Antisymmetric Modes Research Articles

Rest length controlled tunable band structure in periodic tensegrity metastructure – a numerical study using a novel consistent stiffness and mass formulation

Elastic wave propagation in various periodic metastructures and its application to wave filtering, vibration isolation, acoustic cloaking, etc., have gained significant attention among researchers in recent years. Despite the presence of band gaps, traditional lattice structures lack dynamic tunability. The solution lies in using tensegrity as unit cells. This article presents analysis of tunable wave propagation through a metastructure formed by tessellation of a 2D tensegrity unit cell in one dimension. Equations of motion of the unit cell are derived with consideration of flexibility and distributed mass of the bars, which is often neglected in the literature. The formulation is extended for wave dispersion analysis using the Floquet–Bloch theory. Next, the order of the formulation is reduced for decoupled analysis of symmetric and antisymmetric modes. The dispersion relations for different modes have been validated with nonlinear as well as linearized frequency response analysis under impulse load. Next, the effect of rest length of strings and alternating arrangement of bars on band gaps is studied in detail.

Deep learning of buckling instability in geometrically symmetry-breaking kirigami

Kirigami, subjected to escalating strain, frequently exhibits pronounced instability, coupled with remarkable flexibility and extraordinary extensibility. This behavior holds significant relevance for domains associated with malleable and reconfigurable surfaces, including stretchable electronics and modifiable functional devices. Nonetheless, conventional design methodologies, anchored in geometric symmetry and governed by minimum energy principles, tend to manifest buckling instabilities restricted to symmetric and anti-symmetric modes. To scrutinize the mechanisms of buckling behavior that disrupt geometric symmetry and comprehend the influence of geometry on programmability during reconfiguration, we propose an innovative strategy for kirigami’s design. This strategy capitalizes on advanced deep learning methodologies, employing convolutional neural networks (CNNs) for categorizing buckling modes and recurrent neural networks (RNNs) for prognosticating constitutive relationships. Our approach furnishes a programmable design solution adept at identifying optimal kirigami patterns, characterized by their superior tensile strength and distinct buckling conformations, thereby fulfilling a diverse array of functional necessities. Our results illustrate that the proposed method displays a high level of precision in distinguishing between buckling modes of geometric symmetry and patterns that deviate from such symmetry. The buckling mode space has been extended and rediscovered, allowing unique modes to have the potential to be adopted into functional devices. Additionally, it demonstrates minimal losses in predicting constitutive relationships. Intriguingly, we discovered that tensile responses are geometry-centric and adjustable. Buckling modes showcase a dependency on geometry, with certain geometric parameters either significantly augmenting the sensitivity of buckling modalities or causing the buckling instability modes to become apathetic and unresponsive. Guided by the principle of target-led pattern parameter design, we proffer prospective tactics for the design of kirigami capable of delivering the desired mechanical performance. Moreover, we explore the feasibility of employing alternative biological materials in these designs.

Non-Contact Laser Doppler Vibrometer for Characterization of Guided Waves in Timber Structures with Varying Moisture Content and Grain Orientations

Timber structures have been widely used in critical engineering applications throughout history. The need for Non-Destructive Testing of timbers has arisen, and ultrasonic-guided waves (GWs) have proved their efficacy in studying structural integrity. The effect of the grain direction in orthotropic timber structures on the propagation characteristics of GWs is not well understood, especially in the presence of moisture. This study aims to comprehend the effects of timber-grain orientations and the moisture content (MC) on dominant GW modes, specifically, on the anti-symmetric A0 mode. The study is based on samples extracted from a Western White Pine utility pole, in three different orientations including longitudinal, tangential, and radial. The MC is introduced using a desiccator with a saturated salt solution. The studied MC conditions included dry, ambient MC, and high MCs varying from 10% to 27%. The GWs were excited using piezoelectric actuators and sensed with a Scanning Laser Doppler Vibrometer with Free-Free boundary condition. Phase velocities were obtained using the frequency-wavenumber plots of the measured line scans and were compared to the analytical curves for mode analysis. The results showed that the experimental A0-mode phase velocities match well with those generated analytically. The difference was negligible for longitudinally oriented specimens with a percentage difference ranging from 0.28% to 5.34%, as the MC varied. The phase velocity decreased by about 7% as the MC increased from 0% to 27%. A noticeable difference in the phase velocity was measured with different orientations; at dry conditions, the A0 propagated at 958 m/s in the longitudinal specimens, while it decreased in the tangential specimens to about 760 m/s, and had the lowest phase velocity in the radial direction reaching 433 m/s. The results show a high sensitivity of the propagating GWs to the direction of the fibers and the MC present in the timber.

A low-frequency and broadband wave-insulating vibration isolator based on plate-shaped metastructures

A metamaterial vibration isolator, termed as wave-insulating isolator, is proposed, which preserves enough load-bearing capability and offers ultra-low and broad bandgaps for greatly enhanced wave insulation. It consists of plate-shaped metacells, whose symmetric and antisymmetric local resonant modes offer several low and broad mode bandgaps although the complete bandgap remains high and narrow. The bandgap mechanisms, vibration isolation properties, effects of key parameters, and robustness to complex conditions are clarified. As experimentally demonstrated, the wave-insulating isolator can improve the vibration insulation in the ranges of [50 Hz, 180 Hz] and [260 Hz, 400 Hz] by 15 dB and 25 dB, respectively, in contrast to the conventional isolator with the same first resonant frequency.

Innovative approach to modeling propagative, non-propagative and complex modes of ultrasonic guided waves

In the present paper are developed a new hybrid-spectral approach that deals with the dispersion of propagative, non-propagative and complex ultrasonic guided waves in different types of waveguides. First, a mathematical formulation of the eigenvalue and eigenvector problem has been presented. Then, the hybrid approach based on eigenvector processing is presented. A comparison is then made with the frequency and wavenumber approaches, to highlight the strengths of our method. The dispersion curves of propagative, non-propagative and complex modes are plotted in 2D and 3D. From these representations, several observations on mode behavior have been highlighted, notably the phenomenon of conversion of non-propagative modes into propagative modes, and also conversions specific to imaginary modes. The braiding phenomenon between symmetrical and antisymmetrical modes was also analyzed. Single and multi-layer planar and cylindrical geometries were treated with different degrees of anisotropy. The accuracy of the results was checked by comparison with analytical dispersion curves for planar structures and based on the thin plate limit for cylindrical structures. The error evaluated is of the order of 10 − 5 . A computation time analysis has been carried out, showing that the approach developed is the fastest in comparison with those available in the literature. On the basis of the results obtained, the hybrid approach applied to eigenvalue problems resulting from a spectral formulation presents a very good alternative for obtaining dispersion curves. It is stable, convergent, easy to implement and requires very little computing time and it can generate all types of modes (propagative, non-propagative and complex), in contrast to existing approaches in the reference.

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.

Lateral-distortional buckling of frames composed of non-aligned I-members by a simple distortional beam element considering angling effect

Lateral-distortional buckling may occur in frames composed of non-aligned I-members, for which the buckling resistance may be overestimated if the distortional deformation of the cross-section was ignored. In this regard, the geometric stiffness matrix for a novel straight beam element with nine DOFs per node that incorporates the effect of angling (or concentrated transverse stresses induced by in-plane bending moments) between two non-aligned members via the symmetric and anti-symmetric distortion modes is derived. Specifically, the virtual work done by the induced moments by in-plane bending moments near the angled joints when, in buckling, undergoing the angle of twist and the anti-symmetric distortion, is consistently included in the virtual work formulation. Although the local geometric stiffness matrices appear to be asymmetric, the symmetry of the structural stiffness matrix is ensured in the global assembly process, provided that the compatibility and equilibrium conditions at joints in the deformed configuration are satisfied. The reliability of the present distortional beam element is verified by comparing the present solutions with those by the Abaqus shell element in several well-designed examples, by which the superiority of the present element to the non-distortional beam elements is also demonstrated. Comparison study shows that the effect of distortional deformation is extremely significant when the angled frame is composed of short members, or the arch is of high curvature, and when rigid flanges or flexible webs are adopted. Moreover, the distortional beam element excluding the angling effect will produce significant errors in some particular cases.

Symmetric and Antisymmetric Solar Migrating Semidiurnal Tides in the Mesosphere and Lower Thermosphere

AbstractUpward‐propagating solar tides are responsible for a large part of atmospheric variability in the mesosphere and lower thermosphere (MLT) region, and they are also an important source of ionospheric variability. Tides can be divided into the parts that are symmetric and antisymmetric about the equator. Their distinction is important, as the electrodynamic responses of the ionosphere to symmetric and antisymmetric tides are different. This study examines symmetric and antisymmetric tides using 21 years of temperature measurements by the Thermosphere Ionosphere Mesosphere Energetics and Dynamics/Sounding of the Atmosphere using Broadband Emission Radiometry. The main focus is on the solar migrating semidiurnal tide (SW2), which is one of the dominant tides in the MLT region. It is shown that symmetric and antisymmetric parts of SW2 are comparable in amplitude. However, their spatiotemporal characteristics are different. That is, the symmetric part is strongest during March–June at 30–35° latitude, while the antisymmetric part is most prominent during May–September with the largest amplitude at 15–20° latitude. The symmetric and antisymmetric parts can be well described by the first two symmetric and antisymmetric Hough modes, respectively. Amplification is observed in the antisymmetric part during the major sudden stratospheric warmings (SSWs) in January 2006, 2009, 2013 and 2019. Atmospheric model simulations for the 2009 and 2019 SSWs confirm the amplification in the antisymmetric part of SW2. The enhanced antisymmetric tidal forcing explains the previously‐reported asymmetric response of the ionospheric solar‐quiet current system to SSWs.

Investigation of Viscoelastic Guided Wave Properties in Anisotropic Laminated Composites Using a Legendre Orthogonal Polynomials Expansion-Assisted Viscoelastodynamic Model.

This study investigates viscoelastic guided wave properties (e.g., complex-wavenumber-, phase-velocity-, and attenuation-frequency relations) for multiple modes, including different orders of antisymmetric, symmetric, and shear horizontal modes in viscoelastic anisotropic laminated composites. To obtain those frequency-dependent relations, a guided wave characteristic equation is formulated based on a Legendre orthogonal polynomials expansion (LOPE)-assisted viscoelastodynamic model, which fuses the hysteretic viscoelastic model-based wave dynamics and the LOPE-based mode shape approximation. Then, the complex-wavenumber-frequency solutions are obtained by solving the characteristic equation using an improved root-finding algorithm, which leverages coefficient matrix determinant ratios and our proposed local tracking windows. To trace the solutions on the dispersion curves of different wave modes and avoid curve-tracing misalignment in regions with phase-velocity curve crossing, we presented a curve-tracing strategy considering wave attenuation. With the LOPE-assisted viscoelastodynamic model, the effects of material viscosity and fiber orientation on different guided wave modes are investigated for unidirectional carbon-fiber-reinforced composites. The results show that the viscosity in the hysteresis model mainly affects the frequency-dependent attenuation of viscoelastic guided waves, while the fiber orientation influences both the phase-velocity and attenuation curves. We expect the theoretical work in this study to facilitate the development of guided wave-based techniques for the NDT and SHM of viscoelastic anisotropic laminated composites.

Corrosion damage identification based on the symmetry of propagating wavefield measured by a circular array of piezoelectric transducers: Theoretical, experimental and numerical studies

The article investigates the results obtained from numerical simulations and experimental tests concerning the propagation of guided waves in corroded steel plates. Developing innovative methodologies for assessing corrosion-induced degradation is crucial for accurately diagnosing offshore and ship structures exposed to harsh environmental conditions. The main aim of the research is to analyze how surface irregularities affect wave propagation characteristics. An investigation was conducted for antisymmetric fundamental mode A0. Specifically, the study examines the asymmetrical wavefronts generated by nonuniform thickness in damaged specimens. Initially, numerical analysis explores the impact of thickness variation on wave field symmetry. Corroded plates with varying levels of degradation are modeled using the random fields approach, with degradation levels ranging from 0 % to 60 %. Subsequently, the research investigates how the standard deviation of thickness distribution (from 5 % to 20 % of the initial thickness) and excitation frequency (from 50 to 150 kHz) influence recorded signals and the shape of reconstructed wavefronts. Each scenario compares wavefront symmetry levels estimated using rotational and bilateral symmetry degrees as indicative parameters. The numerical simulations are complemented by experimental tests conducted on plates with three different degradation levels. The results demonstrate the efficacy of the proposed wave field analysis approach for assessing structural integrity, as evidenced by the agreement between numerical predictions and experimental observations.

Bound states in the continuum for antisymmetric lamb modes in composite plates made of isotropic materials

In this study, we report a numerical design and observation of bound states in the continuum (BICs) for Lamb waves. BICs for elastic-wave systems, especially in non-periodic configurations, are difficult to obtain due to their intricate polarization states. However, the study in this matter has become very important, especially in the field of opto-mechanics or other multi-field couplings at micro or nanoscales. To illustrate the design concept, we simulate the introduction of a piece of silica (SiO2) into a thin infinite Si plate and show that, for specific aspect ratios, BICs for elastic waves can be predicted. We present numerical results for both two-dimensional (2D) rectangular plates and three-dimensional (3D) disk structures. Moreover, we also investigate the modal contributions of both the background and inclusion media during the occurrence of BICs, further verifying the physical background of our design strategy. Although we have focused our work on asymmetric Lamb modes, the current method can also be applied to construct other types of elastic-wave BICs, providing a powerful tool for metamaterial device prototyping based on the control or guiding of elastic waves.

Understanding the alleviation of “Double-ITCZ” bias in CMIP6 models from the perspective of atmospheric energy balance

The simulation of tropical precipitation has been a challenge to climate models. The multi-model ensemble mean of CMIP6 models only show limited improvement relative to the CMIP3 and CMIP5 models. However, a simple ensemble mean may mask the improvement of individual models. Here we evaluated 20 CMIP6 models and their corresponding earlier version in CMIP5. The results show that the CMIP6 models is significantly improved in the tropical precipitation compared to their counterparts in CMIP5, and the alleviation of bias mainly happened in the top ten model pairs with largest RMSE reduction (TOP10). For the mean of TOP10, the antisymmetric (symmetric) bias mode in CMIP5 is significantly reduced by 55% (78%). Further energetics evaluation shows that, the CMIP5-to-CMIP6 decrease of antisymmetric bias in the bulk of TOP10 models is accompanied by more realistic southward cross-equatorial atmospheric energy transport (AETEQ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${AET}_{EQ}$$\\end{document}), which is mainly contributed by the better representation of the extra-tropical surface turbulent flux (STF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$STF$$\\end{document}). On the other hand, the decrease in the symmetric bias of TOP10 models is associated with the enlargement of the negative bias in the seasonal contrast of AETEQ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${AET}_{EQ}$$\\end{document}, which is caused by the alleviation of the biases in the seasonal contrast of extra-tropical STF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$STF$$\\end{document}. Our analysis revealed the improvement in the simulation of tropical precipitation in CMIP6, and we pointed out that the improvement is associated with the model-generational changes in the simulated atmospheric energy balances.

Quantum phase synchronization via exciton-vibrational energy dissipation sustains long-lived coherence in photosynthetic antennas

The lifetime of electronic coherences found in photosynthetic antennas is known to be too short to match the energy transfer time, rendering the coherent energy transfer mechanism inactive. Exciton-vibrational coherence time in excitonic dimers which consist of two chromophores coupled by excitation transfer interaction, can however be much longer. Uncovering the mechanism for sustained coherences in a noisy biological environment is challenging, requiring the use of simpler model systems as proxies. Here, via two-dimensional electronic spectroscopy experiments, we present compelling evidence for longer exciton-vibrational coherence time in the allophycocyanin trimer, containing excitonic dimers, compared to isolated pigments. This is attributed to the quantum phase synchronization of the resonant vibrational collective modes of the dimer, where the anti-symmetric modes, coupled to excitonic states with fast dephasing, are dissipated. The decoupled symmetric counterparts are subject to slower energy dissipation. The resonant modes have a predicted nearly 50% reduction in the vibrational amplitudes, and almost zero amplitude in the corresponding dynamical Stokes shift spectrum compared to the isolated pigments. Our findings provide insights into the mechanisms for protecting coherences against the noisy environment.

Roughness-Induced Transition in Supersonic Boundary Layers with Wall Heating and Cooling Effects

The laminar–turbulent transition of a supersonic boundary layer induced by an isolated roughness element is investigated using direct numerical simulation, BiGlobal linear stability theory, and the three-dimensional parabolized stability equation. Cylindrical and diamond-shaped roughness elements are investigated in combination with different wall temperatures. Direct numerical simulations show that the cylinder configuration induces an earlier transition than the diamond configuration, with the interaction between the separated shear layer and the counter-rotating vortices causing the transition. BiGlobal analysis and the parabolized stability equation confirm the existence of two unstable instability modes in the wake region, namely, a symmetric mode and an antisymmetric mode, with the former being strongly dominant. The wall cooling and heating effects are studied by changing the wall temperature. Wall heating lifts the inlet boundary layer and weakens the separated shear layer. This, in turn, weakens the wake instability and delays the transition. The antisymmetric model disappears as the wall heating increases. Wall cooling accelerates the transition by enhancing the distortion of the roughness wake, resulting in stronger instabilities. Finally, the Reynolds number based on the momentum defect is used to define the transition criterion, and this is found to be in good agreement with the present simulation results.

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.

Linear and nonlinear Granger causality analysis of turbulent duct flows

This research focuses on the identification and causality analysis of coherent structures that arise in turbulent flows in square and rectangular ducts. Coherent structures are first identified from direct numerical simulation data via proper orthogonal decomposition (POD), both by using all velocity components, and after separating the streamwise and secondary components of the flow. The causal relations between the mode coefficients are analysed using pairwise-conditional Granger causality analysis. We also formulate a nonlinear Granger causality analysis that can account for nonlinear interactions between modes. Focusing on streamwise-constant structures within a duct of short streamwise extent, we show that the causal relationships are highly sensitive to whether the mode coefficients or their squared values are considered, whether nonlinear effects are explicitly accounted for, and whether streamwise and secondary flow structures are separated prior to causality analyses. We leverage these sensitivities to determine that linear mechanisms underpin causal relationships between modes that share the same symmetry or anti-symmetry properties about the corner bisector, while nonlinear effects govern the causal interactions between symmetric and antisymmetric modes. In all cases, we find that the secondary flow fluctuations (manifesting as streamwise vorticial structures) are the primary cause of both the presence and movement of near-wall streaks towards and away from the duct corners.

Nonlinear behavior of wave resonances in moonpool with a recess under wave actions

Nonlinear wave resonance in moonpool with a recess under wave actions is studied by using CFD simulations based on OpenFOAM® package. Compared to the rectangular moonpool, the influence of free surface nonlinearity plays an important role in the wave resonance in the recess moonpool. Harmonic analysis indicates that the higher-order harmonic induced sloshing-mode resonance even approaches the same magnitude as the first-order harmonic induced piston-mode motion. The superposition between them also leads to extreme free surface oscillation in the recess moonpool. A peak appears in the total horizontal wave forces by the higher-order harmonic induced sloshing resonance due to the anti-symmetric mode. In a word, the free surface nonlinearity is an indispensable factor in the response of fluid resonance in moonpool with recess configurations.

Detection of a Submillimeter Notch-Type Defect at Multiple Orientations by a Lamb Wave A0 Mode at 550 kHz for Long-Range Structural Health Monitoring Applications.

The early detection of small cracks in large metal structures is a crucial requirement for the implementation of a structural health monitoring (SHM) system with a low transducers density. This work tackles the challenging problem of the early detection of submillimeter notch-type defects with a semielliptical shape and a groove at a constant width of 100 µm and 3 mm depth in a 4.1 mm thick aluminum plate. This defect is investigated with an ultrasonic guided wave (UGW) A0 mode at 550 kHz to investigate the long range in thick metal plates. The mode selection is obtained by interdigital transducers (IDTs) designed to operate with a 5 mm central wavelength. The novel contribution is the validation of the detection by pulse-echo and pitch and catch with UGW transducers to cover a distance up to 70 cm to reduce the transducers density. The analysis of scattering from this submillimeter defect at different orientations is carried out using simulations with a Finite Element Model (FEM). The detection of the defect is obtained by comparing the scattered signals from the defect with baseline signals of the pristine laminate. Finally, the paper shows that the simulated results are in good agreement with the experimental ones, demonstrating the possible implementation in an SHM system based on the efficient propagation of an antisymmetric mode by IDTs.

Investigating the dispersion characteristics of symmetric and asymmetric modes in rails: A theoretical and experimental study

The propagation law of ultrasonic guided waves in waveguide structures is determined by their dispersion characteristics, and the number of guided waves in symmetric and antisymmetric modes in rails is significant, so the dispersion characteristics are very complex. In order to study the dispersion characteristics of symmetric and antisymmetric modes in rails, this paper derives the wave equation based on the SAFE method with higher order elements, and the correctness of the wavestructure calculation in the SAFE model is verified using the FE method. This paper focuses on the wavestructure state at 0 kHz and the wavestructure changes during mode crossing through and repulsive deflections, and for the first time experimentally verifies the phenomenon of wave structure exchange in rails. The main conclusions are that the dispersion curves between modes with the same symmetry show repulsive deflection, and the dispersion curves between modes with opposite symmetry show crossover; the wavestructure of the rail is mainly rigid body translation and rigid body rotation at frequencies close to 0 kHz; the guided wave at the intersection of symmetric and antisymmetric modes transforms into a fading wave that cannot be continuously propagated in rails; when the dispersion curves are close, the wavestructures between the two modes are linearly superimposed, and when the dispersion curves are deflected by repulsion, the wavestructures of the two modes are exchanged.

Meta-structure enhanced second harmonic S0 waves for material microstructural changes monitoring

Cumulative second harmonic Lamb waves in nonlinear media feature increasing amplitudes with propagation distance, conducive to the monitoring of material microstructural changes in structures. The phenomenon can be readily generated by zero-order symmetric (S0) mode waves in the low-frequency range. However, in a practical piezoelectric-transducer-activated system, both S0 and A0 (zero-order antisymmetric) mode Lamb waves are inevitably excited, while only the former is responsible for cumulative effects. The generation efficiency of the cumulative second harmonics is then affected by the presence of the A0 waves. To tackle the problem, this study develops a metamaterial structure, referred to as a meta-structure, to tactically enhance the cumulative second harmonic S0 Lamb waves by converting the A0 mode components into S0 mode waves. Topology optimization is conducted to design the meta-structure, which is surface-mounted onto the structure under inspection, to achieve high-efficiency A0-to-S0 wave mode conversion. Through tuning the parameters and constraints of the optimization, the designed single-sided meta-structure breaks the structural symmetry in the thickness direction, while facilitating its practical implementation. Typical scenarios with different meta-structure materials are discussed. Numerical simulations demonstrate that the strain amplitudes of the fundamental S0 mode waves can be increased by 60% with the deployment of the meta-structure, alongside an enhancement of the second harmonic S0 mode waves at different sensing distances. Finally, the designed meta-structure is fabricated via 3D printing technique and tested experimentally on an aluminum plate subjected to thermal aging treatment for monitoring the heating-induced microstructural changes inside the structure. Experimental results confirm an increase in the wave amplitudes of the linear S0 mode waves with the assistance of the meta-structure. The developed system improves the sensitivity of nonlinear Lamb wave-based monitoring methods in characterizing material microstructural changes, which shows great promise for detecting incipient damage in practical structural health monitoring applications.