Symmetric Lamb Mode Research Articles

Investigation of a Solid-State Tuning Behavior in Lithium Niobate.

Electric field-based frequency tuning of acoustic resonators at the material level may provide an enabling technology for building complex tunable filters. Tunable acoustic resonators were fabricated in thin plates (h/ λ ∼ 0.05 ) of X-cut lithium niobate (LiNbO3) (90°, 90°, ψ = 170° ). LiNbO3 is known for its large electromechanical coupling ( K 2 ) for the shear and symmetric Lamb modes (SH0: K 2 = 40 %, S0: K 2 = 30 %) in thin plates and, thus, applicability for low-insertion loss and wideband filter applications. We demonstrate the effect of a dc bias in X-cut LiNbO3 to shift the resonant frequency by ~0.4% through direct tuning of the resonator material. A nonlinear acoustic computation predicted 0.36% tuning, which was in excellent agreement with the tuning measurement. For X-cut, we predicted electrical tuning of the S0 mode up to 1.6% and for Y-cut the electrical tuning of the SH0 and S0 modes was up to 7.0% with K 2 = 27.1 %. The mechanism is based on the nonlinearities that exist in the piezoelectric properties of LiNbO3. The X-cut SH0 mode resonators were centered near 335 MHz and achieved a frequency tuning of 6 kHz/V through the application of a dc bias.

An enhanced Lamb wave virtual time reversal technique for damage detection with transducer transfer function compensation

The Lamb wave time reversal method has widely been investigated as a baseline-free damage detection technique for structural health monitoring. Due to the mode tuning effects from the transducer-wave interactions, even for a pristine wave path, the reconstructed signal waveform may differ much from the original excitation waveform. Consequently, it becomes difficult to distinguish the differences between undamaged and damaged wave paths. This article presents an enhanced Lamb wave virtual time reversal (VTR) algorithm with transducer transfer function compensation to eliminate the transducer influence for dispersive, multimodal Lamb waves. This VTR procedure builds upon a complete 2D analytical model for Lamb wave generation, propagation, and reception. The analytical solution shows that, with the transducer transfer function compensation, a perfect reconstruction of the original excitation waveform can be achieved for both symmetric and antisymmetric Lamb modes. In addition, finite element modeling and experimental validations are further performed to verify the enhanced time reversal procedure. Finally, a time reversal tomography experiment is conducted with a piezoelectric transducer array for structural damage imaging. The enhanced VTR method can achieve more accurate and robust damage imaging results. The paper finishes with discussion, concluding remarks, and suggestions for future work.

Analysis of the Directivity of Glass-Etalon Fabry-Pérot Ultrasound Sensors.

Planar glass-etalon Fabry-Pérot (FP) optical ultrasound sensors offer an alternative to piezoelectric sensors for the measurements of high-intensity focused ultrasound (HIFU) fields and other metrological applications. In this work, a model of the frequency-dependent directional response of the FP sensor was developed using the global matrix method, treating the sensor as a multilayered elastic structure. The model was validated against the experimentally measured directional response of an air-backed cover-slip FP sensor with well-known material properties. In addition, the model was compared with the measurements of an all-hard-dielectric sensor suitable for HIFU measurements. The model was then used to calculate modal dispersion curves for both glass-etalon sensors, allowing the features of the directional response to be linked to specific wave phenomena. The features in the directivity of the air-backed cover-slip sensor are due to guided Lamb waves. Symmetric Lamb modes give rise to regions of high sensitivity, whereas anti-symmetric modes cause regions of low sensitivity. For the all-hard-dielectric sensor, two features correspond to the water-substrate and water-spacer compressional and shear critical angles. A region of high sensitivity close to the shear critical angle is associated with a leaky-Rayleigh wave, which has a frequency-dependent phase speed. At higher frequencies, this feature is counteracted by a region of low sensitivity, which occurs when there is no difference in the vertical displacement of the mirrors forming the FP cavity. The model may be used to improve and optimize the design of FP sensors or could be used to assist with the accurate deconvolution of the directional response from array measurements in metrological and imaging applications.

Lensing in the Ultrasonic Domain using Negative Refraction Induced by Material Contrast

The focusing of ultrasound using topographic lenses, typically made of plates with step changes that cause an interaction between forward- and backward-propagating guided waves, has been widely studied in recent years. However, such ‘step-change’ lenses require precise machining and moreover, the thick-thin structure can be unstable during deployment in practical inspection applications. The work reported here follows from the insight that perhaps any approach to induce a mismatch in acoustical impedance as achieved by the step-change can also lead to focusing of ultrasonic guided waves. By carefully choosing the impedance pairing, a novel material contrast lens stacking Aluminium and Molybdenum plates in series is shown to achieve focusing of ultrasound through negative refraction. The interface between the two metals causes the interaction of the forward-propagating second symmetric Lamb mode S2 into the backward- propagating first symmetric S2b. The focusing of Lamb waves is demonstrated using numerical simulations validated by experiments. Comparison with a simple Aluminium-Aluminium plate combination brings out the underlying physics of focusing using the proposed material contrast lens. Simulation results showing super-resolution imaging using the proposed material contrast lens are also presented, demonstrating the power of the proposed approach. This report opens up the possibilities of developing new lensing devices for use in medical imaging and nondestructive evaluation, among other possible applications.

The nonlinear S0 Lamb mode in a plate with a linearly-varying thickness

The aim of this paper is to investigate propagation characteristics and the generation mechanism of the nonlinear lowest-order symmetric Lamb mode (S0) which propagates downslope in free elastic plates with slowly linearly varying-thickness. From theoretical analyses, in a low frequency-thickness product (fd) range, the S0 mode is slightly dispersive, it is easy to generate, and it approximately satisfies the principle of the phase velocity matching. Therefore, if a S0 mode is excited at a proper frequency in the low fd range, the amplitude of the second harmonic wave is linearly increasing in a certain propagating-distance, which is valuable for the practical NDE application of the second harmonic wave. Moreover, numerical simulations and experiments have been carried out to validate theoretical results. Our investigation of properties of the second harmonic wave can be applied to characterize and evaluate micro-structural damages in varying-thickness waveguides.

Ultra-fast tuning of refractive index in Lithium Niobate slab by GHz acoustic wave

Refractive index modulation in optical materials facilitates dynamic control on electromagnetic waves. Ultra fast tuning of both refractive index and its spatial distribution in Y−Z Lithium Niobate slab via strain employed through GHz acoustic perturbation has been simulated and studied. To create acoustic disturbance in taken 500 nm thick slab, the fundamental symmetric Lamb mode at 5 GHz acoustic frequency is excited. Displacement field patterns generated by longitudinal and transverse disturbances of perturbing fundamental symmetric Lamb mode are analyzed under reinstate limits of optical material to create elastic strain. Modification in optical index of Lithium Niobate due to strain generated by longitudinal and transverse acoustic disturbance is then examined. The sinusoidal modulation in refractive index with maximum change of 0.070 along nz and 0.036 along ny is observed. The modulated refractive index has a periodic distribution over space with period equals to wavelength of acoustic disturbance created by fundamental Lamb mode. This acoustically induced ultra-fast change in refractive index and in its spatial distribution depends on perturbing acoustic frequency and thickness of slab. Thus, the slab can optimize dynamically, to control electromagnetic wave for various optical applications.

Transmission of Lamb waves across a partially closed crack: Numerical analysis and experiment

The transmission characteristics of Lamb waves across a partially closed through-thickness crack in a plate are investigated numerically and experimentally. In the numerical analysis, the spectral element method is used to simulate the transmission of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb modes across a crack in a low-frequency range. The analysis is carried out for an open crack with traction-free surfaces as well as for a partially closed crack modeled as a spring-type interface characterized by normal and tangential stiffnesses. The transmission ratios of both modes are obtained from the spectral amplitude of the simulated transmission waveforms for different crack lengths and interfacial stiffnesses. The numerical results show that the transmission ratio of the S0 mode increases monotonically with the interfacial stiffness, but that of the A0 mode depends on the interfacial stiffness in a non-monotonic manner depending on the frequency. The Lamb wave transmission measurements are carried out for aluminum alloy plates with artificial slits or a fatigue crack. The experimental results for the plates with slits show reasonable agreement with the numerical results for open cracks. The measured transmission ratio of the S0 mode is shown to decrease with the tensile load applied to the plate, but that of the A0 mode shows different load dependence for different frequencies. The qualitative features of the experimental results for the fatigue crack are discussed based on the numerical simulation for closed cracks.

Acoustically tunable photonic band gap generation in MgO doped Lithium Niobate micro-dimension plate

Refractive index contrast generation in MgO doped LiNbO3 plate via Lamb wave perturbation for induction of acoustically tunable photonic band gap is theoretically studied. Fundamental symmetric Lamb mode is excited in micro dimension thin plate structure to produce symmetric disturbance for periodic contraction and rarefaction along the length of plate. Effect of contraction and rarefaction on production of refractive index contrast is studied using photo–elastic effect. The generated quasi static low–high optical index region in plate modifies electromagnetic wave propagation and provides photonic band gaps, which are investigated using Bloch's theorem and transfer matrix method. The induced photonic band gap shows great dependency on optical contrast and unit cell dimension created by acoustic frequencies. These acoustically tunable photonic band gaps have rewarding applications in acousto optical devices, laser and sophisticated sensing.

A Boundary Element Model for Structural Health Monitoring Based on the S0 Lamb Wave Mode

The aim of this paper was to carry out numerical simulations of structural health monitoring applications for plate structures using the boundary element method (BEM). The fundamental symmetric Lamb mode (S0) is chosen for the SHM applications. The propagation, reflection and diffraction of the S0 mode Lamb wave are modelled using a boundary element formulation based on the plane stress theory. Piezoelectric (PZT) actuators are mounted on plate surfaces to excite the S0 mode wave. A semi-analytical method is adopted to couple the PZT actuators and the host plate. Numerical results show that BEM is a very efficient simulation method for the structural health monitoring of plates.

Experimental Investigation of Second-Harmonic Lamb Wave Generation in Additively Manufactured Aluminum

The correlation between the nonlinear acousto-ultrasonic response and the progressive accumulation of fatigue damage is investigated for an additively manufactured aluminum alloy AlSi7Mg and compared with the behavior of a conventional wrought aluminum alloy 6060-T5. A dual transducer and wedge setup is employed to excite a 30-cycle Hann-windowed tone burst at a center frequency of 500 kHz in plate-like specimens that are 7.2 mm thick. This choice of frequency-thickness is designed to excite the symmetric Lamb mode s1, which, in turn, generates a second-harmonic s2 mode in the presence of distributed material nonlinearity. This s1-s2 mode pair satisfies the conditions for internal resonance, thereby leading to a cumulative build-up of amplitude for the second-harmonic s2 mode with increasing propagation distance. Measurements of a nonlinearity parameter β derived from the second-harmonic amplitude are plotted against propagation distance at various fractions of fatigue life under constant amplitude loading, for three different stress levels corresponding to low-cycle fatigue (LCF), high-cycle fatigue (HCF), and an intermediate case. The results show both qualitative and quantitative differences between LCF and HCF, and between the additively manufactured specimens and the wrought alloy. The potential use of this nonlinearity parameter for monitoring the early stages of fatigue damage accumulation, and hence for predicting the residual fatigue life, is discussed, as well as the potential for quality control of the additive manufacturing (AM) process.

Effect of ply orientation and through-thickness position of delamination on the reflection of fundamental symmetric S0 Lamb mode in GFRP composite plate structures

This paper studies the interaction of the fundamental symmetric Lamb wave mode S0 with delaminations in 8-layered glass fibre reinforced polymer (GFRP) laminated composites, using numerical models validated against experiments. The validation is performed using experiments on the eight layer quasi-isotropic GFRP composite laminate [0/90/45/−45]S. Further numerical studies were performed on the laminates [0/45/−45/90]S, [0/45/90/−45]S, [90/45/−45/0]S, [90/−45/0/45]S, [45/−45/0/90]S, and [45/90/−45/0]S to study the effect of ply layups on the reflection of S0 Lamb waves. The reflection coefficients calculated for these laminates followed a similar trend as the laminate [0/90/45/−45]S. Physical insight was obtained into the reflection behaviour, based on an analysis of wave dispersion in the sub-laminates. It was difficult to detect the delamination situated at the mid plane of the laminate, where the shear stress was found to be zero for all ply layups. The delaminations present at a depth greater than DL12 (>0.42 mm) from the source of excitation, were found to be accessible for the laminates [0/90/45/−45]S, [0/45/−45/90]S and [0/45/90/−45]S. The sensitivity of the S0 mode reflection depends upon the position of the delamination along the thickness direction and ply layup orientation of the composite laminate. The S0 mode showed higher sensitivity to DL23 and DL34 (0.42 mm to 1.26 mm) in all the laminates that were inspected.

Structural Health Monitoring of Above-Ground Storage Tank Floors by Ultrasonic Guided Wave Excitation on the Tank Wall.

There is an increasing interest in using ultrasonic guided waves to assess the structural degradation of above-ground storage tank floors. This is a non-invasive and economically viable means of assessing structural degradation. Above-ground storage tank floors are ageing assets which need to be inspected periodically to avoid structural failure. At present, normal-stress type transducers are bonded to the tank annular chime to generate a force field in the thickness direction of the floor and excite fundamental symmetric and asymmetric Lamb modes. However, the majority of above-ground storage tanks in use have no annular chime due to a simplified design and/or have a degraded chime due to corrosion. This means that transducers cannot be mounted on the chime to assess structural health according to the present technology, and the market share of structural health monitoring of above-ground storage tank floors using ultrasonic guided wave is thus limited. Therefore, the present study investigates the potential of using the tank wall to bond the transducer instead of the tank annular chime. Both normal and shear type transducers were investigated numerically, and results were validated using a 4.1 m diameter above-ground storage tank. The study results show shear mode type transducers bonded to the tank wall can be used to assess the structural health of the above-ground tank floors using an ultrasonic guided wave. It is also shown that for the cases studied there is a 7.4 dB signal-to-noise ratio improvement at 45 kHz for the guided wave excitation on the tank wall using shear mode transducers.

Transmission characteristics of the S0 and A0 Lamb waves at contacting edges of plates

In order to gain basic insight into the interaction between ultrasonic guided waves and structural discontinuities with contacting surfaces, the transmission characteristics of Lamb waves at contacting edges of two plates are studied experimentally. The edges of two 2.5-mm thick aluminum alloy plates are mated together to constitute a contacting interface of plates and subjected to different levels of compressive loading. The transmission measurements of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb modes across the contacting interface are performed in a frequency range below the cut-off frequencies of the higher-order modes. As a result, it is found that the transmission coefficient of the S0 mode increases monotonically with the applied contact pressure, but the transmission coefficient of the A0 mode exhibits non-monotonic dependence on the contact pressure and the frequency showing a local minimum. For the incidence of the S0 mode, the resonance at the contacting interface is observed as a long-time oscillation tail in the transmission waveform. The resonance frequency is found to increase with the contact pressure. The experimental results are discussed in the light of the theoretical results based on the spring-type interface model. The normal and tangential stiffnesses of the contacting interface are identified from the transmission coefficients as well as from the resonance frequency. The estimated interfacial stiffnesses increase monotonically with the contact pressure, and indicate their dependence on the frequency. Implications of the present results to the Lamb-wave based characterization of the plate contact condition are discussed briefly.

Transmission of Lamb waves and resonance at an adhesive butt joint of plates

The transmission behavior of Lamb waves and the possible occurrence of resonance at an adhesive butt joint of plates are studied experimentally. To this purpose, two 2.5-mm thick aluminum alloy plates are bonded at their edges using cyanoacrylate-based adhesive. Bonded plate specimens with different joint conditions are prepared by changing the bonding procedure. The measurements are performed for the transmission characteristics of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb modes for the frequency range of 0.4–0.6MHz below the cut-off frequency of the higher-order modes. The experimental results show that the transmission coefficients of the S0 and A0 modes exhibit different frequency-dependent characteristics depending on the joint condition. Furthermore, for the incidence of the S0 mode at the center frequency of 1MHz, the transmitted S0 mode in weakly bonded specimens shows a long oscillation tail due to the resonance effect. The experimental results are discussed in the light of the theoretical results based on the spring-type interface model. The interfacial stiffnesses identified from the transmission coefficients are shown to be correlated with the bonding condition of the joint and give reasonable estimates of the resonance frequencies of weakly bonded specimens.

Multimodal sparse reconstruction in guided wave imaging of defects in plates

A multimodal sparse reconstruction approach is proposed for localizing defects in thin plates in Lamb wave-based structural health monitoring. The proposed approach exploits both the sparsity of the defects and the multimodal nature of Lamb wave propagation in plates. It takes into account the variation of the defects’ aspect angles across the various transducer pairs. At low operating frequencies, only the fundamental symmetric and antisymmetric Lamb modes emanate from a transmitting transducer. Asymmetric defects scatter these modes and spawn additional converted fundamental modes. Propagation models are developed for each of these scattered and spawned modes arriving at the various receiving transducers. This enables the construction of modal dictionary matrices spanning a two-dimensional array of pixels representing potential defect locations in the region of interest. Reconstruction of the region of interest is achieved by inverting the resulting linear model using the group sparsity constraint, where the groups extend across the various transducer pairs and the different modes. The effectiveness of the proposed approach is established with finite-element scattering simulations of the fundamental Lamb wave modes by crack-like defects in a plate. The approach is subsequently validated with experimental results obtained from an aluminum plate with asymmetric defects.

Numerical and experimental investigation of nonlinear ultrasonic Lamb waves at low frequency

Nonlinear ultrasonic Lamb waves are popular to characterize the nonlinearity of materials. However, the widely used nonlinear Lamb mode suffers from two associated complications: inherent dispersive and multimode natures. To overcome these, the symmetric Lamb mode (S0) at low frequency region is explored. At the low frequency region, the S0 mode is little dispersive and easy to generate. However, the secondary mode still exists, and increases linearly for significant distance. Numerical simulations and experiments are used to validate the nonlinear features and therefore demonstrate an easy alternative for nonlinear Lamb wave applications.

Electromechanical hybrid metamaterial for the control of ultrasonic guided waves

Last years, a growing number of research has been devoted to the control of the behavior of Phononic crystals and Metamaterials through for instance tunability of the frequency position and/or width of a band gap. This can be achieved by using active materials such as piezoelectric materials. Here, a new class of hybrid metamaterials (HMMs) is proposed to tune the dispersion of guided Lamb waves. The studied HMM is made of a single homogeneous piezoelectric plate on which metallic electrodes are laid on. These electrodes are very thin in comparison to the plate thickness and allow changing locally the electric boundary conditions (EBCs). It is shown, experimentally and theoretically, that by simply modifying the EBCs, coupling between some modes can be induced, leading to the opening of a gap at the edge or within the first Brillouin zone. Moreover, a hybridization gap is observed for the first symmetrical Lamb modes, involving the electrical resonance associated to an inductive electrical circuit connected on electrodes. Such a system opens important perspectives for the development of SAW devices for radiofrequency applications.

Enhanced impact echo frequency peak by time domain summation of signals with different source receiver spacing

The Impact Echo method can be used to measure the thickness of concrete plate like structures. Measurements are based on the identification of a clear thickness resonance frequency which can be difficult in very thick or highly attenuative plates. In this study the detectability of the measured resonant frequency is enhanced by time domain summation of signals with different source receiver spacing. The proposed method is based on the spatial and temporal properties of the first higher symmetric zero group velocity Lamb mode (S1-ZGV) which are described in detail. No application dependent tuning or filtering is needed which makes the method robust and suitable for implementation in automatic IE thickness measurements. The proposed technique is exemplified with numerical data and field data from a thick concrete wall and a highly attenuative asphalt concrete layer.

Effect of lay-up of sub-waveguide on transmission of So mode from main waveguide to sub-waveguides

This paper focuses on transmission characteristics of fundamental symmetric Lamb mode (So) at the junction of a main waveguide and sub-waveguides in composite laminates. Numerical simulations on transmission of So from the main to sub-waveguide revealed that transmission factors of the modes depend on stacking sequence of plies in the waveguides. Experiments were carried out to verify the observations made in numerical simulations. This work gives an insight on the transmission characteristics of So mode while it propagates from a healthy to a delaminated region in a composite laminate.

Poisson's ratio from polarization of acoustic zero-group velocity Lamb mode.

Poisson's ratio of an isotropic and free elastic plate is estimated from the polarization of the first symmetric acoustic zero-group velocity Lamb mode. This polarization is interpreted as the ratio of the absolute amplitudes of the surface normal and surface in-plane components of the acoustic mode. Results from the evaluation of simulated datasets indicate that the presented relation, which links the polarization and Poisson's ratio, can be extended to incorporate plates with material damping. Furthermore, the proposed application of the polarization is demonstrated in a practical field case, where an increased accuracy of estimated nominal thickness is obtained.