Single Lamb Wave Mode Research Articles

Selective generation of Lamb modes by a moving continuous-wave laser.

This Letter focuses on the selectively non-contact generation of Lamb wave modes in plates by using a continuous-wave (CW) laser moving along sample surface. Compared with the generated Lamb waves with broadband, multiple modes (the existence of at least two modes at any given frequency) excited by a pulsed laser, the desired single narrowband mode of the Lamb wave can be generated by a moving CW laser, as long as the scanning speed matches the phase velocity of the mode. Moreover, the dispersion curves of the Lamb wave can be obtained directly from the power spectrum of the time-domain signal recorded at each laser's moving speed. Single A0 mode excitation, coupled resonance phenomenon of A0 mode and S0 mode, single S0 mode excitation, and high-order modes appeared successively as scanning speed increased. Especially, the excitation of the pure single S0 mode can be realized, which is suitable for propagation in the case of liquid loading. It is proposed, for the first time to the best of our knowledge, to realize the selection of a single Lamb wave mode by using the CW laser scanning method, which provides a brand-new way for laser ultrasonic excitation.

Nonpenetrating Damage Identification Using Hybrid Lamb Wave Modes from Hilbert-Huang Spectrum in Thin-Walled Structures

Lamb waves have shown promising advantages for damage identification in thin-walled structures. Multiple modes of Lamb wave provide diverse sensitivities to different types of damage. To sufficiently utilize damage-related wave features, damage indices were developed by using hybrid Lamb wave modes from Hilbert-Huang spectra. Damage indices were defined as surface integrals of Hilbert-Huang spectra on featured regions determined by time and frequency windowing. The time windowing was performed according to individual propagation velocity of different Lamb wave mode, while the frequency windowing was performed according to the frequency of excitation. By summing damage indices for all transmitter-receiver pairs, pixels were calculated to reconstruct a damage map to characterize the degree of damage at each location on structure. Both numerical and experimental validations were conducted to identify a nonpenetrating damage. The results demonstrated that the proposed damage indices using hybrid Lamb wave modes are more sensitive and robust than the one using single Lamb wave mode.

Selective generation of ultrasonic Lamb waves by electromagnetic acoustic transducers**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474361 and 11274388).

In this paper, we describe a modal expansion approach for the analysis of the selective generation of ultrasonic Lamb waves by electromagnetic acoustic transducers (EMATs). With the modal expansion approach for waveguide excitation, an analytical expression of the Lamb wave’s mode expansion coefficient is deduced, which is related to the driving frequency and the geometrical parameters of the EMAT’s meander coil, and lays a theoretical foundation for exactly analyzing the selective generation of Lamb waves with EMATs. The influences of the driving frequency on the mode expansion coefficient of ultrasonic Lamb waves are analyzed when the EMAT’s geometrical parameters are given. The numerical simulations and experimental examinations show that the ultrasonic Lamb wave modes can be effectively regulated (strengthened or restrained) by choosing an appropriate driving frequency of EMAT, with the geometrical parameters given. This result provides a theoretical and experimental basis for selectively generating a single and pure Lamb wave mode with EMATs.

Lamb-wave-based two-dimensional areal scan damage imaging using reverse-time migration with a normalized zero-lag cross-correlation imaging condition

This article presents a two-dimensional, non-contact, areal scanning system to image and quantify multiple sites of damage in isotropic plates using reverse-time migration with a normalized zero-lag cross-correlation imaging condition. The hybrid system composed of a single piezoelectric actuator mounted onto the structure and a laser Doppler vibrometer for two-dimensional scan. The laser Doppler vibrometer scanned a region in the vicinity of the lead zirconate titanate actuator to capture the scattered wavefield introduced by the damage. The proposed damage imaging technique takes into account the amplitude, phase, and all the frequency content of the single-mode Lamb waves propagating in the plate; thus, the size of multiple sites of damage can be imaged without bias, regardless of the damage locations. Damage image quality was used as a metric to compare two-dimensional areal scans and linear scans as well as to compare the proposed method with existing imaging conditions. The experimental results show that the two-dimensional reverse-time migration/normalized zero-lag cross-correlation technique is capable of imaging and quantification of multiple damage sites in an aluminum plate using a single lead zirconate titanate actuator and a nearby, areal laser Doppler vibrometer scan.

Excitation of Single-Mode Lamb Waves at High-Frequency-Thickness Products

Guided wave inspection is used extensively in petrochemical plants to check for defects such as corrosion. Long-range low-frequency inspection can be used to detect relatively large defects, while higher frequency inspection provides improved sensitivity to small defects, but the presence of multiple dispersive modes makes it difficult to implement. This paper investigates the possibility of exciting a single-mode Lamb wave with low dispersion at a frequency thickness of around 20 MHz-mm. It is shown by finite element (FE) analysis backed up by experiments that a signal dominated by the A1 mode can be generated, even in a region where many modes have similar phase velocities. The A1 mode has relatively little motion at the plate surface which means that only a small reflection is generated at features such as T-joints; this is verified numerically. It is also expected that it will be relatively unaffected by surface roughness or attenuative coatings. These features are very similar to those of the higher order mode cluster (HOMC) reported by other authors, and it is shown that the A1 mode shape is very similar to the deflected shape reported in HOMC.

Calculation of leaky Lamb waves with a semi-analytical finite element method

A semi-analytical finite element method (SAFE) has been widely used for calculating dispersion curves and mode shapes of guided waves as well as transient waves in a bar like structures. Although guided wave inspection is often conducted for water-loaded plates and pipes, most of the SAFE techniques have not been extended to a plate with leaky media. This study describes leaky Lamb wave calculation with the SAFE. We formulated a new solution using a feature that a single Lamb wave mode generates a harmonic plane wave in leaky media. Dispersion curves obtained with the SAFE agreed well with the previous theoretical studies, which represents that the SAFE calculation was conducted with sufficient accuracy. Moreover, we discussed dispersion curves, attenuation curves, and displacement distributions for total transmission modes and leaky plate modes in a single side and both two side water-loaded plate.

Lamb wave frequency–wavenumber analysis and decomposition

Lamb waves have shown great potentials in damage detection of thin-walled structures due to their long propagation capability and sensitivity to a variety of damage types. However, their practical adoption has been hindered due to the complexity caused by their multimodal nature. Various wave modes that propagate at various velocities in the structure make the interpretation of Lamb wave signals very difficult. It is desired that the modes can be separated for independent analysis or further employment. In this article, we present our studies on the multimodal Lamb wave propagation and wave mode decomposition using frequency–wavenumber analysis. Wave representation in the frequency–wavenumber domain is obtained using multidimensional Fourier transform, where various Lamb wave modes can be easily discerned. This allows for separating them or extracting a desired wave mode through a filtering process, thus making it possible to use a single-mode Lamb wave for the detection of a certain type of damage in structural health monitoring applications. To retain the temporal and spatial information that is lost during Fourier transformation, a novel wavenumber analysis is also presented. These concepts are illustrated through experimental testing where high spatial resolution wavefields are measured by a scanning laser Doppler vibrometer.

Time reversed Lamb wave for damage detection in a stiffened aluminum plate

According to the concept of time reversibility of the Lamb wave, in the absence of damage, a Lamb wave signal can be reconstructed at the transmitter location if a time reversed signal is sent back from the receiver location. This property is used for baseline-free damage detection, where the presence of damage breaks down the time reversibility and the mismatch between the reconstructed and the input signal is inferred as the presence of damage. This paper presents an experimental and a simulation study of baseline-free damage detection in a stiffened aluminum plate by time reversed Lamb wave (TRLW). In this study, single Lamb wave mode (A0) is generated and sensed using piezoelectric (PZT) transducers through specific transducer placement and amplitude tuning. Different stiffening configurations such as plane and T-stiffeners are considered. Damage cases of disbonding of stiffeners from the base plate, and vertical and embedded cracks in the stiffened plate, are studied. The results show that TRLW based schemes can efficiently identify the presence of damage in a stiffened plate.

Actuating frequency selection of single mode Lamb waves using single piezoelectric transducer

Considering the interaction between the piezoelectric transducer (PZT) and the plate, a frequency adjusting method of generating single mode Lamb waves using single piezoelectric transducer is presented in theory. The application of mode selection in Lamb wave structural health monitoring is experimentally given. The theory has the ability to predict the amplitude of each Lamb wave mode as a function of frequency for given plate material and thickness, and specific PZT size. Optimal actuating frequency can be identified at which the wave amplitude for a particular mode is maximized while the wave amplitudes for other modes are relatively minimized. Numerical results are presented to validate the theory and show the capability of single mode Lamb wave selection. Different frequencies that correspond to a preferential A0 mode, a preferential S0 mode, and both the A0 and the S0 modes are excited for damage imaging, respectively. The results show that the single Lamb wave mode detection can locate the damage more accurately, demonstrating the importance of the mode selection in Lamb wave structural health monitoring.

Study on Single Mode Lamb Wave Interaction with Defect of Plate by Finite Element Model

A finite element model was built for predicting the Lamb wave signals in isotropic material with defect. By acting optimized exciting condition, single mode Lamb wave was generated in the plate with defect. S0 mode and A0 mode are the main modes researched in this paper. A 2-D finite element model was built to analyze the reflection from the defect using S0 mode Lamb wave scattering approach. Complex wavelet transform was applied to extract envelope and arrival time of reflections from defect to evaluate the depth of defect. The predicted signals from finite element model were validated by experimental measurements. In comparison with the results between theory and experiment, it's concluded that the finite element model is effective for predicting the lamb wave signal on UNDE.

Minimizing influence of multi-modes and dispersion of electromagnetic ultrasonic lamb waves

Electromagnetic ultrasonic (EMU) Lamb waves excited by electromagnetic acoustic transducers (EMATs) possess many advantages in NDT. However, their characteristic multi-modes and dispersion are disadvantageous for inspection and restrict further improvements in their real applications. By deducing the excitation equation of EMU Lamb waves, the primary design parameters of EMATs and the characteristic equation of Lamb waves are combined, and excitation curves based on the excitation equation are plotted to aid the design of EMATs. The excitation characteristic of EMU Lamb waves on different thickness of plates is analyzed according to the excitation curves. The influence of multi-modes of EMU Lamb waves is minimized by choosing reasonable operating points and operating zones to excite a single-mode Lamb wave or multi-mode Lamb waves with identical or approximate propagation velocities. The influence of dispersion is minimized by searching corresponding points whose slope of group velocity tends to zero. The validity of the proposed method is verified by experiments.

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.

Damage detection on two-dimensional structure based on active Lamb waves

This paper deals with damage detection using active Lamb waves. The wavelet transform and empirical mode decomposition methods are discussed for measuring the Lamb wave's arrival time of the group velocity. An experimental system to diagnose the damage in the composite plate is developed. A method to optimize this system is also given for practical applications of active Lamb waves, which involve optimal arrangement of the piezoelectric elements to produce single mode Lamb waves. In the paper, the single mode Lamb wave means that there exists no overlapping among different Lamb wave modes and the original Lamb wave signal with the boundary reflection signals. Based on this optimized PZT arrangement method, five damage localizations on different plates are completed and the results using wavelet transform and empirical mode decomposition methods are compared.

Damage Localization on Two-Dimensional Structure Based on Wavelet Transform and Active Lamb Wave-Based Method

Damage characterization was carried out by comparing single mode sensor signals collected before and after the damage event. By subtracting the signals of both conditions from each other, a scatter signal is produced which can be used for damage localization. By using Gabor wavelet to analyze single mode Lamb wave recorded before damage and scatter signal, the difference of time-of-flight can be obtained. Combining with the ellipse technique, the localization experiment on fiberglass plate of dimension 100×100×2mm is completed.

Single mode Lamb waves in composite laminated plates generated by piezoelectric transducers

The technique of permanently attaching piezoelectric transducers to structural surfaces has demonstrated great potential for quantitative non-destructive evaluation and smart materials design. For thin structural members such as composite laminated plates, it has been well recognized that guided Lamb wave techniques can provide a very sensitive and effective means for large area interrogation. However, since in these applications multiple wave modes are generally generated and the individual modes are usually dispersive, the received signals are very complex and difficult to interpret. An attractive way to deal with this problem has recently been introduced by applying piezoceramic transducer arrays or interdigital transducer (IDT) technologies. In this paper, the acoustic wave field in composite laminated plates excited by piezoceramic transducer arrays or IDT is investigated. Based on dynamic piezoelectricity theory, a discrete layer theory and a multiple integral transform method, an analytical–numerical approach is developed to evaluate the input impedance characteristics of the transducer and the surface velocity response of the plate. The method enables the quantitative evaluation of the influence of the electrical characteristics of the excitation circuit, the geometric and piezoelectric properties of the transducer array, and the mechanical and geometrical features of the laminate. Numerical results are presented to validate the developed method and show the ability of single wave mode selection and isolation. The results show that the interaction between individual elements of the piezoelectric array has a significant influence on the performance of the IDT, and these effects can not be neglected even in the case of low frequency excitation. It is also demonstrated that adding backing materials to the transducer elements can be used to improve the excitability of specific wave modes.

Modelling of Lamb waves in composite laminated plates excited by interdigital transducers

The technique of permanently attaching interdigital transducers (IDT) to either flat or curved structural surfaces to excite single Lamb wave mode has demonstrated great potential for quantitative non-destructive evaluation and smart materials design, In this paper, the acoustic wave field in a composite laminated plate excited by an IDT is investigated. On the basis of discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the surface velocity response of the plate due to the IDTs excitation. In this approach, the frequency spectrum and wave number spectrum of the output of IDT are obtained directly. The corresponding time domain results are calculated by applying a standard inverse fast Fourier transformation technique. Numerical examples are presented to validate the developed method and show the ability of mode selection and isolation. A new effective way of transfer function estimation and interpretation is presented by considering the input wave number spectrum in addition to the commonly used input frequency spectrum. The new approach enables the simple physical evaluation of the influences of IDT geometrical features such as electrode finger widths and overall dimension and excitation signal properties on the input-output characteristics of IDT. Finally, considering the convenience of Mindlin plate wave theory in numerical computations as well as theoretical analysis, the validity is examined of using this approximate theory to design IDT for the excitation of the first and second anti-symmetric Lamb modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

Ultrasonic Excitation by Phase Velocity Scanning of Laser Beam and Application to Nondestructive Evaluation

It is essential for advanced nondestructive evaluation that single mode of acoustic waves be selectively generated. We have proposed the phase velocity scanning (PVS) method for this purpose. In this work, we improved the PVS method by using an acoustooptic deflector to scan a laser beam at high velocity with high repeatability. In aluminum plates, we succeeded to generate narrow-band single-mode Lamb waves, which propagated a distance more than 1.7 m. We propose to apply this method to detection of defects on large plate structures.

Diagnostic Lamb waves in an integrated piezoelectric sensor/actuatorplate: analytical and experimental studies

The objective of this study is to model the diagnostic transient waves in anintegrated piezoelectric sensor/actuator plate with a view to using it as a first steptowards establishing an entire structural health monitoring system and toprovide experimental verification of the proposed models. PZT ceramic disksare surface mounted on an aluminum plate acting as both actuators and sensorsto generate and collect A0 mode Lamb waves. Mindlin plate theory is adopted tomodel the propagating waves by taking both transverse shear and rotary inertiaeffects into account. Actuator and sensor models are both proposed. Theinteraction between an actuator and the host plate is modeled based on classicallamination theory. The converse piezoelectric effect of the actuator istreated as an equivalent bending moment applied to the host plate. The sensoracts as a capacitor that converts the sensed strain change into a voltageresponse. An analytical expression for the sensor output voltage in terms ofthe given input excitation signal is derived, and then experimental work isperformed to verify the accuracy of the analytical model. Experimental resultsshow that single-mode Lamb waves in the plate can be successfully generatedand collected through the integrated PZT disks. The experiment also shows thatthe predicted sensor output for both amplitude and phase agrees well withexperimentally collected data.

Single mode Lamb wave excitation in thin plates by Hertzian contacts

We present novel techniques to selectively excite the lowest order symmetric (So) and antisymmetric (Ao) Lamb wave modes in thin solid plates. Hertzian contacts are formed between the plates and the end of specially designed quartz rods which guide extensional waves generated by PZT-5H transducers bonded at their other end. Mode selectivity is achieved by applying shear and/or longitudinal traction at the edge or the surface of the plates according to the results of a two-dimensional normal mode theory. In aluminum plates, mode selectivity is measured as a function of frequency for different traction forces. With normal forces, Ao mode selectivity of more than 46 dB is obtained for fd<0.4 MHz mm. With antisymmetric shear traction at the edge of the plate, a selectivity exceeding 55 dB is achieved for single mode So operation.

Analysis and optimization of wedge transducers for Lamb wave excitation.

Wedge transducers are commonly used to excite and detect Lamb waves in solid plates for NDE purposes. In this paper, the analysis and design of wedge transducers for efficient, single mode Lamb wave excitation in general multilayered anisotropic plates is presented. The incident acoustic field distribution on the surface of the plate due to a wedge transducer with arbitrary apodization is calculated using the angular spectrum method. Then, the particle velocity and stress field distributions in the plate in response to this source is obtained by the surface impedance approach. This field distribution can be expressed as a sum of Lamb wave modes in the structure, since the Lamb waves form an orthogonal mode basis. Once the mode amplitudes are found, the excitation efficiency for the desired Lamb wave mode is calculated. The results indicate a trade‐off between efficiency and multimode excitation, as expected. To achieve both high efficiency and single mode excitation, an optimization scheme is used where the parameters involve the frequency of operation, dimension of the wedge, and the apodization function. The results of this analysis are presented for various practical examples.