotropic composites. The key problem with the investigated Lamb waves was to select a mode to be sensitive to the damage. A hybrid modeling technique was therefore used to conceive transducers that were adapted to achieve such a feature. This modeling technique enabled studying the influence of the transducer characteristics on the Lamb waves propagating in orthotropic plates. It was demonstrated that a Lamb mode could be generated dominantly to other modes by using a multi-element transducer. The effectiveness of this technique was successfully verified experimentally on composite plates. It was shown that the dominant Lamb mode, obtained by use of dual-element transducers, was an appropriate mode for successfully detecting a damage in composites.

A finite element analysis of the time-delay periodic ring arrays for guided wave generation and reception in hollow cylinders

A new guided wave transducer model, time-delay periodic ring arrays (TDPRAs), is proposed and investigated in this paper for guided cylindrical wave generation and reception in hollow cylinders with application interests focusing on non-destructive testing (NDT) of piping/tubing. A finite element simulation has been performed for axisymmetric guided-mode excitation and reception with TDPRAs. By arranging a proper configuration of the time-delay profile and the electric-connection pattern of a ring array, unidirectional excitation and reception of guided waves can be achieved. The numerical results are obtained for the first three axisymmetrical modes and are compared with respect to generation efficiency and mode selectivity. Parametric influences on the performance of TDPRAs are discussed, combining a 2-D phase velocity-frequency spectrum approach with the mode dispersion and displacement structure analyses. The identification of converted modes in guided cylindrical wave reflections with a flexible TDPRA receiver has also been studied through sample notch reflection.

Implementing guided wave mode control by use of a phased transducer array

A multi-channel time-delay system has been built and applied to a transducer array for implementing guided wave mode control. The time-delay system has a capability of sending high energy controllable tone-burst signals from eight independent channels with arbitrary time delays from 0 to 30 microseconds with resolution of 0.025 microsecond. Software time delays are also provided for summing up received signals of each channel. Theoretical discussions indicate the impact of the time delay capability on the bandwidth and sensitivity improvement of a transducer array for guided wave generation. Determination of both physical and software time delay values is based on a knowledge of dispersion curves and element spacing. Based on reference signals, a non-knowledge-based automatic time-delay searching algorithm was introduced for guided wave mode selection. Experiments were conducted with a phased comb transducer array mounted on a carbon steel pipe. The experimental results show that signal to noise ratio has been greatly improved by use of the time-delay system. Some other benefits of the phased array, including unidirection generation and mode control flexibility, are discussed.

Synthetic phase tuning of guided waves

A novel method has been developed to generate and manipulate multi-mode guided waves. This technique uses a linear phased array whose elements are activated according to a prescribed time delay profile obtained from the dispersion curves. It is shown that a desired guided wave mode can be tuned by synthetically constructing a virtual wave from individually acquired waveform data. In addition to the development of such a synthetic phase tuning (SPT) technique, a pseudo pulse-echo (PPE) operation scheme is also developed for nondestructive testing. Experimental results are compared with those obtained by more traditional techniques using variable angle wedges and array transducers. It was shown that the new technique is convenient, robust, and flexible in utilizing multi-mode guided waves for nondestructive evaluation (NDE). It is a dynamic method that can produce desired guided wave modes propagating in the desired direction without any mechanical alignment. The advantages and limitations of the technique are addressed.