Lamb Wave Dispersion Research Articles

Time-frequency energy density precipitation method for time-of-flight extraction of narrowband Lamb wave detection signals.

The time-of-flight of the Lamb wave provides an important basis for defect evaluation in metal plates and is the input signal for Lamb wave tomographic imaging. However, the time-of-flight can be difficult to acquire because of the Lamb wave dispersion characteristics. This work proposes a time-frequency energy density precipitation method to accurately extract the time-of-flight of narrowband Lamb wave detection signals in metal plates. In the proposed method, a discrete short-time Fourier transform is performed on the narrowband Lamb wave detection signals to obtain the corresponding discrete time-frequency energy density distribution. The energy density values at the center frequency for all discrete time points are then calculated by linear interpolation. Next, the time-domain energy density curve focused on that center frequency is precipitated by least squares fitting of the calculated energy density values. Finally, the peak times of the energy density curve obtained relative to the initial pulse signal are extracted as the time-of-flight for the narrowband Lamb wave detection signals. An experimental platform is established for time-of-flight extraction of narrowband Lamb wave detection signals, and sensitivity analysis of the proposed time-frequency energy density precipitation method is performed in terms of propagation distance, dispersion characteristics, center frequency, and plate thickness. For comparison, the widely used Hilbert-Huang transform method is also implemented for time-of-flight extraction. The results show that the time-frequency energy density precipitation method can accurately extract the time-of-flight with relative error of <1% and thus can act as a universal time-of-flight extraction method for narrowband Lamb wave detection signals.

The influence of the initial stresses on Lamb wave dispersion in pre-stressed PZT/Metal/PZT sandwich plates

Within the scope of the plane-strain state, by utilizing the three-dimensional linearized theory of elastic waves in initially stressed piezoelectric and elastic materials, Lamb wave propagation and the influence of the initial stresses on this propagation in a sandwich plate with pre-stressed piezoelectric face and pre-stressed metal elastic core layers are investigated. Dispersion equations are derived for the extensional and flexural Lamb waves and, as a result of numerical solution to these equations, the corresponding dispersion curves for the first (fundamental) and second modes are constructed. Concrete numerical results are obtained for the cases where the face layers' materials are PZT-2 or PZT-6B, but the material of the middle layer is Steel (St) or Aluminum (Al). Sandwich plates PZT-2/St/PZT-2, PZT-2/Al/PZT-2, PZT-6B/St/PZT-6B and PZT-6B/Al/PZT-6B are examined and the influence of the problem parameters such as piezoelectric and dielectric constants, layer thickness ratios and third order elastic constants of the St and Al on the effects of the initial stresses on the wave propagation velocity is studied.

On the Use of Ultrasound-Based Technology for Cargo Inspection

A new guided wave imaging application for fast, low-cost ultrasound-based cargo scanning system is proposed. The ultimate goal is the detection of high-atomic-number, shielding containers used to diminish the radiological signature of nuclear threats. This ultrasonic technology has the potential to complement currently deployed X-ray-based radiographic systems, thus enhancing the probability of detecting nuclear threats. An array of ultrasonic transceivers can be attached to the metallic structure of the cargo to create a guided Lamb wave. Guided medium thickness and composition variation creates reflections whose placement can be revealed by means of an imaging algorithm. The knowledge of the reflection position provides information about the shielding metallic container location inside the cargo. Moreover, due to the low coupling between metallic and nonmetallic surfaces, only the footprint of metallic containers shows up in the imaging results, thus avoiding false positives from plastic or wooden assets. As imaging capabilities are degraded if working with dispersive Lamb wave modes, the operating frequency is tuned to provide a tradeoff between low dispersion and real-time image resolution. Reflected waves in the guided domain bounds may limit the performance of imaging methods for guided media. This contribution proposes a solution based on real-time Fourier domain analysis, where plane wave components can be filtered out, thus removing nondesired contributions from bounds. Several realistic examples, scaled due to limited calculation capabilities of the available computational resources, are presented in this work, showing the feasibility of the proposed method.

Lamb waves dispersion curves for diamond based piezoelectric layered structure

The presence of spurious peaks in the amplitude-frequency response of diamond based piezoelectric layered structure was shown. Excitation of such peaks results in deterioration of an useful acoustical signal. It was shown that such spurious peaks should be associated with Lamb waves in a layered structure. By means of FEM analysis, the propagation of acoustic waves of different types in the piezoelectric layered structure “Al/AlN/Mo/(100) diamond” has been investigated in detail. By analyzing the elastic displacement patterns at frequencies from 0 up to 250 MHz, a set of all the possible acoustic waves, especially Lamb modes, have been studied, and dispersive curves of phase velocity have been plotted. A revised classification of Lamb modes has been introduced.

Detecting the thickness mode frequency in a concrete plate using backward wave propagation.

Material stiffness and plate thickness are the two key parameters when performing quality assurance/quality control on pavement structures. In order to estimate the plate thickness non-destructively, the Impact Echo (IE) method can be utilized to extract the thickness resonance frequency. An alternative to IE for estimating the thickness resonance frequency of a concrete plate, and to subsequently enable thickness determination, is presented in this paper. The thickness resonance is often revealed as a sharp peak in the frequency spectrum when contact receivers are used in seismic testing. Due to a low signal-to-noise ratio, IE is not ideal when using non-contact microphone receivers. In studying the complex Lamb wave dispersion curves at a frequency infinitesimally higher than the thickness frequency, it is seen that two counter-directed waves occur at the same frequency but with phase velocities in opposite directions. Results show that it is possible to detect the wave traveling with a negative phase velocity using both accelerometers and air-coupled microphones as receivers. This alternative technique can possibly be used in non-contact scanning measurements based on air-coupled microphones.

Lamb wave dispersion in a PZT/metal/PZT sandwich plate with imperfect interface

The Lamb wave dispersion in a PZT/Metal/PZT sandwich plate is investigated by employing the exact linear equations of electro-elastic waves in piezoelectric materials within the scope of the plane-strain state. It is assumed that at the interfaces between the piezoelectric face layers and metal core layer, shear-spring and normal-spring type imperfect conditions are satisfied. The degree of this imperfectness is estimated through the corresponding shear-spring and normal-spring type parameters which appear in the contact condition characterizing the transverse and normal displacements’ discontinuity. The corresponding dispersion equation is derived, and as a result of the numerical solution to this equation, the dispersion curves are constructed for the first and second lowest modes in the cases where the material of the face layers is PZT and the material of the middle layer is Steel (St). Consequently, for the PZT/St/PZT sandwich plate, the study of the influence of the problem parameters such as the piezoelectric and dielectric constants, layer thickness ratios, non-dimensional shear-spring, and normal-spring type parameters, is carried out. In particular, it is established that the imperfectness of the contact between the layers of the plate causes a decrease in the values of the wave propagation velocity.

A study of adhesion between dental cement and dentin using non-destructive ultrasonic testing

The retention of indirect dental restoration is reliant on the degree of the adhesion between dental materials and dentin. In this work, we introduce a new approach to characterise the cement-dentin interface using a Brekhovskikh model. This model is used to study the propagation of acoustic waves in a multilayered medium. The reflection coefficient of plane waves has been calculated. Then, the Lamb waves dispersion curves for the considered media have been produced. The difference between the acoustic properties of good and bad adhesion has been found. The amplitude of signal reflection from the cement-dentine interface is higher in the case of the bad bonding than in the case of good adhesion. The analysis of dispersion curves shows that the behaviour of some modes strongly depends on the quality of bonding. The obtained results demonstrate that ultrasound method is a valuable method for analysis of cement-dentin interface.

Defect detection and location in switch rails by acoustic emission and Lamb wave analysis: A feasibility study

An acoustic emission (AE) based approach is proposed in this study to identify and locate newly initiated defects or the propagation of existing defects in railroad switch rails. Defect-induced AE signals are identified through frequency analysis, as frequencies of these signals are much higher than those induced by structural vibration. Continuous wavelet transform (CWT) is employed to analyze the Lamb wave dispersion of the detected signal, so that two characteristic points can be selected on the CWT contour map to locate the defect. Using this approach, defects in a damaged switch rail can be located using a single sensor.

Bayesian parameter identification of orthotropic composite materials using Lamb waves dispersion curves measurement

This paper deals with the problem of elastic constant identification in thin plates made of orthotropic composite materials. The approach is based on the analysis of Lamb wave propagation and the related dispersion curves to find the underlying material elastic constants. In the proposed implementation a scanning laser Doppler vibrometer is used to measure Lamb wave dispersion curves. The Local Interaction Simulation Approach is used simultaneously to find a solution to a high-frequency wave propagation problem. The experimental and simulated data are combined in a Bayesian framework for parameter identification which is robust in condition of parameter, modeling and measurement uncertainty. The results are discussed and compared with the results from a deterministic optimization.

Comparison of laminate stiffness as measured by three experimental methods

Three independent stiffness measurement techniques are applied to characterize virgin glass fiber laminates. Natural frequency based measurements of laminate stiffness are compared to results from simple quasi-static testing and Lamb wave dispersion curves. Genetic algorithm (GA) and a modified two-stage Simplex optimization are employed to solve parameter identification inverse problems. The two-stage Simplex method is shown to converge to similar solutions as global genetic algorithms for Lamb wave optimization. The identified elastic and shear moduli show very good agreement, confirming the feasibility of these methods for material characterization. Poisson's ratios on the other hand were not reliably obtained from these two indirect methods due to low sensitivity.

A rapid, fully non-contact, hybrid system for generating Lamb wave dispersion curves

A rapid, fully non-contact, hybrid system which encompasses an air-coupled transducer (ACT) and a laser Doppler vibrometer (LDV) is presented for profiling A0 Lamb wave dispersion of an isotropic aluminum plate. The ACT generates ultrasonic pressure incident upon the surface of the plate. The pressure waves are partially refracted into the plate. The LDV is employed to measure the out-of-plane velocity of the excited Lamb wave mode at some distances where the Lamb waves are formed in the plate. The influence of the ACT angle of incidence on Lamb wave excitation is investigated and Snell’s law is used to directly compute Lamb wave dispersion curves including phase and group velocity dispersion curves in aluminum plates from incident angles found to generate optimal A0 Lamb wave mode. The measured curves are compared to results obtained from a two-dimensional (2-D) Fast Fourier transform (FFT), Morlet wavelet transform (MWT) and theoretical predictions. It was concluded that the experimental results obtained using Snell’s law concept are well in accordance with the theoretical solutions. The high degree of accuracy in the measured data with the theoretical results proved a high sensitivity of the air-coupled and laser ultrasound in characterizing Lamb wave dispersion in plate-like structures. The proposed non-contact hybrid system can effectively characterize the dispersive relation without knowledge of neither the materials characteristics nor the mathematical model.

Measurement of Quantitative Viscoelasticity of Bovine Corneas Based on Lamb Wave Dispersion Properties

The viscoelastic properties of the human cornea can provide valuable information for clinical applications such as the early detection of corneal diseases, better management of corneal surgery and treatment and more accurate measurement of intra-ocular pressure. However, few techniques are capable of quantitatively and non-destructively assessing corneal biomechanics in vivo. The cornea can be regarded as a thin plate in which the vibration induced by an external vibrator propagates as a Lamb wave, the properties of which depend on the thickness and biomechanics of the tissue. In this study, pulses of ultrasound radiation force with a repetition frequency of 100 or 200 Hz were applied to the apex of corneas, and the linear-array transducer of a SonixRP system was used to track the tissue motion in the radial direction. Shear elasticity and viscosity were estimated from the phase velocities of the A0 Lamb waves. To assess the effectiveness of the method, some of the corneas were subjected to collagen cross-linking treatment, and the changes in mechanical properties were validated with a tensile test. The results indicated that the shear modulus was 137 ± 37 kPa and the shear viscosity was 3.01 ± 2.45 mPa·s for the group of untreated corneas and 1145 ± 267 kPa and was 0.16 ± 0.11 mPa·s for the treated group, respectively, implying a significant increase in elasticity and a significant decrease in viscosity after collagen cross-linking treatment. This result is in agreement with the results of the mechanical tensile test and with reports in the literature. This initial investigation illustrated the ability of this ultrasound-based method, which uses the velocity dispersion of low-frequency A0 Lamb waves, to quantitatively assess both the elasticity and viscosity of corneas. Future studies could discover ways to optimize this system and to determine the feasibility of using this method in clinical situations.

Linearly dispersive signal construction of Lamb waves with measured relative wavenumber curves

Dispersion compensation is a vital issue in Lamb wave identification. Except for time reversal process (TRP), the commonly used compensation methods require the priori-knowledge of Lamb wave dispersion characteristics, which is usually derived in theory using the structure material parameters. However, the parameters could be probably unavailable, making the theoretical wavenumber relations hard to be attained. For the practical situation and considering the complexity of absolute wavenumber determination, linearly dispersive signal construction (LDSC) is presented for dispersion compensation of Lamb waves in this paper. LDSC can be performed not only with theoretical wavenumber curves but also with relative wavenumber curves, which can be easily measured without any structure material parameters. Thus, LDSC has high potential in Lamb wave detection for unknown structures. After the basic LDSC principle is fully explored based on the sensing model simplified in frequency domain, the numerical realization for LDSC is discussed. Then, a narrowband spectroscopy method is introduced for relative wavenumber curve measurement, and the applicability of LDSC with the measured relative wavenumber curves is theoretically investigated, which is subsequently validated with an aluminum plate experiment. Finally, associated with the traditional delay-and-sum algorithm, LDSC is used, as a typical application instance, for high spatial resolution Lamb wave imaging. The efficiency of the proposed LDSC and LDSC-based imaging is demonstrated by the experimental study on a glass fiber reinforced composite plate with unknown material parameters.

Noncontact depth-resolved micro-scale optical coherence elastography of the cornea.

High-resolution elastographic assessment of the cornea can greatly assist clinical diagnosis and treatment of various ocular diseases. Here, we report on the first noncontact depth-resolved micro-scale optical coherence elastography of the cornea achieved using shear wave imaging optical coherence tomography (SWI-OCT) combined with the spectral analysis of the corneal Lamb wave propagation. This imaging method relies on a focused air-puff device to load the cornea with highly-localized low-pressure short-duration air stream and applies phase-resolved OCT detection to capture the low-amplitude deformation with nano-scale sensitivity. The SWI-OCT system is used here to image the corneal Lamb wave propagation with the frame rate the same as the OCT A-line acquisition speed. Based on the spectral analysis of the corneal temporal deformation profiles, the phase velocity of the Lamb wave is obtained at different depths for the major frequency components, which shows the depthwise distribution of the corneal stiffness related to its structural features. Our pilot experiments on ex vivo rabbit eyes demonstrate the feasibility of this method in depth-resolved micro-scale elastography of the cornea. The assessment of the Lamb wave dispersion is also presented, suggesting the potential for the quantitative measurement of corneal viscoelasticity.

Structural damping of composite materials using combined FE and lamb wave method

The article presents the methodology for finding material damping capacity at higher frequency and at relatively lower amplitudes. The Lamb wave dispersion theory and loss less finite element model is used to find the damping capacity of composite materials. The research has been focused on high frequency applications materials. The method was implemented on carbon fiber reinforced polymer (CFRP) and glass fiber reinforced polymer (GFRP) plates. The Lamb waves were generated using ultrasonic pulse generator setup. The hybrid method has been explored in this article and the results have been compared with bandwidth methods available in the literature.

Evaluation of dispersion characteristics of multimodal guided waves using slant stack transform

In this paper slant stack (SL) transform is presented and its application for processing of multi-modal dispersive Lamb waves snapshots is proposed. The SL transform can facilitate the evaluation of dispersion curves based on a set of signals captured at the structure׳s surface. The presented technique leads explicitly to the frequency-phase-velocity representation of the processed signals. Theory behind the technique is presented and the SL results are compared to those obtained using the 2D discrete Fourier transform. The SL is used to process data acquired from an aluminum plate and to investigate anisotropic properties of a composite plate.

Obtaining complementary Lamb wave dispersion information by two signal processing methods on an all-optical non-contact configuration

We present the experimental realisation of an all-optical non-contact tool for the extraction of the Lamb wave propagation dispersion characteristics in thin plates. We describe and assess two different signal processing approaches used to transform the acoustic impulse response optically generated and measured into a frequency response from which to extract the Lamb wave dispersion curves. We demonstrate that the two different techniques enable complementary portions of the ultrasonic transmission path to be addressed.Finally we demonstrate the sensitivity of this approach, in terms of material testing, to thermal changes in the ultrasonic transfer function and its capability to respond to damage to the sample structure.

Derivation and experimental validation of Lamb wave equations for an n-layered anisotropic composite laminate

Lamb waves are ultrasonic guided waves that propagate between two parallel free surfaces and their use for damage detection has been widely explored and demonstrated. Damage in materials/structures can be detected by analyzing the difference between the phase/group velocity and the loss of amplitude of Lamb waves on damaged and un-damaged specimens. The propagation characteristics of Lamb waves are described in the form of dispersion curves, which are plots of phase/group velocities versus the product of frequency-thickness generated by solving the Lamb wave equations. Lamb waves’ dispersion behaviors for isotropic materials are well established in the literature; however, such is not the case for the laminated composites. The most common methods for solving the Lamb wave equations in composites consist of using laminated plate theory or 3D linear elasticity by assuming an orthotropic and/or higher symmetry. This assumption may not be true, if the actuators and sensors in an orthotropic or transversely isotropic laminates are installed in a non-principle direction or the layup is symmetric but not balanced.This paper presents a full derivation of Lamb wave equations for n-layered monoclinic composite laminates based on linear 3D elasticity by considering the displacement fields in all three directions using the partial wave technique in combination with the Global Matrix (GM) approach. In the partial wave technique, the principle of superposition of three upward and three downward travelling plane waves are assumed in order to satisfy the associated boundary conditions. The bounded upper and lower surfaces reflect the waves and the combination of these reflections going towards the upper or lower interfaces results in the propagating guided waves. The GM approach is used to assemble all the equations from each layer to form a global, unified matrix that describes the displacement and stress fields along the entire laminate associated with the wave propagation. A robust method for numerically solving the Lamb wave equations is also presented.The presented method was verified experimentally by analyzing the propagation of Lamb waves in two different composite panels constructed out of unidirectional carbon-fiber epoxy prepreg and fiber-metal laminate (GLARE 3-3/4). The panels were instrumented with lead zirconate titanate (PZT) piezoelectric sensors, which were excited at different frequencies ranging from 20kHz to 500kHz to generate and acquire the waves. The waves were excited and gathered at three different propagation angles of 0°, 45°, and 90° for the carbon-fiber epoxy laminate panel and at six different angles of 0°, 20°, 45°, 70° and 90° for the fiber-metal laminates (GLARE). The phase and group velocities of the fundamental symmetric (So) and anti-symmetric (Ao) Lamb waves were extracted by tracking the peaks of each individual wave phase and the wave envelope respectively using an in-house code developed in MATLAB. It was found that the presented 3D linear elasticity model followed the experimental data closely for both symmetric and anti-symmetric Lamb modes. The analytical method presented in this paper was able to predict the Lamb wave dispersion for both the carbon-fiber epoxy laminate and the hybrid fiber-metal laminate proving the robustness and versatility of the solution method.

Fully Noncontact Wave Propagation Imaging in an Immersed Metallic Plate with a Crack

This study presents a noncontact sensing technique with ultrasonic wave propagation imaging algorithm, for damage visualization of liquid-immersed structures. An aluminum plate specimen (400 mm × 400 mm × 3 mm) with a 12 mm slit was immersed in water and in glycerin. A 532 nm Q-switched continuous wave laser is used at an energy level of 1.2 mJ to scan an area of 100 mm × 100 mm. A laser Doppler vibrometer is used as a noncontact ultrasonic sensor, which measures guided wave displacement at a fixed point. The tests are performed with two different cases of specimen: without water and filled with water and with glycerin. Lamb wave dispersion curves for the respective cases are calculated, to investigate the velocity-frequency relationship of each wave mode. Experimental propagation velocities of Lamb waves for different cases are compared with the theoretical dispersion curves. This study shows that the dispersion and attenuation of the Lamb wave is affected by the surrounding liquid, and the comparative experimental results are presented to verify it. In addition, it is demonstrated that the developed fully noncontact ultrasonic propagation imaging system is capable of damage sizing in submerged structures.

A time–distance domain transform method for Lamb wave dispersion compensation considering signal waveform correction

In Lamb wave identification, time–distance domain mapping (TDDM) is one of the most popular methods for dispersion compensation. However, it is found that the processed signal waveforms are easily deformed by TDDM. To improve the compensation effect, a time–distance domain transform (TDDT) method is presented in this paper. In TDDT, both dispersion removal and signal waveform correction are accomplished to result in more convenience of dispersive signal interpretation. Instead of the complex back-propagation concept, only the basic Fourier transform (FT) properties are used to study the principle of TDDT. The realization of TDDT under broadband excitation and narrowband excitation is discussed, in which the signal waveform maintenance is of particular interest and the reason for TDDM disturbance of the signal waveforms is also investigated. Numerical simulations on A0 or S0 mode signals are implemented for the primary validation of TDDT. Then, in association with the traditional delay-and-sum algorithm, a high spatial resolution imaging method based on TDDT is developed. An experimental study is finally arranged to demonstrate the efficiency of TDDT and the TDDT-based imaging method.