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The analysis of dispersion portraits of Lamb waves propagating in stratified plates satisfying the orthogonal Wiechert condition reveals the crossing of fundamental Lamb modes, leading to a state of possible wave bifurcation, when the wave energy can transfer between fundamental symmetric and asymmetric modes, which results in wave instability. The analysis is based on the combination of Cauchy sextic formalism and the exponential fundamental matrix method. [ABSTRACT FROM AUTHOR]

In this paper, the propagation of Lamb waves in an orthotropic elastic sandwich plate is investigated. The surface layers and the core layer may be compressible or incompressible. The main aim of the paper is to derive explicit dispersion equations. First, the dispersion equations of symmetric modes and asymmetric modes are derived for compressible sandwich plates by using the effective boundary condition method along with the transfer matrices for orthotropic elastic layers. These dispersion equations recover the dispersion equations of Lamb waves propagating in compressible isotropic sandwich plates. The dispersion equations for incompressible sandwich plates are obtained by using the incompressible limit method. It is shown numerically that the thickness ratio and the stiff contrast affect strongly higher modes and the incompressibility has strong influence on symmetric modes. Remarkably, the obtained dispersion equations can be used to analyze the dispersion characteristic of Lamb waves propagating in sandwich plates with honeycomb core layers because the honeycomb core layers can be replaced effectively by transversely isotropic elastic layers by mean of homogenization. [ABSTRACT FROM AUTHOR]

Ice shelves are assumed to flow steadily from their grounding lines to the ice front. We report the detection of ice‐propagating extensional Lamb (plate) waves accompanied by pulses of permanent ice shelf displacement observed by co‐located Global Navigation Satellite System receivers and seismographs on the Ross Ice Shelf. The extensional waves and associated ice shelf displacement are produced by tidally triggered basal slip events of the Whillans Ice Stream, which flows into the ice shelf. The propagation velocity of 2,800 m/s is intermediate between shear and compressional ice velocities, with velocity and particle motions consistent with predictions for extensional Lamb waves. During the passage of the Lamb waves the entire ice shelf is displaced about 60 mm with a velocity more than an order of magnitude above its long‐term flow rate. Observed displacements indicate a peak dynamic strain of 10−7, comparable to that of earthquake surface waves that trigger ice quakes. Plain Language Summary: Ice shelves normally flow steadily toward their boundaries with the open ocean at the ice front. However, seismographs and Global Navigation Satellite System receivers deployed on the Ross Ice Shelf record guided elastic plate waves traveling in the ice as well as permanent displacement of the ice shelf. The elastic waves and ice shelf displacement originate from basal slip events of the Whillans Ice Stream, which flows into the Ross Ice Shelf. The velocity of the elastic waves is about 2,800 m/s, as expected for guided plate waves propagating in an ice shelf. During the passage of the elastic waves, the entire ice shelf with an area of 500,000 square kilometers is displaced about 60 mm in a direction away from the Whillans Ice Stream. These observations show that the strain imparted to the ice shelf by the once or twice daily Whillans Ice Stream basal slip events is sufficient to trigger ice quakes and perhaps enhance the deformation of the ice shelf. Key Points: Extensional Lamb waves propagate across the Ross Ice Shelf, radiated from slip events at the base of the Whillans Ice StreamDuring the passage of the Lamb waves, the entire ice shelf is displaced about 60 mm, with a velocity an order of magnitude above its long‐term flow rateThe displacement pulses produce a peak dynamic strain of 10−7, suggesting that they could trigger icequakes in the ice shelf [ABSTRACT FROM AUTHOR]

The propagation characteristics of Lamb waves in a functionally graded material (FGM) plate with periodic gratings have been studied. The power series technique is employed to solve the governing differential equations with variable coefficients. In the propagation direction, the displacements of Lamb waves are expanded in the Fourier series due to the periodicity of the structure. The convergences of the power series and Fourier series are proved and the method presented in the article is verified by the finite element method (FEM). The band gaps are obtained by the couplings between the different modes of Lamb waves induced by FGM. The effects of the structural parameters (such as the periodicity, mass, and length of the gratings) and gradient coefficient on band gaps are investigated. Numerical results show that the band gaps shift up as the gradient coefficient increases and the second band gap (SBG) is closed when the gradient coefficient is large enough. The conclusions are of practical significance for designing elastic wave filters with high-performance. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The article is devoted to the analytical and numerical study of the pattern of propagation and attenuation, due to Coulomb friction, of shear waves in an infinite elastic thin plate with a circular orifice of radius r 0 lying on a rough base. Considering the friction forces and their influence on the sample of wave propagation in extended rods or thin plates is important for calculating the stress–strain state in them and the size of the area of motion. An exact analytical solution of a nonlinear boundary value problem for tangential stresses and velocities is obtained in quadratures by the Laplace transform, with respect to time. It turned out that the complete exhaustion of the wave front of a strong rupture occurs at a finite distance r * from the center of the orifice, and an elementary formula is given for this distance (the case of tangential shock stresses suddenly applied to the orifice boundary is considered). For various ratios of the magnitude of the limiting friction force to the amplitude of the applied load, the stopping (trailing) wave fronts are calculated. After passing them, a state of static equilibrium between the elastic and friction forces with a nonlinear distribution of residual stresses is established in the region r 0 ≤ r ≤ r * . For the first time, a precise analytical solution was obtained for the boundary value problem of the propagation of elastic shear waves in an infinite isotropic space with a cylindrical cavity, when a tangential shock load is set on its surface. [ABSTRACT FROM AUTHOR]

Purpose: The examination of the behavior of wave propagation through different kinds of materials under various mathematical models certainly brings out new properties of those materials to the fore. In this contribution, the circular-crested Lamb-type waves in an isotropic homogeneous, elasto-thermal plate with voids sandwich-packed by inviscid liquid layers have been examined in the context of Lord–Shulman and Green–Lindsay generalizations. Methods: Helmholtz's decomposition principle has been used to separate the solenoidal part and the lamellar part of the waves. The normal mode analysis technique has been used to obtain solutions to governing equations. With the help of solutions, the obtained partial differential equations have been converted to ordinary differential equations to find the eigenvalues of the elasto-porothermal plate bordered with inviscid liquid layers. The problem has also been solved from a numerical point of view and the results have been portrayed graphically. Results: The transverse horizontal wave being unaltered due to voids and temperature gradient gets separated from the coupled system corresponding to elastic waves (compressional and transverse vertical), thermal waves, and wave motion due to voids. Apart from that, each layer of liquid possesses one longitudinal wave. The frequency equations have been derived for the flexural and longitudinal wave modes by solving the stiffness matrix. The inviscid fluid and voids decrease the magnitude of phase velocity and attenuation coefficient. Thermal relaxation times have a small impact on wave propagation. Conclusions: The problem of circular-crested Lamb-type waves has been solved mathematically which lays a theoretical foundation for further study of Lamb-type wave propagation in plates. The present work may find applications in many fields such as the petroleum industry, earthquake engineering, soil dynamics, hydrology, as well as biomechanics. [ABSTRACT FROM AUTHOR]

To study the acoustic characteristics of sound scattered from laminated structures such as elastic plates and shells, it is usually required to solve the Lamb waves' dispersion equations. Many traditional root-finding methods such as bisection, the Newton–Raphson method, and the Muller method are not able to tackle the problem completely. A simple but powerful method named local peaks search (LPS) is proposed to overcome their drawbacks. Firstly, the non-zero part of the dispersion equation is defined as the dispersion function, and its reciprocal is used to transform the zeros (i.e., roots) into local peaks. Secondly, the chosen complex domain is discretized, and the coarse local domains where the local peaks exist are determined by the direct search method globally. Thirdly, the Muller method is applied to obtain the refined locations of local peaks. Lastly, in order to refine the results, a hierarchical scheme is designed and the iteration of the above procedures is implemented; the error is set to be 10−16 as the stop criteria. The accuracy of the LPS method is validated by comparing it with the bisection method for the problem of elastic plates in the vacuum. The acoustic echo structures are analyzed experimentally. By computation of Lamb waves' phase velocity, the critical angles are derived numerically and compared with the results acquired by an experiment using monostatic sound transducers. In this way, it is validated that the elastic scattered wave components are the highlights shown in the time-angle figure. Furthermore, the work can be applied for non-destructive testing, especially underwater structural health monitoring. [ABSTRACT FROM AUTHOR]

Human health monitoring (HHM) is essential for continued daily task execution, as is structural health monitoring (SHM) for structures to ensure the continual performance of their designed tasks with optimal efficiency. The existence of damage in a structure affects its optimal use through stiffness deterioration. Damage of different forms could occur in a structure but have the singular objective of material degradation, leading to its underuse for a task. Guided wave ultrasonics has shown strength in detecting sundry damage in structures, but most of the damage monitored and detected is unfilled with substances. However, some damage could trap and accumulate substances that could hasten material degradation through corrosion activities under favorable conditions, especially in the oil and gas industry. This study used the ultrasonic-guided waves' pitch–catch inspection technique to identify damage filled with different materials. The assessment was based on the RMSD of the dominant Lamb wave mode's average maximum amplitude and the response signals' transmission coefficient (TC). A five-cycle tone burst of excitation signals of different frequencies was created to generate propagating Lamb waves in the structure. The fundamental antisymmetric mode was found to be more sensitive than the fundamental symmetric mode when detecting damage filled with various substances. At 80 kHz, the deviation of the current response signals from the baseline response signals due to different filled substances in the damage was distinct and decreased with increased fluid viscosity. Given that structures in the oil and gas sector are particularly susceptible to substance-induced damage, the outcomes of this study are paramount. [ABSTRACT FROM AUTHOR]

The creation of a sink in a lossless wave‐bearing medium is achieved using complex frequency signals—harmonic excitations that exponentially grow in time. The wave sink, where incident waves are confined to a point, has attracted interest for imaging and sensing since it may lead to arbitrarily small hotspots that surpass the diffraction limit. However, most methods of creating sinks require careful tuning, such as by impedance matching the sink to free space through the inclusion of loss, which imposes constraints on emerging applications. An alternative method, proposed here, relies on complex frequency excitations, bypassing the need to modify the scattering system by instead shaping the input signal. Eigenvalue zeros derived from a scattering formalism extended to the complex frequency plane reveal operating conditions that induce complete energy trapping under steady‐state conditions in a framework generally applicable to 2D and 3D media. To support the developed theory, an experiment is performed where a sink is realized using elastic waves on a plate with a circular cutout. These findings may lead to imaging and sensing applications relying on subwavelength focal points and nonlinear wave generation due to the high amplitudes achieved over short timescales. [ABSTRACT FROM AUTHOR]

Purpose: Lamb wave is widely used in damage detection and structural health monitoring of plate-like structures. In the current stage, the propagation of non-axisymmetric circular crested Lamb has not been theoretically solved. Therefore, it is essential to find its exact solutions. Methods: The displacement expressions and frequency equations are derived through three-dimensional elastic theory using Helmholtz conversion. Numerical simulations and experiments are conducted on plates for verification of theoretical results. Results: Both axisymmetric and non-axisymmetric waves are obtained from the governing equation with free boundary conditions. Lamb wave travels along the radial direction and holds as a standing wave in circumferential and longitudinal directions. The displacement field is expressed with Bessel functions in the radial direction and trigonometric functions in circumferential and longitudinal directions. Two families of Lamb wave modes are generated, which are identified by radial wavenumber and circumferential order. The amplitudes of displacements decrease with the propagation distance increases, and the circumferential distributions of displacements are affected by the circumferential order. Results obtained from simulation and experiment provide good verification for theoretical predictions. Conclusions: The analytic solutions are presented in non-axisymmetric problems for circular crested Lamb wave in this paper, which provides a theoretical foundation for further investigation of Lamb wave propagation in plates. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The problem of acoustic wave propagation in a predeformed compressible elastic layer interacting with a layer of viscous compressible fluid is considered. The study is based on the three-dimensional equations of the linearized theory of finite strain elasticity for an elastic layer and the three-dimensional linearized Navier–Stokes equations for a layer of viscous compressible fluid. The problem statement and the approach based on the general solutions of linearized equations for the elastic body and the fluid are applied. The dispersion equation describing the propagation of harmonic waves in a hydroelastic system in a wide frequency range for a thick layer of fluid is obtained. The effect of prestresses, as well as the thickness of the elastic body and fluid layers, on the phase velocities and damping factors of generalized Lamb modes is analyzed. The developed approach and the results obtained make it possible to establish the limits of applicability of models based on different variants of the theory of small initial deformations, classical elasticity theory, and the perfect fluid model for wave processes. Numerical results are plotted and analyzed. [ABSTRACT FROM AUTHOR]

We have numerically investigated the transmission of an antisymmetric Lamb wave through a line of silicon pillars erected onto a homogeneous silicon plate when the frequency is tuned to a resonant frequency of the pillars. For either a bending mode or a compressional mode, the resonators emit in the plate a wave 180° out-of-phase with the exciting Lamb wave, resulting in dips in the transmission spectrum. We show that transmission at resonance can be actively controlled by applying an external force, either tangential (bending eigenmode) or axial (compressional eigenmode), on top of the pillars. The transmission coefficient can be precisely controlled by finely tuning either the phase or the amplitude of the external force. For specific dimensions of the structure, both resonant modes arise at the same frequency. This geometry has the advantage of offering an additional degree of freedom for the direction of the external force but is less favorable from an energy point of view. [ABSTRACT FROM AUTHOR]

The aim of this work is to present theoretical tools to study wave propagation in elastic waveguides and perform multi-frequency scattering inversion to reconstruct small shape defects in elastic waveguides and plates. Given surface multi-frequency wavefield measurements, we use a Born approximation to reconstruct localized defect in the geometry of the plate. To justify this approximation, we introduce a rigorous framework to study the propagation of elastic wavefield generated by arbitrary sources. By studying the decreasing rate of the series of inhomogeneous Lamb mode, we prove the well-posedness of the PDE that model elastic wave propagation in two- and three-dimensional planar waveguides. We also characterize the critical frequencies for which the Lamb decomposition is not valid. By using these results, we generalize the shape reconstruction method already developed for acoustic waveguide to two-dimensional elastic waveguides and provide a stable reconstruction method based on a mode-by-mode spacial Fourier inversion given by the scattered field. [ABSTRACT FROM AUTHOR]

A method for the determination of longitudinal and transverse bulk acoustic wave attenuation from measurements of the decay-rate of two independent zero-group-velocity resonances in a couple of matched plates is presented. A linear relation is derived, which links the bulk-wave attenuation coefficients to the decay-rate of plate-resonances. The relation is used to determine the acoustic loss of tungsten at GHz frequencies from noncontact laser-ultrasonic measurements in plates with thicknesses of about 1 µm. The longitudinal and transverse attenuation was found to amount to 1918 m−1 and 7828 m−1 at 2.16 GHz and 3265 m−1 and 12181 m−1 at 2.46 GHz. The presented approach is validated with calculated responses to a thermoelastic source, and the accuracy of the obtained attenuation values is estimated to be in the range of 10%. [ABSTRACT FROM AUTHOR]

In engineering acoustics, the propagation of elastic flexural waves in plate and shell structures is a common transmission path of vibrations and structure-borne noises. Phononic metamaterials with a frequency band gap can effectively block elastic waves in certain frequency ranges, but often require a tedious trial-and-error design process. In recent years, deep neural networks (DNNs) have shown competence in solving various inverse problems. This study proposes a deep-learning-based workflow for phononic plate metamaterial design. The Mindlin plate formulation was used to expedite the forward calculations, and the neural network was trained for inverse design. We showed that, with only 360 sets of data for training and testing, the neural network attained a 2% error in achieving the target band gap, by optimizing five design parameters. The designed metamaterial plate showed a −1 dB/mm omnidirectional attenuation for flexural waves around 3 kHz. [ABSTRACT FROM AUTHOR]

Dispersion curves are plotted and the propagation of generalized Lamb waves over a wide range of frequencies is studied based on the linearized three-dimensional Navier–Stokes equations for the layer of viscous compressible fluid and the linear equations of classical elasticity for the elastic layer. The effect of the viscosity of the fluid, the thickness of the elastic and liquid layers on the phase velocity and the damping factor of generalized Lamb modes is analyzed in the case of a thick liquid layer. For all modes, there are elastic layers of certain thickness for which the effect of the viscosity of the fluid on the phase velocity and the damping factors of the mode is minimum. It is also found out that for some modes, there are both certain thickness and thickness intervals for which the effect of the fluid viscosity on the phase velocity and the damping factors of these modes is significant. In the case of a strongly stiff material of the elastic layer, for some modes, there is a layer thicknesses (frequencies) for which the viscosity of the fluid does not affect the phase velocities of these modes. The approach and the results allow us to establish the limits of applicability of models of wave processes based on the model of a perfect compressible fluid. The numerical results are presented in the form of curves and are analyzed. [ABSTRACT FROM AUTHOR]

In this paper, a novel H-shaped radial phononic crystal (H-RPC) structure is proposed to suppress the anchor loss of a Lamb wave resonator (LWR), which has an ultra-high frequency (UHF) and ultra-wideband gap characteristics. Compared to previous studies on phononic crystal (PC) structures aimed at suppressing anchor loss, the radial phononic crystal (RPC) structure is more suitable for suppressing the anchor loss of the LWR. By using the finite element method, through the research and analysis of the complex energy band and frequency response, it is found that the elastic wave can generate an ultra-wideband gap with a relative bandwidth of up to 80.2% in the UHF range when propagating in the H-RPC structure. Furthermore, the influence of geometric parameters on the ultra-wideband gap is analyzed. Then, the H-RPC structure is introduced into the LWR. Through the analysis of the resonant frequency, it is found that the LWR formed by the H-RPC structure can effectively reduce the vibration energy radiated by the anchor point. The anchor quality factor was increased by 505,560.4% compared with the conventional LWR. In addition, the analysis of the LWR under load shows that the LWR with the H-RPC structure can increase the load quality factor by 249.9% and reduce the insertion loss by 93.1%, while the electromechanical coupling coefficient is less affected. [ABSTRACT FROM AUTHOR]

Here, we examine Lamb waves, propagating parallel to plate surfaces, reinforced by two families of strong straight fibres. Since fibres are much stronger than the matrix, anisotropic properties are highly emphasized. Coordinate-free constitutive relations give a possibility to consider fibres embedded in such materials as extensible or inextensible. When constraints of inextensibility are imposed on fibres, the so-called constrained fibre-reinforced material may be obtained from materials with extensible fibres in a limiting process. Often used to represent such materials is an epoxy resin carbon fibres composite whose material constants, for materials reinforced by one family of fibres, are determined with ultrasound methods. In the plate, reinforced by two families of fibres, of finite thickness, examined here, waves propagate as dispersive either as bending waves or extensional waves. The plate made of the described materials shows some interesting dynamic properties in the propagation of elastic waves. We apply the perturbation method, in particular the matched composite expansion, to examine plane wave propagation. Some interesting results of dynamic behaviour when a material has strong anisotropy will be displayed. [ABSTRACT FROM AUTHOR]

In this contribution, the thermoelastic Lamb waves in the homogeneous, transversely isotropic, plate with voids have been investigated in the context of classical and non‐classical theories of thermoelasticity. To investigate the problem, the fundamental governing equations have been developed in a unified way. On the solutions of these governing equations, the thermal and mechanical stress‐free boundary conditions, as well as constraints due to voids, have been imposed. The solutions of governing equations indicate that there exists a coupled system of wave motion called thermal waves (T‐mode), void wave motion (V‐mode), and elastic waves (E‐mode). However, the shear horizontal component of elastic wave decouples from the system is unaffected by elasto‐poro‐thermal coupling. For the symmetric and anti‐symmetric families of vibrations, the secular equation for the wave motion along with its special cases has been derived. To discover the wave characteristics, the secular equation has been solved using the numerical‐functional iteration method in MATLAB software, and the findings have been manifested by plotting the graphs. It has been concluded that the presence of voids affects the magnitudes of phase velocity, attenuation coefficient, and specific loss. This work may be helpful for geophysicists and engineers in the field of earthquake engineering. The developers of modern facilitating things such as acoustic touch screens, liquid viscosity sensors, etc. which are based on Lamb‐type wave propagation may also get benefitted. [ABSTRACT FROM AUTHOR]

Devices based on piezoelectric semiconductors (PSCs) have recently received particular attention due to their wide bandgap where strain energy band engineering under both static and time-harmonic deformations is the key. In this paper, we investigate and characterize the elastic waves propagating in an anisotropic n-type PSC plate. To achieve our goals, we first introduce the new notations for the extended displacements, stresses, strains, and modulus to arrive at a mathematically elegant extended Stroh formalism. Then, the elastic wave problem is converted into a linear eigenvalue system from which the extended displacements and stresses are expressed in terms of the eigenvalues and eigenvectors. Finally, making use of the boundary conditions on the top and bottom surfaces of the plate, wave dispersion and attenuation are derived analytically. Numerical examples are presented to systematically study the effect of the surface boundary condition, steady-state carrier density, plate thickness, and biasing electric field on the wave speed and attenuation of both shear horizontal and Lamb waves in the transversely isotropic ZnO PSC plate. Some interesting characteristics of the elastic waves observed in this paper could be helpful as theoretical guidance when designing PSC-based devices. [ABSTRACT FROM AUTHOR]

The asymptotic solution of a boundary value problem modelling the propagation of nonlinear shear horizontal (SH) waves in a plate consisting of two layers with uniform thickness is constructed by employing the multiple scales method. Constituent materials in layers are isotropic, vertically heterogeneous, and have different hyperelastic mechanical properties. The nonlinear modulation of SH waves is governed asymptotically by a nonlinear Schrödinger equation. The effects of heterogeneity of the nonlinear layers on the existence of bright solitary SH waves are discussed. [ABSTRACT FROM AUTHOR]

The mutual interactions of Lamb waves in nonlinear elastic plates are studied in this article. Many researchers have investigated the interactions of Lamb wave modes at nonlinear higher harmonics. However, little is known about nonlinearity-driven Lamb modulations from two primary modes with different frequencies. In this study, the existence of symmetric or antisymmetric mode due to Lamb wave mutual interactions is firstly theoretically formulated. Then, an approach is proposed to evaluate the intensity of phase velocity matching for selecting primary modes. Finally, the characteristics of the modulated wave generation are investigated and demonstrated. The generation of modulated waves in an aluminum plate and fatigue crack can be detected by mutual interactions of Lamb waves. The main contribution of this work is the proposed mutual interaction theory of Lamb waves in fatigue plates, which can guide fatigue detection in the metal plate. [ABSTRACT FROM AUTHOR]

The results of experimental studies of propagation of elastic bending waves in a metamaterial element are presented; the element is a wedge whose thickness varies by the parabolic law. The specimen is prepared by 3D printing from ABS polymer. The experimental setup for generation and recording of elastic bending waves in the fabricated wedge specimen is described. Elastic waves in the wedge are recorded and imaged by a laser scanning vibrometer. The peculiarities of bending wave propagation parallel and perpendicular to the edge of the fabricated wedge specimen are experimentally investigated. The experimental results are analyzed. The performed studies show that the wedge prepared in this study is a waveguide concentrating the acoustic wave energy, which is important in developing acoustic metamaterials and absorbing devices working under the principle of an acoustic black hole. [ABSTRACT FROM AUTHOR]

• Elastic spin is explicitly derived and experimentally observed for all basic modes in rods. • Unidirectional wave routing is observed due to spin-momentum coupling. • Asymmetric transmission of longitudinal mode requires extremely elliptical chiral source. • Spin-momentum coupling of torsional mode depends on cross-section warping effect. The unusual topology of elastic waves in continuum systems has been recently uncovered. Prominently, the spin of Rayleigh-Lamb waves has been experimentally observed and used to achieve the unidirectional wave propagation. In this work, the elastic wave spin in thin rod systems is theoretically predicted and experimentally observed, for all the three basic wave modes, i.e., the zero-order flexural, longitudinal and torsional modes. By elaborately building up the subwavelength chiral sources, the spin-momentum locking has been achieved for these three modes within broad frequency range. Interestingly and surprisingly, the spin-momentum locking occurs for flexural and longitudinal modes in both circular and non-circular thin rods; the spin-momentum locking for torsional modes only exits in non-circular thin rods, due to the warping effect in non-circular cross-section rods. Our results open up the door for elastic wave spin in thin rod systems, and provide general tips for the research on basic modes in diverse thin rods, based on either the continuum media or the artificial metamaterials in future. [Display omitted] [ABSTRACT FROM AUTHOR]

• Phononic crystals, elastic metamaterials, ABHs and elastic metasurfaces are considered. • The principles of suppressing vibration and sound radiation by these artificial structures are introduced. • The advances in suppressing vibration and sound radiation by wave manipulation are reviewed. • The further works of suppressing vibration and sound radiation by wave manipulation are prospected. The newly generated artificial structures, including phononic crystals, elastic metamaterials, acoustic black holes (ABHs) and elastic metasurfaces, can abnormally control wave propagations. In this paper, focusing on plate structures and from the perspective of the suppression of vibration and especially sound radiation by manipulating flexural waves, we give a thorough review of the advances of above-mentioned artificial structures, involving their extraordinary characteristics, corresponding mechanisms of vibration and sound radiation suppression, design methods of phase-gradient elastic metasurfaces, and some representative works on suppressing vibration and sound radiation of plates by flexural wave manipulations. Additionally, we compare the advantages and disadvantages of these artificial structures in vibration and sound radiation suppression. Finally, we look forward to the prospects on vibration and sound radiation suppression of plates based on wave manipulations. This paper will provide a timely and practical assistance to academic and technical researchers in the field of vibration and noise reduction. [ABSTRACT FROM AUTHOR]

Klein tunneling is an intriguing phenomenon in quantum mechanics, which refers to the unity transmission of particles through a higher energy barrier without hindrance in the case of normal incidence. The introduction of phononic crystals enables the direct observation of this phenomenon from a different point, giving rise to a broader application prospect. In this paper, we aim at realizing the Klein tunneling for elastic plate waves. To this end, we combine two kinds of Y-shaped phononic crystals with different Dirac point energies to structure a sandwich-like plate, which supports the propagation of Lamb waves while artificially introducing a potential barrier. Under such a configuration, perfect wave transmission regardless of the barrier in a wide frequency range can be realized, which also enables the numerical prediction and experimental observation of the Klein tunneling phenomenon in Lamb waves. The results of this work provide a direction and reference for the design and applications of phononic crystal devices, such as the chip-scale elastic waveguides. [ABSTRACT FROM AUTHOR]

In this paper, we study wave propagation in elastic plates incorporating honeycomb arrays of rigid pins. In particular, we demonstrate that topologically non-trivial band-gaps are obtained by perturbing the honeycomb arrays of pins such that the ratio between the lattice spacing and the distance of pins is less than 3; conversely, a larger ratio would lead to the appearance of trivial stop-bands. For this purpose, we investigate band inversion of modes and calculate the valley Chern numbers associated with the dispersion surfaces near the band opening, since the present problem has analogies with the quantum valley Hall effect. In addition, we determine localized eigenmodes in strips, repeating periodically in one direction, that are subdivided into a topological and a trivial section. Finally, the outcomes of the dispersion analysis are corroborated by numerical simulations, where a time-harmonic point source is applied to a plate with finite arrays of rigid pins to create localized waves immune to backscattering. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'. [ABSTRACT FROM AUTHOR]

Leaky waves are an important class of waves, particularly for guiding waves along structures embedded within another medium; a mismatch in wavespeeds often leads to leakage of energy from the waveguide, or interface, into the medium, which consequently attenuates the guided wave. The accurate and efficient identification of theoretical solutions for leaky waves is a key requirement for the choices of modes and frequencies required for non-destructive evaluation inspection techniques. We choose a typical situation to study: an elastic waveguide with a fluid on either side. Historically, leaky waves are identified via root-finding methods that have issues with conditioning, or numerical methods that struggle with the exponential growth of solutions at infinity. By building upon a spectral collocation method, we show how it can be adjusted to find exponentially growing solutions, i.e., leaky waves, leading to an accurate, fast, and efficient identification of their dispersion properties. The key concept required is a mapping, in the fluid region, that allows for exponential growth of the physical solution at infinity, whilst the mapped numerical setting decays. We illustrate this by studying leaky Lamb waves in an elastic waveguide immersed between two different fluids and verify this using the commercially available software disperse. [ABSTRACT FROM AUTHOR]

The paper deals with elastic wave propagating in a layer on a half-space induced by a vertical force. The focus is on the effect of a sliding contact along the interface and its comparative study with a perfect one. The effective boundary conditions substituting the presence of the layer are derived. The leading order term in these conditions corresponds to vertical inertia of the layer, whereas next order correction involves the effect of plate waves in the coating. Analysis of the associated dispersion relation confirms the existence of a Rayleigh-type wave, along with extensional and shear plate waves. An asymptotic hyperbolic-elliptic formulation for surface wave field is also presented. This includes a hyperbolic equation singularly perturbed by a pseudo-differential operator playing a role of a boundary condition for the elliptic equation governing decay over the interior. The sign of the coefficient at the pseudo-differential operator is demonstrated to be always negative, corresponding to a local maximum of the phase speed at zero wave number, and consequently to a distinct receding type of the Rayleigh-type wave quasi-front induced by an impulse load. [ABSTRACT FROM AUTHOR]

Purpose: Flexural wave propagation in non-homogeneous plates has wide engineering backgrounds, such as the out-of-plane vibration of the decks in buildings, and so on, and the corresponding research will provide some useful suggestions for the vibration control of the associated structures. Method: Taking the out-of-plane vibration of the basal plate bonded with electronic elements encapsulated in the spacecraft induced by the impact series as the background, the flexural wave propagation in the square damping thin plate bonded with two cylinders symmetrically is investigated by the structure-preserving approach in this paper. Based on the variational principle, the dynamic equation describing the flexural wave propagation in the square damping non-homogeneous plate is deduced. Employing the structure-preserving method, the wave propagation in the plate excited by the impact series is simulated. Results and Conclusions: In the numerical simulation, the impact series is classified into two types and different sizes of the cylinders are considered. From the numerical results, we find that the flexural elastic wave forms are symmetric if the impact series is symmetric and the vibration induced by the impact acting on the bolts located at the center of the edge is more severe than that induced by the impact acting on the bolts located at the corner of the plate if the impact series is asymmetric. In addition, the effects of the size of the cylinders on the flexural wave propagation in the non-homogeneous plate are also investigated by the numerical simulation. [ABSTRACT FROM AUTHOR]

The classical problem of reflection of Lamb waves from a free edge perpendicular to the centre line of an elastodynamic plate is studied. It is known that Lamb wave expansions for the displacement and stress fields poorly represent the irregular behaviour near corners, leading to the slow convergence of a series of such waves. The form of the irregularity for an elastodynamic corner is derived asymptotically, and a new solution method, which incorporates this corner behaviour analytically, is then implemented. Results are presented showing that this new approach represents the near-field and far-field behaviour very accurately, requiring very modest numbers of Lamb wave and corner modes. Further, it is revealed that the method can recover the trapped-mode phenomenon encountered in this configuration at the Lamé frequency and a specific Poisson's ratio that we find to be approximately 0.224798 . [ABSTRACT FROM AUTHOR]

For systems that require complete metallic enclosures (e.g., containment buildings for nuclear reactors), it is impossible to access interior sensors and equipment using standard electromagnetic techniques. A viable way to communicate and supply power through metallic barriers is the use of elastic waves and ultrasonic transducers, introducing several design challenges that must be addressed. Specifically, the use of multiple communication channels on the same enclosure introduces an additional mechanism for signal crosstalk between channels: guided waves propagating in the barrier between channels. This work numerically and experimentally investigates a machined phononic crystal to block MHz Lamb wave propagation between ultrasonic communication channels, greatly reducing wave propagation and the resulting crosstalk voltage. Blind grooves are machined into one or both sides of a metallic barrier to introduce a periodic unit cell, greatly altering the guided wave dispersion in the barrier. Numerical simulations are used to determine a set of groove geometries for testing, and experiments were performed to characterize the wave-blocking performance of each design. The best-performing design was tested using piezoelectric transducers bonded to the barrier, showing a 14.4 dB reduction in crosstalk voltage. The proposed periodic grooving method is a promising technique for completely isolating ultrasonic power/data transfer systems operating in a narrow frequency range. [ABSTRACT FROM AUTHOR]

In this work, a newly developed Smoothed Particle Hydrodynamics (SPH) algorithm for nonlinear elasticity is combined with an incompressible SPH fluid solver to investigate the dynamics of a floating plate under impacts of regular water waves with a high steepness. Two scenarios of the plate's rigidity are investigated. The simulation results show that deformations of the stiffer plate mainly occur in a simple bending mode with small amplitudes, and the plate is almost submerged by a strong fluid flow over its surface. In the other scenario, the plate deforms more complexly with much higher deformation amplitudes but experiences a much weaker overwash. The more flexible plate is less resistant to wave motions and converts more wave energy into elastic deformations, and therefore, the overwash is less severe. A strong overflow exerts a pressure force onto the plate that alters the plate's dynamics and adds a viscous (damping) effect on the plate's elastic vibrations, especially in high-frequency modes. A rigorous examination of the numerical convergence and validation using the linear thin plate theory is also carried out. The new SPH algorithm for nonlinear elasticity shows its stability and reliability in evaluating finite and large elastic deformations. Therefore, it is promising for simulating elastic structures in fluid–structure interaction problems. [ABSTRACT FROM AUTHOR]

[Display omitted] • A novel two-stage non-destructive procedure for determination of elastic constants was proposed. • Ultrasonic waves were successfully used to characterize elastic behaviour of AM samples with different raster angles. • Integrated use of bulk and guided waves was proved to be a simple but robust approach. • The method allowed characterization of samples represented by transversely isotropic and orthotropic material models. The subject of the current work was a simple but robust novel two-stage procedure for the non-destructive determination of effective elastic constants using ultrasonic wave propagation. First, ultrasonic bulk wave velocities measured on cubic samples were used to calculate most of the elements of the stiffness matrix. Secondly, the remaining elements were determined using the dispersion curves of elastic guided waves measured on plate samples. Based on the complete stiffness matrix it was possible to calculate the complete set of effective elastic constants. The algorithm was verified for AM elements produced from PLA filament satisfying the conditions of transversely isotropic and orthotropic material models. For the transversely isotropic samples, Young's moduli (E) varied from 2.6 to 2.9 GPa, shear moduli (G) equalled between 0.9 and 1.2 GPa, whereas Poisson's ratios (ν) ranged between 0.20 and 0.32. In orthotropic sample the corresponding values were: E = 1.3–2.8 GPa, G = 0.6–1.2 GPa, and ν = 0.07–0.59. The results of the current study have been compared with references from the literature, giving satisfactory agreement. [ABSTRACT FROM AUTHOR]

• Guided waves in nano-aluminum plates are simulated by molecular dynamics. • The polynomial method is developed to study the nonlocal strain gradient models. • The size parameters of the nonlocal strain gradient theory are calibrated. • Lamb waves and SH waves have different size parameters. The nonlocal strain gradient theory (NSGT) describes long-range interatomic interactions and higher-order strain gradients by introducing size parameters. However, the NSGT is constrained in studying the elastic wave propagation problems due to the difficulty in obtaining the precise size parameters. In this paper, the molecular dynamics (MD) simulations of the elastic wave propagation in the aluminum nano-plate are conducted, and the size parameters in the NSGT are calibrated based on the MD simulation results. The MD simulation process is divided into three stages: relaxation, excitation, and free vibration analysis. The embedded atom method is used to describe the interactions between the metal atoms. During the MD simulations, appropriate boundary conditions and excitation methods are proposed to obtain the group velocities of the elastic bulk, Lamb and SH waves. In addition, based on the three-dimensional (3D) elasticity theory and analytical integration Legendre polynomial method, the theoretical dispersion curves of the elastic wave propagation in the NSGT model are obtained. It is found that both the nonlocal theory and the NSGT can predict the guided elastic wave group velocity, and the NSGT prediction and MD simulation can be well matched when the size parameters are restricted to a certain calibrated regional band. The vibration of atoms in the Lamb wave propagation process is more complex than that in the SH wave propagation, leading to a more substantial size effect on the Lamb wave dispersions. [Display omitted] [ABSTRACT FROM AUTHOR]

• Mode-entangled resonance (MER) enables mode-preserving full transmission of a Lamb wave. • Symmetric (S) or asymmetric (A) Lamb wave can pass through an asymmetric waveguide using the MER. • MER develops when S- and A-modes individually satisfy specific phase-matching conditions. • Super-enhancement of transduction efficiency for A-mode is achievable using the MER. 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. [Display omitted] [ABSTRACT FROM AUTHOR]

Motivated by the importance of lattice structures in multiple fields, we numerically investigate the propagation of flexural waves in a thin reticulated plate augmented with two classes of metastructures for wave mitigation and guiding, namely metabarriers and metalenses. The cellular architecture of this plate invokes the well-known octet topology, while the metadevices rely on novel customized octets either comprising spherical masses added to the midpoint of their struts or variable node thickness. We numerically determine the dispersion curves of a doubly-periodic array of octets, which produce a broad bandgap whose underlying physics is elucidated and leveraged as a design paradigm, allowing the construction of a metabarrier effective for inhibiting the transmission of waves. More sophisticated effects emerge upon parametric analyses of the added masses and node thickness, leading to graded designs that spatially filter waves through an enlarged bandgap via rainbow trapping. Additionally, Luneburg and Maxwell metalenses are realized using the spatial modulation of the tuning parameters and numerically tested. Wavefronts impinging on these structures are progressively curved within the inhomogeneous media and steered toward a focal point. Our results yield new perspectives for the use of octet-like lattices, paving the way for promising applications in vibration isolation and energy focusing. [ABSTRACT FROM AUTHOR]

Metamaterials, together with transformation optics, have been exploited to study the effects of curved spacetime predicted by Einstein's general theory of relativity in the laboratory. However, the stringent requirements in metamaterial fabrications and the narrow operating frequency make their realistic implementations challenging. In this work, we propose and demonstrate experimentally a paradigm to mimic the gravitational lensing effect using flexural waves in an elastic plate without using metamaterials. The needed refractive index field is fulfilled just by slightly varying the local thickness of plates. The generated focusing effect has a broad band from 5 to 100 kHz and shows robustness against changes on structural shapes and thicknesses of the lens. This work provides insight to study nontrivial gravitational phenomena analogically using conventional solid structures and may suggest a possible route to regulate elastic waves arbitrarily. [ABSTRACT FROM AUTHOR]

The cantilever plate structure in a T-beam bridge with a large aspect ratio will cause vibration under the influence of environmental disturbance and self-stress, resulting in fatigue damage of the plate structure. Wave control based on elastic wave theory is an effective method to suppress the vibration of the cantilever plate structure in a beam bridge. Based on the classical thin plate theory and the wave control method, the active vibration control of the T-shaped cantilever plate with a large aspect ratio in the beam bridge is studied in this paper. The wave mode control strategy of structural vibration is analyzed and studied, the controller is designed, the vibration mode function of the cantilever plate is established, and the control force/sensor feedback wave control is implemented for the structure. The dynamic response of the cantilever plate before and after applying wave control force is analyzed through numerical examples. The results show that the response of the structure is intense before control, but after wave control, the structure increases damping, absorbs the energy carried by the elastic wave in the structure, weakens the sharp response, and changes the natural frequency of the structure to a certain extent. [ABSTRACT FROM AUTHOR]

We report on experimental and numerical implementations of devices based on the negative refraction of elastic guided waves, the so-called Lamb waves. Consisting in plates of varying thickness, these devices rely on the concept of complementary media, where a particular layout of negative index media can cloak an object with its anti-object or trap waves around a negative corner. The diffraction cancellation operated by negative refraction is investigated by means of laser ultrasound experiments. However, unlike original theoretical predictions, these intriguing wave phenomena remain, nevertheless, limited to the propagating component of the wave-field. To go beyond the diffraction limit, negative refraction is combined with the concept of metalens, a device converting the evanescent components of an object into propagating waves. The transport of an evanescent wave-field is then possible from an object plane to a far-field imaging plane. Twenty years after Pendry's initial proposal, this work thus paves the way towards an elastic superlens. [ABSTRACT FROM AUTHOR]

Cloaking invisibility is a novel technique that prevents the object from being detected in the background field. The development of new artificial materials and structures promotes the emergence of new achievements in cloaking research. In this work, a broadband square cloaking configuration of elastic wave metamaterial plate is designed and fabricated by the external active control system. The approximate parameters of the flexural wave cloak can be obtained by the coordinate transformation and achieved by alternating layers of the Acrylonitrile Butadiene Styrene (ABS), polydimethylsiloxane (PDMS), and piezoelectric (PZT) patches. With the introduction of active control systems, the square cloak has a wide effective frequency range. The simulation and experimental results show that the square cloak of flexural waves exhibits a good invisible performance in the frequency region of 500–2200 Hz. Compared to the structure without active control systems, the frequency region 2200–2750 Hz is extended for the active cloak. The design and fabrication of the broadband cloak is wished to be helpful during the practical engineering. [ABSTRACT FROM AUTHOR]

Directional routing of one-way classical wave has raised tremendous interests about spin-related phenomena. This sparks specifically the elastic wave study of pseudo-spin in meta-structures to perform robust manipulations. Unlike pseudo-spin in mathematics, the intrinsic spin angular momentum of elastic wave is predicted quite recently which exhibits selective excitation of unidirectional propagation even in conventional solids. However, due to the challenge of building up chiral elastic sources, the experimental observation of intrinsic spin of elastic wave is still missing. Here, we successfully measure the elastic spin in Rayleigh and Lamb modes by adopting elaborately designed chiral meta-sources that excite locally rotating displacement polarization. We observe the unidirectional routing of chiral elastic waves, characterize the different elastic spins along different directions, and demonstrate the spin-momentum locking in broad frequency ranges. We also find the selective one-way Lamb wave carries opposite elastic spin on two plate surfaces in additional to the source chirality. 'Following up on the recent theoretical demonstration here the authors bring us a step closer to the real implementation of efficient ultrasonic chiral sources. They experimentally demonstrate the presence of elastic spin waves, Rayleigh and Lamb waves, generated by a chiral-meta source, characterizing their basic properties. [ABSTRACT FROM AUTHOR]

Theoretical study of the effect of uniaxial pressure on the propagation characteristics of plate modes as Lamb and SH waves in a lithium niobate plate is carried out. A change in the effective crystalline symmetry, as well as the effective elastic constants under the pressure influence, has been derived. The controlling coefficients describing the pressure influence on the plate modes’ phase velocities are calculated for the various applications of uniaxial pressure. The uniaxial pressure influence on the hybridization of the elastic waves is discussed. [ABSTRACT FROM AUTHOR]

It is known that the nonlinear interaction between closed cracks and primary elastic waves can lead to the generation of a second-harmonic component. In this work, the temporal S0-mode Lamb wave and closed-crack-interaction-induced second harmonic (abbr. closed-crack-induced second harmonic, CCISH) Lamb waves that were extracted for closed-crack characterization through a weighted and structured sparse decomposition (WSSD) algorithm. A 3D finite-element model of a thin aluminum plate based on the bilinear stiffness model is established to numerically study the nonlinear interaction between closed cracks and primary Lamb waves. Under S0-mode Lamb wave excitation, the temporal S0-mode CCISH signals are extracted from the original response using the pulse-inversion technique and a band-pass filter. A dictionary, whose columns are the normalized predicted CCISH waveforms generated by the proposed analytical CCISH generation and propagation model, is built to sparsely decompose the extracted array CCISH signals using adaptive weights. Images are generated using sparse coefficients to define the pixel values after solving the WSSD problem. Closed cracks with different locations and orientations are simulated, and imaging results show that the proposed method can characterize their location and orientation but not their length from the generated images. [ABSTRACT FROM AUTHOR]

This study aims to investigate elastic wave localization that leverages defect band splitting in a phononic crystal with double defects through in-depth analysis of comparison of numerical and experimental results. When more than one defect is created inside a phononic crystal, these defects can interact with each other, resulting in a distinctive physical phenomenon from a single defect case: defect band splitting. For a phononic crystal consisting of circular-hole type unit cells in a thin aluminum plate, under A0 (the lowest antisymmetric) Lamb waves, both numerical simulations and experiments successfully confirm the defect band splitting phenomenon via frequency response functions for the out-of-plane displacement calculated/measured at the double defects within a finite distance. Furthermore, experimental visualization of in-phase and out-of-phase defect mode shapes at each frequency of the split defect bands is achieved and found to be in excellent agreement with the simulated results. Different inter-distance combinations of the double defects reveal that the degree of the defect band splitting decreases with the increasing distance due to weaker coupling between the defects. This work may shed light on engineering applications of a multiple-defect-introduced phononic crystal, including broadband energy harvesting, frequency detectors, and elastic wireless power transfer. [ABSTRACT FROM AUTHOR]

Objective: Estimating the elasticity distribution in the cornea is important because corneal elasticity is usually influenced by corneal pathologies and surgical treatments, especially for early corneal sclerosis. Because the thickness of the cornea is typically less than 1 mm, high-resolution ultrasound elastography as well as the Lamb wave model is required for viscoelastic property estimation. In the present study, an array high-frequency ultrasound (HFUS) elastography method based on ultrafast ultrasound imaging was proposed for estimating the viscoelastic properties of porcine cornea. Methods: The elastic wave was generated by an external vibrator, after which the wave propagation image was obtained using a 40-MHz array transducer. Viscoelasticity estimation was performed by fitting the phase velocity curve using the Lamb wave model. The performance of the proposed HFUS elastography system was verified using 2-mm-thick thin-layer gelatin phantoms with gelatin concentrations of 7% and 12%. Ex vivo experiments were carried out using fresh porcine cornea with artificial sclerosing. Results: Experimental results showed that the estimated elasticity was close to the standard value obtained in the phantom study when the Lamb wave model was used for elasticity measurement. However, the error between the standard elasticity values and the elasticity values estimated using group shear wave velocity was large. In the ex vivo eyeball experiments, the estimated elasticities and viscosities were respectively 9.1 ± 1.3 kPa and 0.5 ± 0.10 Pa·s for a healthy cornea and respectively 15.9 ± 2.1 kPa and 1.1 ± 0.12 Pa·s for a cornea with artificial sclerosis. A 3D HFUS elastography was also obtained for distinguishing the region of sclerosis in the cornea. Conclusion: The experimental results demonstrated that the proposed HFUS elastography method has high potential for the clinical diagnosis of corneal diseases compared with other HFUS single-element transducer elastography systems. [ABSTRACT FROM AUTHOR]