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• 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]

• 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]

• Proposing a kind of non-resonant metasurfaces to guide and manipulate flexural waves. • Clarifying the difference between the metasurface-guided and conventional flexural waves. • Establishing a theoretical framework to solve the dispersion relations of the guide waves. • Realizing wave manipulations for rainbow reflection, mode conversion and topological interface state. Elastic metasurfaces, being the subject of much attention and discussion, are first designed by phase modulation and now are also considered as a kind of structures with subwavelength size, e.g., layer structures in 3D space or strip structures in 2D space. However, most of elastic metasurfaces, especially those with phase gradient subunits, cannot support elastic wave propagations along them. In this research, we construct non-resonant metasurfaces with an array of slots in plates and explore a unique form of flexural waves propagating along and decaying exponentially with the increasing of the distance from the metasurfaces, which are called metasurface-guided flexural waves. A theoretical framework is established to solve the dispersion relations of these waves by coupling high-order diffraction and waveguide modes. On the basis of this framework, we design three metasurfaces for rainbow reflection, mode conversion and topological interface state, which are realized and verified by finite element simulations and experiments. Our work provides a new idea for the manipulation of flexural waves in plates, which may have wide potential applications in vibration control, structural health monitoring and acoustic device design. [Display omitted] [ABSTRACT FROM AUTHOR]

• A full 3-D analytical model for interpreting nonlinear aspects of guided ultrasonic waves modulated by a fatigue crack of "breathing" behavior. • An analytical insight into the generation of contact acoustic nonlinearity from fatigue crack. • A nonlinearity index for quantitatively evaluating fatigue crack including crack length. • A capacity of predicting initiation of a fatigue crack at an embryonic stage. • Rigorous experimental validation and numerical validation. Previously, a two-dimensional (2-D) analytical model for interpreting the modulation mechanism of a "breathing" crack on guided ultrasonic waves (GUWs) is developed [1]. Based on the theory of wave propagation in three-dimensional (3-D) waveguides and using an elastodynamic analysis, the 2-D model is extended to a 3-D regime, to shed light on the nonlinear aspects of GUWs disturbed by cracks with "breathing" traits. With the model, generation of contact acoustic nonlinearity (CAN) embodied in GUWs, subjected to the key parameters of a "breathing" crack (e.g., crack length), is scrutinized quantitatively. On this basis, a nonlinearity index is defined to link crack parameters to the quantity of extracted CAN. In virtue of the index, initiation of an undersized fatigue crack in a 3-D waveguide can be delineated at its embryonic stage, and, in particular, the crack severity can be quantitatively depicted. This facilitates prognosis of imminent failure of the monitored structure. Experimental validation is performed in which a hairline fatigue crack is evaluated, and the results well corroborate the crack parameters predicted by the 3-D analytical model. [ABSTRACT FROM AUTHOR]

Highlights • Dynamic fundamental solutions are derived for the first time for the Kane–Mindlin plate theory. • First BEM formulation based on the higher-order plate theory for extensional motion of plates. • The formulation is efficient for modelling high-frequency S0 Lamb wave mode. • The formulation is able to handle thickness-stretch displacement of the S0 mode and out-of-plane loads. Abstract This paper presents a new boundary element formulation for modelling the fundamental symmetric Lamb wave (S0 mode) propagating in the high frequency range. At such high frequencies, the S0 mode reveals significant dispersive character. Conventional BEM formulations governed by the generalised plane stress theory fail to accurately represent the dispersive properties of the S0 mode and to handle out-of-plane loads because the effects of thickness-stretch are not considered. Therefore, a new BEM formulation is proposed based on the dynamic fundamental solutions which are derived for the first time for a higher-order plate theory (Kane–Mindlin) taking into account coupling between extensional motion and the first mode of thickness vibration. Only plate edges are required to be discretized using simple line elements in the proposed BEM formulation. Three benchmark examples are presented where the solutions from the new BEM formulation are shown to be in excellent agreement with analytical and three-dimensional finite element results. Furthermore, the advantage of the proposed formulation is demonstrated through comparisons with the BEM results based on the generalised plane stress theory. [ABSTRACT FROM AUTHOR]

Highlights • The new series of differential equations of free vibration of thick functionally graded plates, including the lateral extension, have been derived. • Based on the dispersion relation and Lamb wave velocity, the validation of the differential equations has been investigated. • Legendre spectral element method is utilized to analyze the thick functionally graded plates subjected to impulsive loading. • The accuracy of the numerical simulation is examined by comparing the group wave velocity of first symmetrical and asymmetrical modes of Lamb waves derived from the dispersion relations and numerical models. Abstract In this paper, a new series of differential equations which can predict the propagation and dispersive behavior of first symmetric and antisymmetric Lamb wave modes in functionally graded material (FGM) thick plates are developed. Then, given the accuracy and cost effectiveness of Legendre spectral element method in combination with central difference method, these methods are utilized to set up the numerical models and solving the dynamic discretized differential equations. Finally, based on the wave front velocity, the percentage of error is estimated and it is shown that considering some limitations which are inherently included in the utilized method of error estimation, the proposed equations and the numerical procedure can predict the behavior of first symmetric and antisymmetric Lamb wave modes in FGM thick plates precisely. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

• A eulerian compressible fluid model combines the isentropic single fluid model to solve shock wave propagation and water cavitation of water-filled double plate model. • A freestanding or softly supported outer plate has a minimal effect on the impulse transmitted to the inner plate and its motion. • Stiff support spring of the outer plate can reduce the shock wave transmitted to the gap water and also the motion of the inner plate. • Cavitation initiates in gap water near the inner plate and spreads towards the external water. • Stiff support spring of the inner plate will suppress water cavitation. Water-filled double hulls are a prevalent design for underwater warships. Studying the propagation of underwater shock wave in such structures is essential to comprehend their shock resistance. The aim of this paper is to investigate the propagation of underwater shock wave and water cavitation in a water-filled double plate. To achieve this objective, the paper establishes a Eulerian compressible fluid model that combines the isentropic single fluid model and Newton's second law. The accuracy of the numerical solver is confirmed through validation tests. The reflection and transmission characteristics of shock wave, the dynamic response of the plate, and the cavitation in external and gap water are analyzed. It also examines the effects of the supporting springs of outer and inner plates and the area density of the outer plate on the shock wave propagation and cavitation evolution. The findings indicate that the transmitted wave in the gap water is influenced by the area density and supporting spring of the outer plate. A thicker outer plate can reduce the peak value of the transmitted wave, and a stiffer supporting spring can decrease the transmitted impulse. On the other hand, if the outer plate is freestanding or softly supported, it has minimal effects on the response of the inner plate. Moreover, the water cavitation is determined by the supporting spring of the inner plate in the case of a softly supported outer plate, and the cavitation initially develops in the gap water near the inner plate before expanding towards the external water. When the supporting spring of the outer plate is stiff, it significantly reduces the occurrence of cavitation in the external water, while the cavitation in the gap water is still determined by the support spring of the inner plate. These research findings are valuable for analyzing the shock resistance of typical double-hull submarines. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper seeks to present the design and bandgap optimization of multi-scale composite origami-inspired metamaterials (MCOMs) reinforced with grapheme platelets (GPLs) and carbon fibers. The MCOMs are constructed with a series of hybrid origami single-configuration that spatially reconfigure within prescribing valley and mountain lines. A semi-analytical periodic spectral plate method for the wave analysis of two-dimensional (2D) periodic origami-inspired metamaterials is proposed based on the Mindlin plate theory, higher-order spectral elements, and the Bloch theorem. Various significant parameters, including the weight fraction of GPLs, the volume fraction of carbon fibers, and the fiber orientations, are considered to investigate wave propagation in MCOMs. The results indicate that complete bandgaps (BGs) can be realized in MCOMs with three different spatial configurations, and distributions of nano-reinforced materials cause extraordinary changes in band structures. Subsequently, given that the BG at low frequencies is more attractive in practical engineering applications, the main objective of this paper is to maximize the sum of bandwidths of the first and second BGs employing various significant parameters. The optimization framework is suggested by incorporating the semi-analytical method in an optimization scheme based on particle swarm optimization (PSO). The design objective of MCOMs with three different spatial configurations generated from the proposed method achieves 185.6%, 10.2%, and 61.5% improvement compared with that obtained from the initial design, respectively, which proves that the proposed novel MCOMs and non-uniform distributions of nano-reinforced materials are quite effective for broadband wave attenuation. This work can provide a new thought for designing novel composites and metamaterials. [Display omitted] • A semi-analytical method suitable for two-dimensional periodic origami-inspired metamaterials is proposed. • Band structures and vibration transmittance of multi-scale composite origami-inspired metamaterials are investigated. • The optimization framework is established by incorporating the semi-analytical method in particle swarm optimization. • The non-uniform distributions of the reinforcements can significantly broaden the bandwidths of bandgaps. [ABSTRACT FROM AUTHOR]

• The sub-wavelength focusing is realized via two adjacent lenses. • A critical angle distinguishing sub-wavelength focusing from normal focusing is proposed. • The sub-wavelength focusing is validated via FEM and experiments. • The sub-wavelength focusing is broadband. A novel method for achieving sub-wavelength focusing of reflected flexural waves in a single-phase plate is proposed in this paper. The original plane lens is divided into two adjacent lenses, and modulating the internal angle between them, more reflected wave components from broader directions can arrive at the focusing position, which leads to the sub-wavelength focusing phenomenon with the focusing size smaller than half wavelength. Firstly, Mindlin plate theory is adopted to solve the reflected wave, and lenses with different width values are designed based on phase modulation for wave focusing. After that, the sub-wavelength focusing is exemplified numerically and experimentally, with the reason explained systematically. Remarkably, the focusing size perpendicular to wave propagation direction locates (0.4 λ , 0.5 λ), which is controlled by the internal angle. It is demonstrated that the subwavelength focusing is general because it is still suitable when the lenses are designed via the thickness variation or other phase distribution. Additionally, the lenses exhibit broadband property, which can work in a certain frequency region centered the designed frequency. Not limited by flexural wave in plates, the design methodology in this paper can also lay the foundation for wave control in electromagnetics and acoustics. [Display omitted] [ABSTRACT FROM AUTHOR]

• The dispersion relations of SH waves in PS plates incorporating surface effect are presented. • The frequency and phase velocity spectrum relations and the cut-off frequencies are size dependent. • The surface effect reduces the frequency, phase velocity, and cut-off frequency of SH waves. • The surface effect becomes more prominent for SH waves within high frequency range. Elastic wave-based devices made of piezoelectric semiconductors (PSs) find wide applications in modern scientific and technological fields. Elastic waves propagating in PS nanostructures have a rich variety of propagation characteristics due to the interaction between deformation, polarization, and charge carrier, as well as the influence of surface effect. Based on the Gurtin-Murdoch surface model, we conduct an analysis of horizontally polarized shear (SH) waves propagating in an infinite n-type PS plate with nano-thickness in this paper. For the open-circuit and electrically isolated boundary conditions, the analytical frequency and phase velocity spectrum relations and cut-off frequencies of SH waves with anti-symmetric and symmetric modes are presented. The influence of the surface effect, initial electron concentration, and thickness of the PS plate on the propagation characteristics of SH waves, such as frequency spectrum, phase velocity, and cut-off frequency, are elaborated in detail. Numerical results show that propagation characteristics of SH waves are size-dependent, and the macroscopic effective shear rigidity is softened at the nanoscale due to surface effect, which thus leads to the reduction of the frequency and phase velocity of SH waves. Moreover, the propagation characteristics of SH waves can be manipulated by changing the initial electron concentration. [Display omitted] [ABSTRACT FROM AUTHOR]

• A forward model for guided waves propagating along the ground silicon wafer is established. • Acoustic mode conversion caused by wafer thinning is studied. • A Bayesian approach is used for quantifying subsurface damage (SSD) and its uncertainty. • Effect of acoustic mode conversion on the quantization results of SSD is analyzed. A multimode photoacoustic method has been applied for evaluating the degree of subsurface damage (SSD) in the ground silicon wafer. Mode conversion of laser-generated broadband guided waves is caused by wafer thinning. Bayesian inversion is applied to quantify the effective elastic constants of the SSD layer together with the corresponding uncertainty estimates from the experimental dispersion data of multimode guided waves. Laser ultrasonic experiments have been performed on the polished and ground silicon wafers with different thicknesses to determine the ability of the method to characterize SSD and the effect of acoustic mode conversion on the quantization results. The experimental results show that the mode of the laser-generated broadband guided waves will gradually change from Rayleigh wave to Lamb wave as the wafer is thinned. Both the Rayleigh mode and the A 0 Lamb mode can accurately estimate the effective elastic constants of SSD, but the A 0 Lamb mode leads to longer confidence intervals, which has been theoretically explained. [Display omitted] [ABSTRACT FROM AUTHOR]

• Fully non-contact laser ultrasonic system developed based on the Sagnac effect. • Nonlinear Lamb wave mixing is achieved by applying laser line-array excitation. • The influence of microcracks on nonlinear mixed-component generation was quantified. • Single microcracks were successfully detected by scanning the Lamb wave-mixing zone. In this study, a non-contact nonlinear Lamb wave mixing technique based on laser line-array excitation is developed for microcrack detection in plate-like structures. Specifically, a pulsed laser with a line-array pattern (LAP) source is created to generate two narrowband Lamb waves with distinctive frequencies; subsequently, a vibrometry is used to measure the corresponding ultrasonic responses. The presence of microcrack caused nonlinear wave mixing between the two generated Lamb waves; consequently, nonlinear mixed components are generated at the sum and difference of the two input frequencies. The novel contributions of this study are as follows: (i) a fully non-contact laser ultrasonic system with a Sagnac interferometer is developed for narrowband Lamb wave generation; additionally, a vibrometry is employed to identify the mixed components; (ii) the proposed system allows two Lamb waves with distinctive frequencies to be simultaneously generated by a single laser source; (iii) the proposed system allows the user to selectively implement the Lamb wave mode at the desired input frequency by simply adjusting the optical lens; and (iv) unlike the slit mask method, the Sagnac interferometer system yields laser LAP sources that can produce sufficient energy (exceeding 80%) to generate input waves in structures. Moreover, the performance of the developed laser ultrasonic system is experimentally validated by applying it to aluminum specimens containing microcracks. The results indicate that the proposed system can locate and detect microcracks in a plate by scanning the wave-mixing zone. [Display omitted] [ABSTRACT FROM AUTHOR]

In this paper, the propagation of evanescent Lamb waves in the one-dimensional viscoelastic phononic metastrip is studied. Complex band structures and transmission spectra are calculated by using the finite element method. The effect of viscosity is included according to the Kelvin–Voigt model. Two types (namely H-type and I-type) of metastrips are fabricated in either steel or epoxy. A theoretical model is developed to predict the distribution of the displacements of evanescent waves in the finite metastrip. The effect of different cutting forms on the complex band structure is also investigated. It is found that the spatial attenuation of evanescent waves is clearly observed in both simulation and measurement. Numerical and experimental results agree well for steel metastrips when only the elastic stiffness matrix is considered, whereas good agreement for epoxy metastrips is achieved when viscoelasticity is taken into account. The displacement distribution of evanescent waves can be accurately predicted from the two least evanescent waves identified in the complex band structure. Different slicing forms for the metastrip result in the reconstruction of evanescent waves, leading to the opening or closing of bandgaps. The present work lays the numerical and experimental foundation for practical application of phononic metastrips. [Display omitted] • Complex band structure for evanescent Lamb waves is calculated by using finite element method. • Numerical and experimental distributions of evanescent waves agree well and can be accurately predicted. • Evanescent waves are reconstructed for different cutting forms, leading to the opening or closing of bandgaps. [ABSTRACT FROM AUTHOR]

• Method for multiple scattering by scatterers with unmatched midplanes is proposed. • The method can analyze coupled flexural and in-plane extensional motions. • Mode conversions between different elastic waves are observed. • Stop bands of shear and flexural waves are captured simultaneously. • Broadband scattering polarization of flexural waves is achieved by multiple scattering. Out-of-plane flexural and in-plane extensional motions are independently analyzed in available studies of multiple scattering due to the assumption of the consistent mid-plane between the scatterer and host medium. When mid-planes of the scatterer and the host medium are inconsistent, such as flat-bottomed indentations, the coupled out-of-plane flexural and in-plane extensional motions should be considered. This paper aims to investigate a general numerical procedure to solve the three-dimensional multiple scattering problem of elastic waves on a plate with cylindrically flat-bottomed indentations. Wave expansion functions derived from the Poisson and Mindlin plate theories are used to express three-dimensional displacements of the host plate and flat-bottomed indentations. A linear matrix representing analytical relationships between wave expansion coefficients of exciting and scattered fields is deduced by the continuity conditions of flat-bottomed indentations. A set of linear algebraic equations is then developed by the fact that the exciting fields around a scatterer are the sum of scattered fields coming from all other scatterers. The numerical collocation method is used to solve the preceding algebraic equations. Simulation results verify mode conversions between compressional, shear, and flexural waves. Details of stop-band formations of shear and flexural waves are captured simultaneously. Furthermore, far-field scattering polarizations of shear and flexural waves are found in the case of multiple scattering. [Display omitted] [ABSTRACT FROM AUTHOR]

• On-chip valley phononic crystals with graded topological interfaces are built up. • Gapped feature of graded topological edge states is demonstrated. • Abnormal refraction is observed behind graded topological interfaces. In this work, we construct on-chip valley phononic crystal plates by building up triangular silicon pillars on the silicon plate. We introduce the graded interface sliding for two typical interfaces ψ BA and ψ AB , by modulating the horizontal lattice constant in a selected region in PC plate. Based on simulation and laser ultrasonic technique, we present the frequency range evolution of topological edge states from the gapless feature to gapped one. We demonstrate the displacement distribution of topological edge states in two graded interfaces, magnifying numerically the topological rainbow phenomena. In particular, we characterize the plate wave propagation through both types of graded interfaces, observe the abnormal refraction pattern behind the truncated interfaces, and underline abnormal refraction to the splitting of wave vector in PC plate. Our graded interfaces provide new clue to control elastic wave propagation based on valley degree of freedom. [Display omitted] [ABSTRACT FROM AUTHOR]

• Spectral FEM within the bi-potential framework is developed for modeling CAN. • A semi-explicit algorithm is proposed to facilitate high computational efficiency. • Contact force can be calculated by bi-potential method without defined parameters. • Computational efficiency of the proposed method is much higher than that of FEM. • The proposed method can capture classical contact acoustic nonlinearity features. Nonlinear ultrasonic guided waves are of great importance in structural health monitoring, since they have both the large-area inspection capability of guided waves and the desirable sensitivity to incipient defects from nonlinear ultrasonic features. Efficient numerical methods play a key role in investigating the nonlinear features of guided waves. In this work, a time domain spectral finite element method (TDSFEM) combined with the bi-potential contact theory is developed to capture the nonlinear interactions between guided waves and breathing cracks. The bi-potential approach has better accuracy than the conventional penalty method, since there is no any user-defined parameter for computation in the former method while the latter one requires a user-experience-based penalty factor. In addition, a semi-explicit algorithm is proposed to integrate the wave equation, which can take full advantage of the diagonal mass matrix of TDSFEM while not sacrificing numerical stability. Numerical verifications against ANSYS show that the computational efficiency of the bi-potential method-based TDSFEM is much higher than that of the FEM via the penalty method. Numerical case studies are then performed to investigate the nonlinear interactions between Lamb waves and breathing cracks. Results show that the proposed method can successfully capture the classical nonlinear features, such as higher harmonic generation and zero frequency (DC) response. Moreover, the influence of the length and gap of a breathing crack on the contact acoustic nonlinearity (CAN) is investigated. As an efficient numerical approach, the bi-potential method-based TDSFEM may be a good tool for investigating the CAN. [Display omitted] [ABSTRACT FROM AUTHOR]

• Controlling flexural wave in thin plates was achieved by notched metasurface. • The proposed metasurface can support full phase independent modulation through four parameters. • The flexural wave focusing effect of the present work are brilliant in the available literature. • The four notched metasurfaces shown good focusing effect in the experimental validation. There are two severe limitations of current flexural wave metasurface based on local resonance mechanism or modal conversion method: low transmittance and only a single manipulation parameter. Inspired by the interaction between notches and flexural waves, we propose a high transmittance and multi-parameter independent manipulation metasurface composed of an array notches. Firstly, based on the phase shift accumulation method, a full 2π phase shift is achieved by modulating four notch parameters independently. Secondly, the refraction and focusing metasurfaces are designed based on the generalized Snell's law and compared with the simulation results. Finally, the designed focusing metasurfaces is validated by corresponding experiments. The four metasurfaces have a good performance for broadband flexural wave focusing, and the numerical and experimental focal lengths are in great agreement with the theoretical values. The notched metasurface provides an innovative way to manipulate flexural waves without resonators, which can be used in the applications of energy harvesting, waveguide design and ultrasonic detection. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a computationally efficient scheme to simulate Lamb wave propagation in symmetric laminated composite is presented and used to study time reversibility of Lamb wave. The technique proposed is a modified version of the wavelet spectral finite element (WSFE) which has been earlier developed for one- and two-dimensional wave propagation. The method follows a finite element procedure in the transformed frequency-wavenumber domain. The transformations are done using Daubechies scaling function approximation in time and one spatial dimension. Here, the modified WSFE method is used to simulate time domain Lamb wave response in doubly bounded, symmetric composite laminates. The results have been validated by comparing the wave velocities derived from these simulations with those obtained from experiments. The technique has also been used to emphasize and analyze the time reversibility phenomenon of Lamb wave. Finally, the constraint of the simulation in terms of wrap-around problem is explained with numerical examples. [Copyright &y& Elsevier]

• The interaction of solitary waves with pristine and corroded plates is investigated. • Analytical and coupled discrete/finite element models are presented to predict the reflected solitary waves. • Numerical results are in good agreement with the experimental results. • The sensitivity of reflected solitary waves to corrosion is evaluated in plates of different thicknesses. • The sensitivity of the method in granular chains of different material and geometric properties is studied. Over the last decade, a novel nondestructive evaluation (NDE) method based on the application of highly nonlinear solitary waves has emerged. The method is based on the actuation and detection of solitary waves propagating along a medium made of uniform spherical particles, the last of which is in contact with the material to be assessed noninvasively. The hypothesis is that the dynamic interaction between the wave and the material/structure to be inspected is dependent upon the condition of the material/structure. The study presented in this paper aims at designing and developing the NDE framework for the detection of localized corrosion in metals. In particular, this paper presents a numerical investigation of the interaction of highly nonlinear solitary waves with plates in pristine and corroded conditions. A coupled discrete/finite element model is used to predict the time of flight and the relative amplitudes of the reflected solitary waves as localized corrosion progresses in the plate. The sensitivity of the method is quantified in terms of different parameters such as plate thickness, chain length, and particles' mechanical and geometric properties. It is found that the sensitivity, i.e. the ability to detect corrosion at earlier stages, of this novel NDE technique is inversely proportional to the plate thickness and is proportional to the diameter and the stiffness of the particles. In the future, the findings of this study can be used to optimize the design of solitary wave transducers, which are devices that can be used to trigger, sustain, and detect the propagation of the solitary waves and their interaction with the structure of interest. [Display omitted] [ABSTRACT FROM AUTHOR]

• A plane wave expansion method is developed to calculate the dispersion relation of multi-layered periodic piezoelectric composited plates. • The band structures of di_erent guided wave modes are calculated sepa-rately, which help to extract speci_c wave mode from multiple wave modes. • The mode bandgaps calculated by the proposed analytical framework are veri_ed by the transmission spectra obtained by _nite element method. • The inuences of piezoelectricity and con_guration of the unit cell on the band structures of each guided wave mode are investigated by the developed method. The multi-mode and dispersion natures of guided waves in plate bring big challenges of functional phononic crystal (PC) plate design for wave control. For designing a periodic multilayer piezoelectric plate to control specific guided wave propagation, it is vital to study the dispersion relation of each guided wave mode. In this paper, a plane wave expansion method is developed to calculate the dispersion relation of each guided wave mode in the periodic multilayer piezoelectric plate with a mirror plane. To quantitatively demonstrate the effectivity of the developed method, the band structures of PC plates with different kinds of piezoelectric scatterers are discussed to reveal the influences of geometry and polarization effect of piezoelectric scatterer on the guided wave propagation. Results show that the mode bandgaps of symmetric mode Lamb waves, anti-symmetric mode Lamb waves, and shear horizontal waves can be obtained separately by the proposed method, and they exhibit different responses with the changes of piezoelectric scatterer. Therefore, the proposed method can provide an effective analysis way of band structures for designing smart guided wave control devices based on multilayered piezoelectric PC plate. [Display omitted] [ABSTRACT FROM AUTHOR]

• Bending the flexible surface acoustic wave devices in concave or convex geometries will cause the particle pattern lines to converge towards or diverge away from the centre of the curvature of the geometry. • Particle patterning is more efficient on Lamb wave devices compared to and Rayleigh wave devices with the same concave geometry. • For the same convex geometry, the particle patterning is more clear and regular on Rayleigh wave devices compared to Lamb wave devices. • Twisting the flexible surface acoustic wave devices deforms the IDTs and the particles pattern into lines parallel to the inclined direction of the twisted IDTs. • Manipulating and patterning yeast cells using our flexible surface acoustic wave devices demonstrates the possibility of applying our flexible acoustofluidic systems into biomedical applications. Surface Acoustic Wave (SAW) based microfluidic devices provide active techniques to manipulate fluid and particles, which can be used for precise and controllable patterning of microparticles and biological cells, with a high efficiency in a non-invasive and contact-free manner. This paper investigates flexible and bendable SAW microfluidic devices and explores the effects of bending and twisting of SAW devices on microparticle and cell patterning, using both experimental and numerical modelling. We showed that bending flexible SAW devices changes the distribution of particle pattern lines significantly. In devices with concave bending the particle pattern lines converge towards the centre of the curvature, whereas for devices with convex bending, they diverge away from it. Comparing the particle patterning using Lamb and Rayleigh wave devices with concave bending, we found that particle alignment is more efficient in the flexural mode Lamb wave device, whereas for the devices with convex bending, the particle patterning is more clear and regular when Rayleigh waves are used. We further investigated the effects of twisting the flexible SAW devices and observed that the particles are patterned into lines parallel to the deformed interdigital transducers (IDTs). We finally patterned yeast cells using our flexible SAW devices, and demonstrated the possibility of using our flexible acoustofluidic device for biomechanical systems such as body conforming technologies, wearable bio-sensors, and flexible point-of-care devices for personalized health monitoring. [Display omitted] [ABSTRACT FROM AUTHOR]

• The double-sided symmetric phononic crystal (PC) plates are built up in C3v lattice. • Energy flux and intrinsic spin are shown at the K of PC. • Multi-branch topological edge states are observed between PCs with opposite valley Chern numbers. • Different transverse symmetry is shown for edge states. • Distinct robustness against imperfections is presented for multiple edge states. We build up phononic crystals (PCs) by attaching triangular pillars symmetrically to the double sides of a thin plate in the triangular lattice. The degeneracy of multiple Dirac cones is simultaneously lifted for the same PC plate, due to the mirror-inversion symmetry breaking caused by the rotation of triangular pillars; opposite Berry curves and valley Chern number are got at the lower and upper branches of each valley band. The multi-branch topological protected edge states are then created on the interface between PC plates with opposite topological phase. Interestingly enough, those edge states present various transverse symmetries and distinct robustness against sample imperfection such as cavity defect, rotation angle disorder, or sharp bending. Our results present the rich behaviors of multiple branches of topological edges. [Display omitted] [ABSTRACT FROM AUTHOR]

• Wave collimation and focusing with annular acoustic black hole arrays are addressed. • A reconstructed Gaussian basis is proposed to describe the displacement field. • The basis is forced to fulfill the Bloch-Floquet conditions of the ABH unit cells. • A parametric analysis follows based on dispersion curves and equifrequency contours. • New designs of curved arrays and focusing waveguides are suggested. While embedding acoustic black holes (ABHs) in plates has proved to be a lightweight and useful solution for noise and vibration reduction, their potential for wave manipulation is only in its beginnings. Recent studies seem to indicate that amazing properties can be attained with them. A plate with ABH indentations can be viewed as a single-phase metamaterial that can alter wave propagation direction thanks to the ABH power-law thickness profile. Some typical unconventional dispersion properties of multi-phase metamaterials, like collimation or negative refraction, can be recovered in a simple way. This work focuses on the collimation of flexural waves in plates by means of ABH arrangements. The first goal of the paper is to propose a predictive semi-analytical method to describe such phenomenon in an efficient manner. The method is also expected to allow one to perform quick parametric analyses for different ABH configurations. To that purpose, the Gaussian expansion method (GEM) is extended to deal with ABH phononic crystals on infinite plates. The Lagrangian for a single cell is built and a new basis of Gaussian functions is constructed satisfying the periodic boundary conditions of the problem. The Rayleigh-Ritz method is then adopted to compute the displacement field of annular and circular ABH arrays. The accuracy of the reconstructed GEM approach is validated by comparing dispersion curves and modal shapes with those obtained from finite element simulations. Equi-frequency contours are then used to determine the frequency bands prone to collimation. The focus is placed on annular ABH configurations which allow one to achieve collimation at lower frequencies than the circular ones. The second main contribution of this work therefore consists of a thorough analysis to characterize the influence of geometric parameters on the performance of ABH arrays. Moreover, new designs of annular ABH arrangements on plates are proposed for wave conduction, including curvature, and energy focusing in the long wavelength limit. [ABSTRACT FROM AUTHOR]

• Material property requirement to enable rectangular-like and parallel-line-like equi-frequency contours (EFCs) is newly proposed. • Adjoining the frequency ranges of two EFCs achieves the broadband self-collimation. • Broadband self-collimation of an anisotropic phononic crystal is experimentally validated. One extraordinary phenomenon exhibited by phononic crystals (PnCs) is that they can manipulate oblique incident waves in a target direction via proper refraction, commonly called wave self-collimation. Although prior studies have demonstrated self-collimation of electromagnetic and acoustic waves, only a few studies have examined elastic waves in this context. If a PnC is designed to represent rectangular-like and/or parallel-line-like equi-frequency contour (EFCs), elastic waves can be self-collimated in either horizontal or vertical directions. However, in the existing literature, there is no theoretical rationale for realizing rectangular-like and/or parallel-line-like EFCs; besides, broadband self-collimation of elastic waves has not yet been explored. Therefore, we propose to derive the material property requirement for an anisotropic PnC to exhibit rectangular-like EFCs (a range of low frequencies) and parallel-line-like EFCs (a range of high frequencies) in the case of elastic waves. Furthermore, by inherently adjoining two frequency ranges of the rectangular-like and parallel-line-like EFCs at a certain frequency, broadband self-collimation covering the entire range of frequencies can be achieved. With the designed anisotropic PnC that fulfills the proposed material property requirement, self-collimation for S 0 Lamb waves is numerically simulated and experimentally demonstrated over a broad range of frequencies. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• In micro-crack regions, a resonant Lamb wave can be generated when the special resonance condition ω S 0 / ω A 0 = 2 κ / (κ + 1) is satisfied. • The acoustic nonlinear parameter is feasible to characterize micro-cracks. • The resonant wave's signal is capable of locating micro-crack regions. It is crucial to detect and evaluate early material degradation caused by micro-cracks in key engineering structures. This paper investigates the resonant behavior of one-way Lamb mixing waves in thin plates with randomly distributed micro-cracks by numerical simulations. It is found that when the resonance condition ω S 0 / ω A 0 = 2 κ / (κ + 1) is satisfied, a resonant A 0 mode wave can be generated by a pair of A 0 and S 0 mode waves mixed in the micro-crack damage region. Meanwhile, it is manifested that the acoustic nonlinearity parameter increases with the crack density and the length of the micro-crack region, which is also related to the resonant frequency. Furthermore, it is proven that the location of the micro-crack region can be determined by the time-domain signals of the resonant wave. This study numerically reveals that the one-way Lamb mixing method is feasible to quantitatively identify micro-crack damage in thin plates. [ABSTRACT FROM AUTHOR]

• First enriched finite element for general wave propagation problems in piezoelastic media. • First element to accurately predict electroelastic, narrowband guided waves to broadband impact waves. • Results show the need of enriching both displacement and electric potential fields. • Accurately captures free edge stress field with steep gradients at piezoelectric actuator-structure interface. • Exhibits much greater computational efficiency, accuracy and faster convergence than conventional FE. A two dimensional finite element (FE) is developed by enriching the conventional Lagrange interpolation functions with local element domain wave functions, for accurate solution of general wave propagation problems in piezoelastic media. The enrichment functions, applied to both displacement and electric potential fields, satisfy the partition of unity condition, and vanish at the nodes. The formulation is developed using the extended Hamilton's principle for piezoelastic solids, considering two-way electromechanical coupling. The enriched FE is shown to perform equally well in terms of computational efficiency and accuracy for broadband impact induced electroelastic wave to narrowband ultrasonic guided wave propagation problems, unlike the other available elements. The solution for impact in a piezoelectric plate is shown to alleviate the spurious undulations in both velocity and electric potential fields, which are encountered in the conventional FE solutions. For the problem of high frequency Lamb wave actuation and sensing in a thin plate bonded with piezoelectric actuator/sensor patches, the element shows significant improvement in the computational efficiency over the conventional FE. Further, the free edge effect of steep gradients in the shear stress distribution at the actuator-plate interface is accurately captured by the proposed element using much fewer degrees of freedom than the conventional FE. [ABSTRACT FROM AUTHOR]

• Controlling elastic SV waves in solids was achieved by manipulating the induced flexural waves in the thin plates of the metasurface. • An uniaxial scaling transformation method (USTM) was proposed to elaborate the material to constitute the thin plates of the metasurface. • To control the length of metasurface to be smaller than the wavelength at the working frequency, the innovation of this work was to combine the approach of plate thickness variation and the USTM to design a realizable elastic metasurface. • Two elastic metasurfaces for wave focusing and abnormal refraction were designed to verify the feasibility of the proposed approach. Controlling wave propagation is a popular research field; however, progress with regard to the study of elastic waves is slow because of the coupling of different types of waves. In this paper, we report a novel approach to design elastic metasurfaces for controlling elastic shear vertical (SV) waves in solids. The metasurface is composed of separate parallel thin plates connected at both ends to half-space solids. The elastic SV-waves in solids were controlled by manipulating the induced flexural waves in the thin plates of the metasurface. Based on the form invariance of the governing equation for flexural waves in a thin plate under linear coordinate transformations, the uniaxial scaling transformation method (USTM) has been put forward to alter the material to constitute the thin plates of the metasurface. The transformed material is transversely isotropic, which greatly reduces implementation difficulties. To tune the traveling times of the flexural waves in the thin plates, different values of the scaling parameter α and plate thickness h were assigned for different thin plates based on the Kirchhoff plate theory. By combining the plate thickness variation approach with the USTM, the plate length of the metasurface could be effectively controlled to be smaller than the wavelength at the working frequency. To demonstrate the performance of the proposed approach, two designs of elastic metasurfaces for wave focusing and abnormal refraction were described in detail, and full numerical simulations were conducted. The present approach opens a promising avenue toward the realization of metasurfaces for controlling elastic waves. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• A semi-analytical wave form solution of the rectangular thin plate is developed with clear physical implication. • Concise and unified form of the solution and the convenient application to wave based method. • Applicability of the solution for rectangular thin plates with general elastic support boundary conditions. • Coupling and decoupling of in-plane waves of rectangular thin plates with elastic support boundary conditions. A semi-analytical solution for in-plane free waves analysis of rectangular thin plates with general elastic support boundary conditions (BCs) is developed. Based on the classical thin plate theory, the governing differential equations of the rectangular thin plate are introduced. The semi-analytical solution is obtained by superposition of in-plane waves of different patterns and different propagation directions. And it is validated by comparisons of the present results with those given in literatures. Eigensolutions for general BCs and the specific expressions of characteristic equations for various classical BCs are demonstrated. Characteristic curves of the dimensionless wavenumbers of the in-plane longitudinal wave and the in-plane shear wave of the rectangular thin plate with various BCs are presented and discussed. Perfect orthogonality of the in-plane longitudinal wave and the in-plane shear wave of different mode numbers is presented in the characteristic curves of the rectangular thin plate with two opposite sides simply supported. The characteristic curves corresponding to the rest of the classical BCs and all of the non-classical BCs show non-orthogonality of different extents, which reveals the formation mechanism of the variety of the mode shapes of the rectangular thin plate with various BCs. The strengthening and weakening process of the orthogonality and the formation of the intertwinement or independence of the characteristic curves of different mode numbers are elaborated through analysis on elastic support BCs intermediate between two classical BCs, which shows the influence of the BCs on the intrinsic characteristics of in-plane waves of the rectangular thin plate. Image, graphical abstract [ABSTRACT FROM AUTHOR]