Symmetric Wave Research Articles

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.

An Improvised Modulation and Control Approach for Dual Active Bridge DC–DC Converter System

Aimed at the control and modulation of dual active bridge bi-directional dc (DAB-BIDC) converter, an unconventional approach is applied to explore its effect in symmetrical wave-based isolated dc-dc converters. The existing control schemes of DAB-BIDC converter with unified or optimal phase shift (UPS/OPS) modulation have the constraints like complex control schemes, light load efficiency, current stress, and reactive power. Since a 50 Hz, grid-connected conventional converter system uses the sinusoidal pulse width modulation method to minimize the requirement for passive filters. Similarly, this work investigates the same analogy for the high-frequency (HF) symmetrical wave converters to get effective modulation and control scheme for the DAB-BIDC converter. Furthermore, the proposed sinusoidal pulse width-phase shift (SPW-PS) modulation scheme has been implemented by the optimally derived control parameters using Lagrange's Multiplier Method (LMM) to minimize the reactive power flow and current stress reduction at the HF link. Therefore, the DAB-BIDC converter with the proposed modulation and control approach can be used for EV charging and solid-state transformers applications. Finally, the proposed work is validated using MATLAB simulation and experimental setup having turn ratio 36/12 V, fundamental frequency 5-kHz, and switching frequency 100-kHz for the experimental validation using OPAL-RT.

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.

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.

Wave Manipulation in Intelligent Metamaterials: Recent Progress and Prospects

AbstractMetamaterials (MMs), which include phononic crystals (PCs) as a particular type, exhibit anomalous wave propagation properties through artificial design of topologies or lattice forms of unit‐cells. Recent advancements in MMs signify an ascendant research trend, providing promising design ideas and means for unprecedented wave propagation properties. The imperative for on‐demand, real‐time active control of wave propagation underscores the significance of tunable manipulation of acoustic/elastic waves, promoting the design and development of tunable MMs. Furthermore, the versatility of intelligent materials and their ongoing development and innovation contribute significantly to the emergence of diverse intelligent MMs. This comprehensive survey provides an overview of recent advancements and current research trends in the interdisciplinary field of intelligent MMs with electro‐/magneto‐mechanical couplings. The primary objective of the review is to emphasize significant progress in agile manipulation of acoustic/elastic waves in electro‐/magneto‐mechanical coupled MMs, followed by an in‐depth exploration of intelligent metasurfaces, topological MMs, non‐Hermitian parity‐time symmetric wave systems, odd elastic MMs, and spatiotemporally modulated MMs. Special emphasis is given to multi‐field coupling effects. The review concludes with a summary and outlines potential prospects, offering a timely and informative guide for future studies on actively tunable PCs and MMs in practical engineering applications.

Breather solutions for a radially symmetric curl-curl wave equation with double power nonlinearity

This paper is concerned with breather solutions of a radially symmetric curl-curl wave equation with double power nonlinearity ρ(x)utt+∇×(M(x)∇×u)+μ(x)u+vp(x)|u|p−1u+vq(x)|u|q−1u=0,where (x,t)∈R3×R, u:R3×R→R3 is the unknown function, M:R3→R3×3 and ρ,μ,vp,vq:R3→(0,+∞) are radially symmetric coefficient functions with 1<p<q. By considering the solutions with a special form u=y(|x|,t)x|x|, we obtain a family of ordinary differential equations (ODEs) parameterized by the radial variable r=|x|. Then we characterize periodic behaviors and analyze the joint effects of the double power nonlinear terms on the minimal period and the maximal amplitude. Under certain conditions, we construct a 2πρ(0)/μ(0)-periodic breather solution for the original curl-curl wave equation and find such a solution which can generate a continuum of phase-shifted breathers.

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.

Non-reflective Propagation of Kink Waves in Magnetic-Flux Tubes in the Solar Atmosphere

We study the non-reflective propagation of kink waves in inhomogeneous magnetic-flux tubes. We use the thin-tube and zero-beta plasma approximations. The wave equation with the variable velocity is reduced to the Euler–Poisson–Darboux equation. This equation contains one dimensionless parameter. There are two infinite sequences of this parameter, one monotonically increasing and the other monotonically decreasing, when exact analytical solutions for the Euler–Poisson–Darboux equation can be obtained. For the monotonically increasing sequences the Euler–Poisson–Darboux equation becomes the equation describing spherically symmetric waves in multi-dimensional spaces. The general results are applied to kink-wave propagation in coronal magnetic loops. We consider a coronal magnetic loop of a half-circular shape. We find that for a fixed loop height there is a one-parametric family of dependences of the loop cross-sectional radius on the coordinate along the loop corresponding to the non-reflective kink-wave propagation.

Synthetic Aperture Ladar Motion Compensation Method Based on Symmetric Triangle Linear Frequency Modulation Continuous Wave Segmented Interference

Synthetic Aperture Ladar (SAL) is a sensor that combines laser detection technology with synthetic aperture technology to achieve ultra-high-resolution imaging. Due to its extremely short wavelength, SAL is more sensitive to motion errors. The micrometer-level motion will affect the target’s azimuth focus. This article proposes an SAL motion compensation method based on Symmetric Triangular Linear Frequency Modulation Continuous Wave (STLFMCW) segmented interference, utilizing the characteristics of a triangular wave, to solve the problem of target azimuth defocusing. This article first establishes an STLFMCW echo signal model based on the SAL system under the influence of motion errors. Secondly, the radial velocity gradient along the azimuth direction is extracted using the triangular-wave-positive and -negative frequency modulation signals segmented interference method. Then, for the initial phase wrapping problem, the frequency spectral cross-correlation method is used to accurately estimate the initial radial velocity error. The radial velocity gradient is integrated along the azimuth to obtain the platform motion trajectory. Finally, the compensation functions are constructed to complete the echo Range Cell Migration (RCM) correction and residual phase compensation, resulting in a focused SAL image. This article verifies the practical effect of this method in eliminating motion errors using only one-period STLFMCW signal through simulation and real experiments. The quantitative results show that compared with the traditional method, the proposed method reduces the azimuth Peak Sidelobe Ratio (PSLR) by 8dB and the Integrated Sidelobe Ratio (ISLR) by 9 dB. This method has significant improvements and is of great significance for high-resolution FMCW SAL imaging.

Symmetric elastic wave cloak design for underground protective structures based on multi-center coordinate transformation

Symmetric elastic wave cloak design for underground protective structures based on multi-center coordinate transformation

Compressive Perception Image Reconstruction Technology for Basic Mixed Sparse Basis in Metal Surface Detection

&lt;p&gt;Applying Compressed Sensing (CS) technology to robot vision image transmission, an effective method for image reconstruction in robot imaging is proposed to improve the accuracy of reconstruction. Reconstructing images using a mixed sparse representation of DCT and circularly symmetric contour wave transform, the basic algorithm used is the Smoothed Projection Landweber (SPL) algorithm, which optimizes the coefficients under different sparse transformations by incorporating hard thresholding and binary thresholding methods for different sparse bases during iterations. The experiment shows that compared with single sparse base image reconstruction, the proposed reconstruction method has improved reconstruction accuracy.&lt;/p&gt; &lt;p&gt;&amp;nbsp;&lt;/p&gt;

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.

Generation and modulation of shock waves in two-dimensional polariton condensates

Due to the ability of exciton-polariton condensates formed in semiconductor microcavities to be achieved at room temperature and their characteristics such as non-equilibrium and strong interactions, they have become an ideal platform for studying the nonlinear properties of non-equilibrium quantum systems. In 2013, the research group led by L. Dominici observed two-dimensional symmetric shock waves in the polariton condensate driven by coherent pump. However, owing to the characteristics of this system, theoretical researches have lagged behind. In one-dimensional polariton condensates, disregarding cross-interaction of the system, a type of asymmetric shock wave was respectively discovered by A. M. Kamchatnov in 2012 and A. M. Belounis in 2017. In 2023, utilizing the adiabatic approximation, our research team not only uncovered sparse wave, symmetric, and asymmetric shock waves in the system, but also revealed that the symmetric shock waves are triggered by cross-interaction. At present, there is no theoretical research on shock waves in two-dimensional polariton condensate. In this paper, spectral methods and fourth-order Runge-Kutta methods are used to explore the generation and control of shock waves in two-dimensional polariton condensates. It is found that when the cross-interaction between the condensate and the polariton thermal reservoir is quenched at high condensation rates, the initially prepared bright solitons can be modulated into two types of rotationally symmetric shock waves with different velocities, while the initial dark-like solitons can only transform into a single velocity rotationally symmetric shock wave. If quenching the external potential, the dark-like solitons can be transformed into anisotropic supersonic shock waves, and the dependence of shock wave on the width of the external potential is also shown. When the external potential and incoherent pumping are controlled at low condensation rates, multiple anisotropic shock waves can be excited in a uniform condensate, and their amplitudes can be used to control the wave number and amplitude of the shock waves and the range of widths for the external potential or incoherent pumping to excite shock waves is also demonstrated. The proposed methods in this paper not only provide theoretical guidance for the generation and control of shock waves in exciton-polariton condensates, but also find symmetric shock waves similar to experiments (&lt;ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://www.nature.com/articles/ncomms9993"&gt;&lt;i&gt;Nat. Commun.&lt;/i&gt; &lt;b&gt;6&lt;/b&gt; , 8993&lt;/ext-link&gt;) without adopting any approximation, and open up a universal pathway for exciting shock waves in non-equilibrium or non-integrable systems, which may become a paradigm for transforming solitons into shock waves and significantly propel the rapid development of shock wave theory in different domains.

Влияние несплошностей на распространение волн Лэмба в пластинах

A mathematical model of the Lamb propagation of the zero mode in a thin steel plate on propagation propagation has been developed. Wave excitation was carried out on the basis of the wedge method in the Comsol Multiphysics program. The paper calculates the measurement of the equivalent voltage and the von Mises voltage during wave propagation, as well as the average equivalent voltage on the inclined surface of the prism, which plays the role of a receiver and emitter. The article considers the shape of the obtained symmetric and antisymmetric waves of the zero mode. The influence of the defect dimensions on the Lamb propagation velocity and, consequently, on the fixation time of the transmitted signal is shown.

Self-purification and entanglement revival in lambda matter

In this study, we explore the dynamics of entanglement in an ensemble of qutrits with a lambda-type level structure interacting with single-mode bosons. Our investigation focuses on zero-energy states within the subspace of totally symmetric wave functions. Remarkably, we observe a universal two-stage dynamics of entanglement with intriguing revival behavior. The revival of entanglement is a consequence of the self-purification process, where the quantum state relaxes and converges universally to a special dark state within the system.

Investigation of different influence functions in peridynamics

Peridynamics is a non–local numerical method for solving fracture problems based on integral equations. It is assumed that particles in a continuum are endowed with volume and interact with each other at a finite distance, as in molecular dynamics. The influence function in peridynamic models is used to limit the force acting on a particle and to adjust the bond strength depending on the distance between the particles. It satisfies certain continuity conditions and describes the behavior of non-local interaction. The article investigates various types of influence function in peridynamic models on the example of three-dimensional problems of elasticity and fracture. In the course of the work done, the bond-based and state-based fracture models used in the Sandia Laboratory are described, 6 types of influence functions for the bond-based model and 2 types of functions for the state-based model are presented, and the corresponding formulas for calculating the stiffness of the bond are obtained. For testing, we used the problem of propagation of a spherically symmetric elastic wave, which has an analytical solution, and a qualitative problem of destruction of a brittle disk under the action of a spherical impactor. Graphs of radial displacement are given, raster images of simulation results are shown.

Investigation of guided wave propagation in nanoscale layered periodic piezoelectric plates based on Eringen's nonlocal and strain gradient theory

This paper investigates the dynamic propagation behavior of guided waves in nanoscale media composed of alternating layers of piezoelectric phases. The study employs Eringen's nonlocal and strain gradient theories to derive equations for symmetric wave propagation and the scattering relations of guided waves perpendicular to these structures. Dispersion curves are calculated and plotted to compare these theories, considering the influence of nanoscale size-effect, volume ratio of constituent layers, and material length scale. Using the strain gradient theory, the paper explores the impact of length scale parameters on the propagation behavior of horizontally polarized guided waves in an alternating layer structure of nanoscale piezoelectric material, specifically nanoscale piezoelectric laminates. The analysis involves calculating localization factors and dispersion curves to analyze the effects of size-effect and length scale parameters on wave propagation and band structures. Additionally, the study plots and analyzes changes in mechanical displacement and electrical potential, followed by an investigation and discussion of nanoscale size effects and the effects of the material's length scale parameter on dispersion curves and conversion modes within specific regions. The results highlight that the length scale effect parameter significantly impacts the mode conversion zones and band gap structures, more so than the NLPE continuum theory suggests. As the strain gradient parameter increases, these zones shift towards higher wavenumbers and to the right . Furthermore, introducing the length scale factor results in a substantial decrease in both the formation of conversion zones and the density of dispersion curves.

Simultaneous tensile and shear measurement of the human cornea in vivo using S0- and A0-wave optical coherence elastography

Understanding corneal stiffness is valuable for improving refractive surgery, detecting corneal abnormalities, and assessing intraocular pressure. However, accurately measuring the elastic properties, specifically the tensile and shear moduli that govern mechanical deformation, has been challenging. To tackle this issue, we have developed guided-wave optical coherence elastography that can simultaneously excite and analyze symmetric (S0) and anti-symmetric (A0) elastic waves in the cornea at around 10 kHz frequencies, enabling us to extract tensile and shear properties from measured wave dispersion curves. We verified the technique using elastomer phantoms and ex vivo porcine corneas and investigated the dependence on intraocular pressure using acoustoelastic theory that incorporates corneal tension and a nonlinear constitutive tissue model. In a pilot study involving six healthy human subjects aged 31 to 62, we measured shear moduli (Gzx) of 94±20 kPa (mean±standard deviation) and tensile moduli (Exx) of 4.0±1.1 MPa at central corneas. Our preliminary analysis of age-dependence revealed contrasting trends: -8.3±4.5 kPa/decade for shear and 0.30±0.21 MPa/decade for tensile modulus. This OCE technique has the potential to become a highly useful clinical tool for the quantitative biomechanical assessment of the cornea. Statement of SignificanceThis article reports an innovative elastography technique using two guided elastic waves, demonstrating the measurement of both tensile and shear moduli in human cornea in vivo with unprecedented precision. This technique paves the way for comprehensive investigations into corneal mechanics and holds clinical significance in various aspects of corneal health and disease management.

Phonon and maxon instability in Bose–Einstein condensates with parity-time symmetric spin–orbit coupling

Parity-time () symmetry has drawn great research interest in non-Hermitian physics. Recently, there is an emerging model of -symmetric spin–orbit coupling (SOC) which could be realized with spin-1/2 atomic Bose–Einstein condensates (BECs) when the two spin components are respectively subjected to momentum-dependent gain and loss (Qin et al 2022 New J. Phys. 24 063025). In this model, inter-atom interaction has no influence on the -symmetric plane waves. Thus, collective excitation playing the role of fingerprint of inter-atom interaction is investigated in this paper. For the phonon excitation, it is shown that the repulsive interaction between atoms in different spin states, which tends to drive the atoms to populate in only one spin component, can break the -symmetry, and leads to a phonon instability. Whereas, for the case of the phonon-maxon-roton collective excitation spectrum, the repulsive interaction between atoms in different spin states can lead to a maxon instability, which does not occur in Hermitian BEC systems (dipolar BECs or BECs with Raman induced SOC). Simulation of the time evolution of the plane wave solution against small noise shows that the maxon instability can result in the formation of a supersolid-like stripe pattern at the initial stage, but the non-Hermitian nature of the system finally destroys the pattern. The phase diagram of stability shows that the Rabi coupling and repulsive interaction between the atoms in the same spin state can stabilize the system.

Black holes and non-perturbative gravitational waves in f(R) gravity

Exact solutions of spherically symmetric black hole and gravitational wave are explored in f(R) gravity in arbitrary dimension. We find two exact solutions for the radiation and absorption of null dust. In the framework of general relativity, the Birkhoff theorem strictly forbids the existence of spherical gravitational waves in vacuum space. We find spherical non-perturbative gravitational waves, which are shear-free, twist-free, but expanding.