Antisymmetric Lamb Wave Research Articles

Enhancement of high-frequency harmonics in resonators using multilayered structures with polarity-inverted layers

Periodically Poled Piezoelectric Film (P3F) stacks have recently been reported as a promising platform for next-generation radio-frequency acoustic filters that extend into cm- and mm-wave bands. By demonstrating the potential for developing high-performance acoustic devices with frequencies up to 20 GHz, P3F structures based on lithium niobate (LiNbO3) films have opened up new possibilities. In this study, the influence of key parameters such as the number of layers, crystal orientation, duty factor, and variation in thicknesses between the layers on the efficiency of the n-th harmonic excitation and spurious modes was examined. To enhance higher-order harmonics, which are suppressed in P3F structures, a novel multilayered stack with Aperiodically Polarized Piezoelectric Films (APPF) is proposed. Optimizing the ratio between layer thicknesses can enhance higher-order harmonics. An optimization principle is described and illustrated by examples of three-layered APPF structures optimized for the generation of antisymmetric Lamb wave harmonics A3-A17, with electromechanical coupling continuously decreasing with frequency. High-frequency modes excited in APPF structures fill the gaps in frequencies and electromechanical coupling coefficients between the modes generated in P3F stacks and can provide greater diversity of device performance.

6 GHz lamb wave acoustic filters based on A1-mode lithium niobate thin film resonators with checker-shaped electrodes

The first-order antisymmetric (A1) mode lamb wave resonator (LWR) based on Z-cut LiNbO3 thin films has attracted significant attention and is widely believed to be a candidate for next-generation reconfigurable filters with high frequency and large bandwidth (BW). However, it is challenging for traditional interdigitated electrodes (IDTs) based LWR filters to meet the requirement of a clean frequency spectrum response and enough out-of-band (OoB) rejection. To solve the problem, we propose LWRs with checker-shaped IDTs for the design of filters that meet the Wi-Fi 6E standard. By taking advantage of checker-shaped IDTs with unparalleled boundaries, the fabricated 6-GHz resonators successfully suppress higher-order A1 spurious modes, demonstrating a spurious-free impedance response and a high figure-of-merit (FOM) up to 104. Based on the demonstrated checker-shaped electrode design, the filter features a center frequency (f0) of more than 6 GHz, a 3 dB BW exceeding 620 MHz, and an excellent OoB rejection >25 dB, consistent with the acoustic-electric-electromagnetic (EM) multi-physics simulations. Furthermore, through the capacitance-inductance matching network technology, the filter’s voltage standing wave ratio (VSWR) is successfully reduced below 2, showing an excellent 50 Ω impedance matching. This study lays a foundation for ultra-high-frequency and ultra-wideband filters for the Wi-Fi 6/6E application.

A variable kinematic multi-field model for lamb wave propagation analysis in smart composite panels

The study explores the propagation of symmetric and antisymmetric fundamental Lamb waves in laminated composite strips, employing multi-field piezo-elastic plate models. The findings indicate the necessity of employing higher-order kinematic models to enhance the accuracy of wave propagation assessments. To further optimize computational efficiency, node-dependent kinematic models are utilized. The research delves into the tradeoff between reducing computational costs and maintaining result accuracy demonstrating a reduction of up to 60% in computational expenses in simple models while keeping the error below 1%. Two-dimensional wave propagation in laminated composite plates was further considered, expanding the scope due to material orthotropy.

A0 mode Lamb wave propagation in a nonlinear medium and enhancement by topologically designed metasurfaces for material degradation monitoring

This paper intends to provide an application example of using metamaterials for elastic wave manipulation inside a nonlinear waveguide. The concept of phase-gradient metasurfaces, in the form of artificially architectured structures/materials, is adopted in nonlinear-guided-wave-based structural health monitoring (SHM) systems. Specifically, the second harmonic lowest-order antisymmetric Lamb waves (2nd A0 waves), generated by the mutual interaction between primary symmetric (S) mode and antisymmetric (A) mode waves, show great promise for local incipient damage monitoring. However, the mixing strength is adversely affected by the wave beam divergence, which compromises the 2nd A0 wave generation, especially in the far field. To tackle this problem, a metasurface is designed to tactically enhance the 2nd A0 waves through manipulating the phases and amplitudes of both primary waves simultaneously. After theoretically revealing the features of the 2nd A0 wave generation in a weakly nonlinear plate, an inverse-design strategy based on topology optimization is employed to tailor-make the phase gradient while ensuring the high transmission of the primary waves, thus converting the diverging cylindrical waves into quasi-plane waves. The efficacy of the design is tested in a 2nd-A0-wave-based SHM system for material degradation monitoring. Results confirm that the manipulated S and A mode waves can propagate in a quasi-planar waveform after passing the surface-mounted metasurface. Changes in material properties inside a local region of the host plate can be sensitively captured through examining the variation of the 2nd A0 wave amplitude. The concept presented here not only showcases the potential of metamaterial-enhanced 2nd A0 waves for material degradation monitoring, but also illuminates the promising direction of metamaterial-aided SHM applications in nonlinear waveguides.

A guided wave propagation method for delamination detection in fiber-metal laminates

This study aimed to assess the delamination detection in FMLs via the finite element (FE) simulations of Lamb wave propagation. An FE model of an FML specimen with [Al/902/Al/902/Al] layup was developed. Delamination damage of 10 and 25 mm diameters was induced between different layers of the FML specimen. The fundamental antisymmetric Lamb wave mode (A0) at 60 kHz and the fundamental symmetric Lamb wave mode (S0) at the frequency of 206 kHz were propagated on the developed FE models. The Lamb wave phase velocity was obtained from the FE models and compared with those obtained from the Lamb wave propagation tests. The sensitivity of the A0 and S0 Lamb wave modes to the delamination and its diameter were examined. The inverse Lamb wave propagation problem was then solved, and the elastic modulus of the FML specimen was estimated in the intact and delamination regions. It was observed that the phase velocity of the S0 Lamb wave mode had a higher sensitivity to the delamination damage compared to that of the A0 Lamb wave mode. The phase velocity of the A0 Lamb wave mode was more sensitive to the delamination diameter. The capability of the proposed simulated Lamb wave propagation method as a virtual lab for detecting delamination in the FMLs was confirmed.

The Dispersion Calculator - a free software for calculating dispersion curves of guided waves

The nondestructive inspection of components by means of guided waves is an emerging technology in fields like aerospace or pipeline construction and maintenance. The guided waves' capability of propagating many meters in a structure is utilized for swift inspection tasks as well as structural health monitoring. The German Aerospace Center uses Lamb waves for the quality assurance of large-scale aerospace vehicle components made from carbon composites. However, the use of guided waves in NDT requires knowledge of the dispersion curves. DISPERSE is the most renown software for the calculation of dispersion curves. This paper presents the open source Dispersion Calculator (DC). The MATLAB® -based DC is an interactive and fully validated software for the computation of dispersion curves and mode shapes of guided waves in isotropic plates and multilayered anisotropic composites. Damping caused by viscoelasticity and fluid-loading can be considered. DC features the capability of calculating laminates consisting of several hundreds of layers so that even the largest specimens, like rocket booster pressure vessels, can be calculated. This is made possible through the implementation of the stiffness matrix method. DC is also able to distinguish the different mode families, like symmetric, antisymmetric, and nonsymmetric Lamb, shear horizontal, and Scholte waves, depending on the symmetry and coupling properties of a given layup. Lastly, DC features a highly efficient and robust dispersion curve tracing algorithm. DC is available at GitHub, and it has gained many users world-wide since its initial release in 2018.

Thermal stress estimation of a constrained metallic plate using symmetric and antisymmetric Lamb wave group velocities

This paper presents a technique for estimating thermal-induced stress in constrained metallic plates using the group velocity of Lamb waves, the accuracy of which is crucial for assessing the structural integrity and serviceability of metallic structures. However, without the ability to gauge the current stress levels, obtaining such measurements is technically challenging. To overcome this, we propose a thermal stress estimation technique that uses changes in the group velocities of the fundamental symmetric (S0) and antisymmetric (A0) Lamb wave modes caused by thermal and stress variations. First, this study introduces a theoretical-based zero-crossing algorithm to measure the group velocities of S0 and A0 Lamb wave modes. Next, leveraging the acoustoelastic coefficients corresponding to the S0 and A0 modes, which are determined before the plate’s installation, this study generates the lines depicting the changes in group velocity induced by temperature variations (CT) for both the S0 and A0 modes. These CT lines are derived from the lines illustrating changes in group velocity due to thermal stress variations (CTS), which are obtained after plate installation. Ultimately, the generated CT lines can be used to estimate thermal stress throughout the entirety of the plate’s operational life span by isolating the distinct stress variation effects from the CTS lines. The numerical validation results show favorable accuracy in thermal stress estimation in a constrained plate subjected to temperature variation using both S0 and A0 Lamb wave modes, with average errors of 0.63 % and 0.91 %, respectively.

Elliptic pillars based metasurface for elastic waves focusing in a plate

In this paper, the ability of a metasurface made of resonant elliptical pillars to focus flexural Lamb waves in the sub-wavelength regime is investigated. We report on the influence of the ellipticity parameter on the local resonances of the pillars, in particular the monopolar compressional and dipolar bending modes that are responsible for the desired focusing effect. We also discuss how the transmission through a line of pillars reveals these modes when the orientation of the pillars is changed with respect to the incident wave. Both the resonances can be superimposed for a particular choice of the ellipticity parameter, allowing a phase shift of 2π in the transmission coefficient for an incident antisymmetric Lamb wave, which is a necessary condition for the design of the metasurface. Finally, a gradient design for the pillar ellipticity is investigated, and its capacity to choose the focusing directionality of the transmitted wave at different targeted points is demonstrated.

Detecting Cracks on Plates Using Reflections of Fundamental Symmetric and Anti-symmetric Lamb Waves from Defect

Introduction: Ultrasonic Lamb waves can achieve long-range inspection on plate-like structures and can even detect unreachable cracks and defects. There are multiple modes under a certain generation frequency with most of them dispersive. Method: The dispersion curves of Lamb wave in a steel plate were given by numerical calculation. A 2-D finite element (FE) model of a steel plate was promoted. The fundamental symmetric and antisymmetric Lamb waves were generated by uploading symmetrical and anti-symmetrical displacements on one side of the plane. The wave reflects when it comes across the defect and the edge of the plate. Mode conversion will occur after the asymmetrical discontinuities of the structure. Result: The theoretical and numerical results of the values of group velocities of S0 and A0 in a steel plate show well agreement. The maximum amplitude of the converted A0 wave from the interaction of the incident S0 wave with the cracks was observed. The amplitude will first rise then fall under any depth of the defects. The relationship between the defect reflection and the length as well as the depth of defects were simulated based on the FE model. Phase reversion and phase delay were discovered by controlling the defect size changing in one dimension. The reflection coefficient increases linearly with the defect length while the depth is constant, as well as the defect depth while the length is constant. method: Using finite element (FE) method to simulate Lamb wave motion in a plate, as well as experiments on steel plates with artificial defects. Conclusion: Experiments on steel plates with artificial defects including thorough holes and tapered holes were carried out using ISONICA STAR. The results also show that when the defect size changes in one dimension such as the thorough holes, the reflection coefficient increases linearly correspondingly. However, the testing results of the taper holes were inconsistent with the regulation as the size increases in both the length and the depth. result: The values of group velocities were calculated by time-of-flight method to identify specific modes. The results were calibrated and showed well agreement with theoretical data. Mode conversion will appear when the wave comes across asymmetric discontinuities of the structure.

Robust transport and topological valley refraction of fundamental symmetric lamb waves in perforated phononic crystal plates

Lamb waves can be divided into antisymmetric Lamb waves (type A) and symmetric Lamb waves (type S), which are widely used in health monitoring of engineering structures and nondestructive evaluation of materials. However, due to the fact that each mode of Lamb wave has the setting group velocity in a certain bandwidth range, it is easy to cause the aliasing of multi-mode Lamb waves, partly limiting the application scenarios of Lamb wave. In this paper, a hexagonal lattice meta-structure is designed and the zero-order symmetric (S0) Lamb wave in a finite thickness plate is successfully separated. By breaking the spatial C 3v symmetry, a valley topological phononic crystal (PnC) plate for the pure S0 mode is constructed, and its robust topological transports are demonstrated. Firstly, the valley topological phase transition of S0 mode is realized by changing the angle of scatterer in PnC plate and the valley edge state of S0 mode is obtained. Furthermore, by introducing structural mismatch, it is verified that the edge state of S0 mode is robust to various bends and defect. Finally, by changing the material property of the terminal, the valley refraction with different directionality is realized. The results offer a route to individually study the symmetric modes of Lamb waves, and have potential application prospects in rapid and accurate ultrasonic nondestructive testing based on Lamb waves.

In Vivo Evaluation of Corneal Biomechanics Following Cross-Linking Surgeries Using Optical Coherence Elastography in a Rabbit Model of Keratoconus.

Validation of the feasibility of novel acoustic radiation force optical coherence elastography (ARF-OCE) for the evaluation of biomechanical enhancement of the in vivo model of keratoconus by clinical cross-linking (CXL) surgery. Twelve in vivo rabbit corneas were randomly divided into two groups. Both groups were treated with collagenase type II, and a keratoconus model was obtained. Then, the two groups were treated with CXL procedures with different irradiation energy of 15 J and 30 J (CXL-15 J and CXL-30 J, respectively). An ARF-OCE probe with an ultrasmall ultrasound transducer was used to detect the biomechanical properties of cornea. An antisymmetric Lamb wave model was combined with the frequency dispersion relationship to achieve depth-resolved elastography. Compared with the phase velocity of the Lamb wave in healthy corneas (approximately 3.96 ± 0.27 m/s), the phase velocity of the Lamb wave was lower in the keratoconus region (P < 0.05), with an average value of 3.12 ± 0.12 m/s. Moreover, the corneal stiffness increased after CXL treatment (P < 0.05), and the average phase velocity of the Lamb wave was 4.3 ± 0.19 m/s and 4.54 ± 0.13 m/s after CXL-15 J and CXL-30 J treatment. The Young's moduli of the keratoconus regions were significantly lower than the healthy corneas. Moreover, the Young's modulus of the keratoconus regions was significantly higher after CXL-30 J treatment than after CXL-15 J treatment. We demonstrated that the ARF-OCE technique has great potential in screening keratoconus and guiding clinical CXL treatment. This work accelerates the clinical translation of OCE systems using ultrasmall ultrasound transducers and is used to guide CXL procedures.

Mode-entangled resonance for lamb waves in a plate

We report a novel resonance phenomenon called the mode-entangled resonance. It can occur at a specific frequency in a plate carrying both symmetric and antisymmetric Lamb wave modes. We show that at this resonance, a symmetric or antisymmetric Lamb wave can be fully transmitted with its mode preserved from one plate to another through a matching plate geometrically misaligned with the two base plates. This phenomenon appears to be counter-intuitive because both symmetric and antisymmetric waves are generally formed in the reflected and transmitted wave fields when the misaligned plate is used as a matching plate. Our analysis shows that if both symmetric and antisymmetric Lamb wave modes at the resonance are entangled in the misaligned matching plate to satisfy the established phase matching condition, the matching plate fully transmits any wave mode across the two base plates. The discovered phenomenon is related to the classical Fabry-Perot resonance (FPR), but FPR is only applicable for single-mode transmission through a matching plate aligned with two base plates. Numerical and experimental results were presented to validate the discovered mode-entangled resonance phenomenon. Furthermore, we show that the discovered phenomenon can be used for super-amplification of the amplitude of the antisymmetric Lamb wave when it is excited by plate-surface-mounted patch transducers.

Ultrasonic Non-Contact Air-Coupled Technique for the Assessment of Composite Sandwich Plates Using Antisymmetric Lamb Waves

This paper describes the design and implementation of an ultrasonic non-contact air-coupled technique (UNCACT) using antisymmetric Lamb waves (ALW) for NDT assessments in novel composite sandwich plates of a car body shell. This technique is complemented with a C-Scan image implementation using guided waves. The finite element method (FEM) was developed using Comsol 6.1 for the interpretation of the several wave modes presented in the experiments, including the ALW mode. This FEM model is indispensable for the correct interpretation of the received signals and contributes to a better implementation of this technology. This is a novel contribution building upon previously reported work. Additionally, the phase velocity method (PVM) was applied for the verification of the ALW mode in the portion of the RF signal necessary for the C-Scan image.

Antisymmetric Lamb Wave Simulation Study Based on Electromagnetic Acoustic Transducer with Periodic Permanent Magnets.

Due to its multi-mode and dispersion characteristics, Lamb waves cause interference to signal processing, which profoundly limits their application in nondestructive testing. To resolve this issue, firstly, based on the traditional EMAT, a horizontal polarization periodic permanent magnet electromagnetic acoustic transducer (HP-PPM-EMAT) was proposed. A 2-D finite element model was then developed to compare magnetic flux density, Lorentz force, and signal strength between the traditional EMAT and the HP-PPM-EMAT. The simulation results show that the HP-PPM-EMAT enhances the A0 mode Lamb wave (A0 wave) and suppresses the S0 mode Lamb wave (S0 wave). Finally, the influence of structural parameters of the HP-PPM-EMAT on the total displacement amplitude ratio of A0 and S0 was investigated using orthogonal test theory, and the width of magnet units was improved based on the orthogonal test. The results show that the total displacement amplitude ratio of A0 to S0 of the improved HP-PPM-EMAT can be improved by a factor of 7.74 compared with that of the traditional Lamb wave EMAT, which can produce higher-purity A0 mode Lamb waves.

Classification of solutions for guided waves in fluid-loaded viscoelastic composites with large numbers of layers.

Guided ultrasonic waves are used for the inspection of multilayered composite aerospace structures. Calculating the corresponding dispersion diagrams is challenging for thick-walled composites with more than 100 layers, such as in modern rocket booster pressure vessels. The Dispersion Calculator (DC) is an open source software for calculating such dispersion diagrams and mode shapes of guided waves. Attenuation caused by viscoelasticity and fluid-loading makes the dispersion curve tracing much more difficult than in the nonattenuated case because the modal solutions are sought in the complex wavenumber plane. The tracing problem is mastered by a reliable algorithm. Whereas leaky Lamb and Scholte waves in coupled and decoupled cases are modeled using the stiffness matrix method, shear horizontal (SH) waves are traced using the transfer matrix method without facing the numerical instability. Through implementation of mode family specific dispersion equations in both matrix techniques for nonattenuated and attenuated cases, symmetric, antisymmetric, and nonsymmetric leaky Lamb, Scholte, and SH waves can be traced separately with better efficiency and robustness. The capabilities of DC are demonstrated by calculating dispersion diagrams and mode shapes for a viscoelastic composite with 400 layers immersed in water. Results are compared against DISPERSE (Imperial College London, London, UK) for selected cases.

Harnessing negative refraction and evanescent waves toward super-resolution Lamb wave imaging

We numerically and experimentally demonstrate super-resolution focusing of the lowest anti-symmetric (A0) mode Lamb waves in a thin aluminum plate. The subwavelength focusing/imaging is achieved by exploiting the anisotropy in phononic crystal (PC) lattices and amplification of evanescent waves. To this end, we embedded a PC flat lens in the aluminum plate, consisting of holes arranged in a square lattice formation. We revealed that the bound slab phonon modes amplify evanescent waves, as previously observed for electromagnetic and acoustic waves. Hence, the slab mode helps propagate subwavelength information through the PC lens to reach the near-field image formed due to negative refraction and result in the high resolution image.

Rayleigh's and Wood's anomalies at the edge-type phononic structure

Anomalies in reflection from periodic structures, well known in optics, result from either the transition from specular reflection to diffraction of light (Rayleigh's anomaly) or by coupling to the leaky surface mode supported by the structure (Wood's anomaly). Experimental observation and detailed analysis of both kinds of anomalies are presented here in the case of antisymmetric Lamb wave (A0) incidence at the 1D periodic structure located along the edge of the elastic plate. A structure with a strong phononic effect has been chosen, which enables the separation of both effects in terms of frequency. Another distinct feature of elastic waves in the periodic structure considered in this work is the existence of several localized modes, which leads to the multiple Wood's anomalies. Here, we report the experimental observation of double Wood's anomaly in addition to the Rayleigh's type of anomaly.

Mode purification for multimode Lamb waves by shunted piezoelectric unimorph array

Guided wave-based nondestructive testing and structural health monitoring methods have been developed to exhibit attractive potentials and best prospects for rapid and sensitive detection of defects or damage in engineering structures. Different modes of guided waves can provide different sensitivities of damage detection. However, the multimode and mode conversion nature of guided waves poses significant challenges to mode purification of received signals. This study aims to design a metamaterial-based smart transducer for mode purification of Lamb waves in a plate, which can filter out an undesired mode of the Lamb wave to enhance sensing and actuating signals of a dominated mode. The smart transducer consists of a periodic array of shunted piezoelectric unimorphs with staggered polarization directions and is bonded on the surface of a host plate. Numerical and experimental results show that a local resonance bandgap for an anti-symmetric Lamb wave, rather than a symmetric Lamb wave, can be obtained and tuned through the shunting inductance circuit. Within such mode bandgap, the wave control for propagating a specific mode of the Lamb wave can be further realized, i.e., the mode of the Lamb wave is purified. The design presented herein offers enhanced capabilities in controlling guided wave propagation for engineering applications and nondestructive testing techniques.

Electroelastic metasurface with resonant piezoelectric shunts for tunable wavefront control

In this paper, we design a tunable phase-modulated metasurface composed of periodically distributed piezoelectric patches with resonant-type shunt circuits. The electroelastic metasurface can control the wavefront of the lowest antisymmetric mode Lamb wave (A 0 mode) in a small footprint due to its subwavelength features. The fully coupled electromechanical model is established to study the transmission characteristics of the metasurface unit and validated through numerical and experimental studies. Based on the analysis of the metasurface unit, we first explore the performance of electroelastic metasurface with single-resonant shunts and then extend its capability with multi-resonant shunts. By only tuning the electric loads in the shunt circuits, we utilize the proposed metasurface to accomplish wave deflection and wave focusing of A 0 mode Lamb waves at different angles and focal points, respectively. Numerical simulations show that the metasurface with single-resonant shunts can deflect the wavefront of 5 kHz and 6 kHz flexural waves by desired angles with less than deviation. In addition, it can be tuned to achieve nearly three times displacement amplification at the designed focal point for a wide range of angles from to 75∘. Furthermore, with multi-resonant shunts, the piezoelectric-based metasurface can accomplish anomalous wave control over flexural waves at multiple frequencies (i.e. simultaneously at 5 kHz and 10 kHz), developing new potentials toward a broad range of engineering applications such as demultiplexing various frequency components or guiding and focusing them at different positions.

Lamb waves manipulation by piezoelectric metasurface with tunable diffraction orders

In this paper, a piezoelectric metasurface is proposed to manipulate the anti-symmetric mode Lamb wave by altering the diffraction order. The metasurface attached to a host plate is symmetrically arranged by out-of-plane polarized piezoelectric patches connected with synthetic inductance circuits. Without changing the physical configuration, the transmitted phase of the anti-symmetric mode Lamb wave can be shifted arbitrarily in 0 ∼ 2π range by the metasurface. Furthermore, the relationship between the phase gradient and diffraction order is investigated, and different orders of diffraction waves can be obtained by adjusting the shunting inductance circuits. The symmetric transmission and asymmetric transmission from a couple of axis symmetric incident waves can be realized by utilizing +1st-order and −1st-order diffraction. Moreover, omnidirectional wave reflection and wave trapping in channelized waveguides can also be realized by utilizing the 0th-order diffraction. The results indicate that the proposed piezoelectric metasurface has great potentials in manipulating guided waves with a large incident angle and isolating wave propagation.