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Due to the tunable characteristics of elastic waves, the vibroacoustic coupling behavior of a mechanical metastructure is a hot topic of underwater vehicles. In this work, a metastructure shell with active feedback control is presented and fabricated. The dynamic effective density and sound pressure level are derived to find the influences of acceleration and displacement feedback control. Different from a single cylinder, a double cylinder structure has both in-phase and anti-phase modes. Numerical results are obtained by Fourier transform and harmonic series expansion. With the introduction of an active feedback control system, the reduction of acoustic radiation shows low-frequency and broadband characteristics. In addition, finite element simulation is applied to support numerical results and present vibroacoustic characteristics. Finally, an experiment is performed in the anechoic chamber to illustrate the quiet metastructure shell, which can be applied to new designs of underwater vehicles. [ABSTRACT FROM AUTHOR]

As a significant extension of classical structures, elastic wave metamaterials are widely applied to the vibration isolation and turning wave propagation. However, little attention has been paid on their fracture and arrest properties. In this work, the dispersion curves and arrest property of mode II crack in 2D elastic wave metamaterials are studied, in which both nonlocal interactions and local resonators are considered. Because every unit cell is connected to the second nearest neighboring one with the massless spring along the x-direction, the nonlocal interaction is achieved. The dynamic effective mass is derived and influences of nonlocal interactions on the dispersion relation are analyzed. Moreover, the energy release ratio which characterizes the arrest ability is derived and the effects of structural parameters are discussed. The theoretical predictions are also compared to the finite element simulation. Numerical results show that the crack propagation resistance of mode II crack can be improved significantly by introducing proper nonlocal springs within a finite steady-state region. But in the oscillation region, the energy release ratio G0/G is unstable. Furthermore, an additional energy barrier can be generated before the region in which the crack propagates stably. [ABSTRACT FROM AUTHOR]

In this work, the duality of mechanical Kagome lattices with internal microstructures is studied and its non-Abelian characteristics of wave packet evolution are discussed. Based on Bloch's theorem, the dynamical and duality matrices are obtained during elastic wave propagation. By regulating the twisting angles of the Kagome lattices and internal microstructures, global twofold degeneracy and unequal Berry phase can be obtained. A fourfold degeneracy appears at Γ point when the mechanical metamaterial is subjected to a special twisting state. Numerical calculations of non-Abelian mechanics and duality are performed, in which band structures with special twisting angles are the same. In addition, the solution of the Wilson operator is derived by the elastic wave equation and gauge transformation, which has non-exchangeable product and leads to the non-Abelian Berry curvature. If the time-reversal symmetry is broken, non-commutative elastic wave responses can be generated. The generalized polarization and wave propagation become different when the acting sequences of external forces are exchanged. [ABSTRACT FROM AUTHOR]

This investigation is focused on the nonreciprocal transmission of the non-collinear mixing wave in a nonlinear elastic wave metamaterial. The nonlinear elastic wave metamaterial with asymmetric structure is used to break the traditional reciprocal transmission, which is composed of a nonlinear material and a linear phononic crystal. When two non-collinear shear waves following the resonant condition interact with each other, the sum frequency longitudinal wave can be generated and propagate together with fundamental and second harmonics. Based on the transfer and stiffness matrices, band gaps and transmission coefficients are derived. The changing of band structures results in manipulating elastic waves with different frequencies. In the nonreciprocal frequency region, elastic waves can propagate along the positive direction while the reverse case is prohibited. The mixing of two incident SV waves in the nonlinear elastic wave metamaterial is verified by experiments and the results can support the theoretical analysis and numerical calculations. Because of material nonlinearity and asymmetric structure, the nonlinear elastic wave metamaterial can behave as a mechanical diode. The present work shows the possibility to design nonreciprocal elastic wave device by nonlinear wave mixing methods. [ABSTRACT FROM AUTHOR]

In the underwater sonar or similar devices where the high pressure field is required, the concentrating and black hole like structures have important applications in harvesting energy systems of elastic waves. In this work, a new kind of active elastic metamaterials with cavities and an acoustic concentrator are presented. By the feedback control gain of piezoelectric diaphragms, we can obtain both the controllable effective bulk modulus and density within a wide frequency range. Based on the coordinate transformation method and by the feedback control on the periodic arrangement of acoustic cavities, an acoustic concentrator with multilayered alternative homogeneous materials can be achieved. Numerical results show that the acoustic wave is perfectly limited within the core region of the concentrator, which can enhance the acoustic energy. These characteristics with the tunable effective bulk modulus and density within a very wide frequency range are expected to be helpful for the design of practical acoustic concentrators. [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]

As emerging artificial structures, elastic wave metamaterials can show some unique properties in special frequency regions. In this study, the elastic wave scattering by a pair of parallel semi-infinite cracks in mechanical metamaterials with local resonators is studied. According to the discrete Wiener–Hopf method, the far field displacement solution is obtained. At the same time, the dynamic negative effective mass and band gaps can be observed with local resonators. Our attention is focused on how the internal microstructure affects the crack faces. Numerical results show that because of the stop band, the crack can be prevented from being disturbed by incident waves in specific frequency regions. As a result, the possibility of crack initiation and instability propagation is reduced considerably. This present work is expected to provide a way to improve arrest performance of elastic waves metamaterials. [ABSTRACT FROM AUTHOR]

Previous investigations on wave scattering and crack propagation in the discrete periodic structure are concentrated on the conditional mass–spring model, in which the internal mass is not included. In this work, elastic wave metamaterials with local resonators are studied to show the scattering of elastic waves by a semi-infinite crack and the arrest behaviour. The influences of internal mass–spring structure are analysed and the discrete Wiener–Hopf method is used to obtain the displacement solution. Numerical calculations are performed to show that the dynamic negative effective mass and band gaps can be observed owing to the local resonance of the internal mass. Therefore, the scattering of an elastic wave with a specific frequency by a semi-infinite crack can be avoided by tuning the structural parameters. Moreover, the energy release ratio which characterizes the splitting resistance is presented and the meta-arrest performance is found. It is expected that this study will increase understanding of how to control the scattering characteristics of elastic waves by a semi-infinite crack in locally resonant metamaterials and also help to improve their fracture resistance. [ABSTRACT FROM AUTHOR]

In this investigation, the bandgaps and nonreciprocal transmission of the nonlinear piezoelectric phononic crystal and elastic wave metamaterial are studied. Analytical solutions for the wave motion equations with the electro-mechanical coupling are obtained. According to the continuous conditions, the stop bands and transmission coefficients of both fundamental wave and second harmonic are derived by the stiffness matrix method. Some particular examples are presented to show the nonreciprocal transmission of the nonlinear elastic waves. Additionally, nonlinear ultrasonic experiments are applied to verify the theoretical analyses and numerical simulations. This work is intended to be helpful in the design and fabrication of devices of the elastic wave diode with piezoelectric materials. [ABSTRACT FROM AUTHOR]

Elastic wave metamaterials have been widely exploited with their dynamic superior properties and outstanding acoustic responses. However, it is difficult to directly manipulate sound pressure in low frequencies. In this study, we propose a new kind of elastic wave metamaterial which consists of vertical and lateral resonators as well as orthogonal stiffeners. The active feedback control system is applied to extend to the tunable scope for both lower and higher frequency regions and change the characteristics of acoustic-structure coupling. Its effective mass density is also discussed with different feedback constants. In order to present effects of the fluid-solid interaction, we considered that the elastic wave metamaterial is immersed in different fluid medium and its sound transmission loss (STL) is calculated. This work provides a feasible method for creating mechanical/acoustic models with multi-functional potentials. [ABSTRACT FROM AUTHOR]

The invisible cloak has attracted great attention due to its significant influences on science and engineering. Active elastic wave metamaterials provide superior controllable characteristics for the flexural wave cloak that is obviously different from the conventional structure. In this work, a broadband flexural wave cloak is designed and fabricated by the coordinate transformation method and active control system. The cloaking configuration consists of 16 alternative concentric layers with the polydimethylsiloxane (PDMS) and piezoelectric (PZT) patches which are connected with the active control systems. The results of the finite element simulations and experiments show that the effective frequency range of the flexural wave cloak with the active control systems is extended from 900 Hz to 1200 Hz. The design and fabrication of the elastic cloak with broadband characteristics have shielding applications. [ABSTRACT FROM AUTHOR]

• The effects of the initial stresses on the tunable propagation behavior in nonlinear phononic crystal and elastic wave metamaterial are presented. • The influences of the initial stresses on both in-plane and anti-plane modes are discussed. • The initial stresses can result in the movement to the low frequency regions of the central frequencies of the band gaps and the nonreciprocal zones. In this investigation, the nonreciprocal transmission of elastic waves is achieved by the combination of asymmetric structure and nonlinear material. Our attention is focused on the effects of the initial stresses on the tunable propagation behavior in nonlinear phononic crystal and elastic wave metamaterial. Different components of the initial stresses are considered for both in-plane and anti-plane modes. Based on the Bloch's law and transfer/stiffness matrix method, the corresponding band structures and transmission coefficients of the generated fundamental and second harmonic waves are calculated and discussed. We find that the central frequencies of the band gaps and the nonreciprocal zones shift towards the low frequency regions as the initial stresses increase. This present work can be expected to provide a way to tune the transmission behaviors in nonlinear elastic wave metamaterial and mechanical diodes. [ABSTRACT FROM AUTHOR]

• This work proposes the elastic wave metamaterial composed of parallel platforms with active control. • The topological phase transition is identified by the eigenstates and topological invariants. • Based on the k· p perturbation method, the effective Hamiltonian of two Dirac degeneracies is derived. Topological propagation in elastic wave metamaterials is widely investigated due to the superior transmission performance but most studies are focused on a single frequency range. This work proposes the elastic wave metamaterial composed of parallel platforms with active control, which illustrates topological interface states in two separate frequency ranges. In order to show basic features, band gap properties and localized modes in the rectilinear structure are considered at first. Then, the honeycomb system is investigated to present dynamic behaviors with two Dirac cones which belong to two frequency regions. The topological phase transition is identified by the eigenstates and topological invariants, respectively. Based on the k·p perturbation method, the effective Hamiltonian of two Dirac degeneracies is derived. Due to different stiffness of two platforms within a unit cell, two nontrivial degeneracies will be destroyed. Two band gaps support the interface states with topological protection and robust characteristic between lattices with different valley Hall phases. In addition, the topological transmission can be flexibly tuned by the active control system, which is supported by experiments. This work wishes to provide new designs of mechanical metamaterial with multiple functions. [ABSTRACT FROM AUTHOR]

Highlights • A new class of active elastic metamaterials is presented. • A cloaking design consisting of double Helmholtz cavities with active control action is proposed. • Some interesting phenomena (e.g. negative effective bulk modulus and cloaking) are shown. Abstract Wave invisibility has quite special meaning on marine vehicles under water, which encourages people to search effective methods for a long history. Initiated by this point, we propose a new class of active elastic metamaterials and a cloaking design consisting of double Helmholtz cavities. By changing external voltage with different piezoelectric diaphragm stiffness, this structure shows a controllable effective bulk modulus in which a negative value appears over a wide frequency range. This configuration with double active cavities provides better tunable abilities to achieve the effective bulk modulus than that with a single cavity. In order to design a multilayered cloak and a non-blind cloak, the coupling of the adjacent cavity cells is considered and the control strategy for the periodic cavities with active Helmholtz resonators is developed. The parameters of the multilayered acoustic cloak can be obtained by the coordinate transformation method and the corresponding effective medium theory. This action can be implemented by the active control on each unit cell to drive the distribution of effective bulk modulus. These characteristics with a tunable effective bulk modulus at a very wide frequency range are significant to control elastic wave propagation. Graphical abstract Image, graphical abstract With the active control action, a non-blind cloak is compared. The pressure field of the non-blind cloak is well distributed because of the active control. And the pressure field of the non-blind cloak is nearly undisturbed. [ABSTRACT FROM AUTHOR]

• The effects of nonlocal connection on band structures and dynamic behaviors of rectilinear lattices are studied. • The honeycomb lattice with nonlocal interactions is investigated, which realizes interface transmission and hybrid order topological states. • The active feedback control systems can change the Young's modulus of nonlocal metamaterials, which flexibly tune the topological characteristic of elastic waves. Topological elastic wave metamaterials provide a new mechanism to tune wave energy and provide engineering applications which are difficult to realize by traditional structures. This work reports topological characteristics of nonlocal elastic wave metamaterials with active feedback control. The effects of nonlocal connection on band structures and dynamic behaviors of rectilinear lattices are studied. Then, the honeycomb lattice with nonlocal interactions is investigated, which realizes interface transmission and hybrid order topological states. The introduction of active feedback control systems can change the Young's modulus of nonlocal metamaterials, which flexibly tune the topological characteristic of elastic waves. According to finite element simulation and experiment, the interface transmission and hybrid order can be generated by active feedback control, which agrees with theoretical predictions. [ABSTRACT FROM AUTHOR]

In this work, negative refraction and exceptional point (EP) in piezoelectric mechanical metamaterials are considered, which corporates with the Parity–Time (PT) symmetry. The oblique incidence of anti–plane shear wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes. In periodic layers, propagation characteristics are illustrated by the dispersion relation and transfer matrix method. The normal mode decomposition is developed and time average Poynting vector is used to derive the refraction angle at the interface of piezoelectric metamaterials. The beam splitting is shown with different incident angles, as well as the pure negative refraction is achieved. Due to the mechanical and electric coupling, the complex conjugate of Bloch wave number appears in the dispersion relation and degenerates to the exceptional point. In addition, a defect layer is introduced to study the transmission coefficient of two phononic crystals with different arrangements. When the gain and loss are introduced into the metamaterials, the Parity–Time symmetry system is realized and a complete transmission with a unidirectional zero reflection at exceptional point can be achieved. • The negative refraction and Parity–Time symmetry of piezoelectric mechanical metamaterial are discussed. • Poynting vector is presented to provide the elastic wave characteristics. • Experiments are performed to discuss about the beam splittin. [ABSTRACT FROM AUTHOR]

The interaction between elastic waves and nonlinear materials can generate second harmonics, which makes inherent properties of linear systems can be broken in nonlinear ones. In this work, two half-spaces composed of nonlinear and linear solids are used to break the symmetric transmission, in which a corrugated interface is considered. Affected by interface corrugations, additional irregularly reflected and transmitted waves of the incident fundamental wave and its second harmonic can be generated. Based on Fourier series and Taylor expansion approximation, the amplitude ratios of irregular waves are derived. Numerical results show that the incident frequency and corrugation length can manipulate the propagation of irregular waves. Due to the asymmetry of material nonlinearity, second harmonics can enter the linear half-space form the nonlinear one, but the reverse transmission is not allowed. Both the theoretical analysis and experimental results can support the in-plane non-symmetric transmission in the two half-spaces, which is an extension of the nonreciprocal phenomena in nonlinear metamaterials. • The in-plane non-symmetric transmission in the two half-spaces with a corrugated interface is studied. • The reflection and transmission of a longitudinal wave and its second harmonic along opposite directions are considered. • The incident frequency and corrugation length can manipulate the propagation of irregular waves. [ABSTRACT FROM AUTHOR]

Different from the linear phononic crystals, elastic waves can exhibit more interesting phenomena in periodic structures with nonlinear properties. By the active control action, elastic wave characteristics can be tuned based on the demand in practical application. This work discusses the possibility of the active control action on elastic waves in phononic crystals with the weakly nonlinear monoatomic lattice chain. Based on the Lindstedt-Poincaré method, the approximate solution of the dispersion relation is derived. Numerical calculations are performed to discuss the influences of the active control action on wave propagation properties. In order to present the features of nonlinear elastic wave dynamics, it is mainly focused on the effects of active control accompanied by the changes of the elastic wave amplitude, nonlinear degree, hard and soft nonlinearities. It is expected to extend the analysis and design of new phononic crystal devices for both the theory and application fields. [ABSTRACT FROM AUTHOR]

Abstract: In this Letter, the effects of the viscous fluid on the propagation characteristics of elastic waves in carbon nanotubes are studied. Based on the nonlocal continuum theory, the small scales effects are also considered. The equations of wave motion are derived and the dispersion relation is presented. Numerical simulations are performed with the consideration of different scale coefficients to discuss the influence of the viscous fluid. From the results, it can be observed that the dispersion relation can be changed by the fluid viscosity obviously. Moreover, due to the fluid viscosity, the wave frequency will be reduced to a low region and the elastic wave behaviors can be significantly influenced by the viscous fluid velocity. [Copyright &y& Elsevier]

In this paper, the propagation and localization of elastic waves in randomly disordered layered three-component phononic crystals with thermal effects are studied. The transfer matrix is obtained by applying the continuity conditions between three consecutive sub-cells. Based on the transfer matrix method and Bloch theory, the expressions of the localization factor and dispersion relation are presented. The relation between the localization factors and dispersion curves is discussed. Numerical simulations are performed to investigate the influences of the incident angle on band structures of ordered phononic crystals. For the randomly disordered ones, disorders of structural thickness ratios and Lamé constants are considered. The incident angles, disorder degrees, thickness ratios, Lamé constants and temperature changes have prominent effects on wave localization phenomena in three-component systems. Furthermore, it can be observed that stopbands locate in very low-frequency regions. The localization factor is an effective way to investigate randomly disordered phononic crystals in which the band structure cannot be described. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the stop band properties of elastic waves in three-dimensional piezoelectric phononic crystals with initial stress are studied taking the mechanical and electrical coupling into account. The band gap characteristics for three kinds of lattice arrangements (i.e. sc, bcc and fcc) are investigated by the plane wave expansion (PWE) method. Regarding the variables of mechanical and electrical fields as the elements of the generalized state vector, the expression of the generalized eigenvalue equation for three-dimensional piezoelectric periodic structures is derived. Numerical calculations are performed for the PZT-2/polymer and ZnO/polymer phononic crystals. It can be observed from the results that the fcc lattice is more favorable to create the stop band than the sc and bcc lattices for the piezoelectric phononic crystals, which has also been proved for the pure elastic periodic structures. Compared with the PZT-2/polymer systems, the band gap of the sc lattice for the ZnO/polymer structures is narrower. However, the widths of the bcc and fcc lattices for the ZnO/polymer phononic crystals are much larger than those for the PZT-2/polymer structures. The lattice arrangements and the piezoelectricity have remarkable influences on the stop band behaviors. [Copyright &y& Elsevier]

Abstract: In this paper, the propagation characteristics of the longitudinal wave in nanoplates with small scale effects are studied. The equation of the longitudinal wave is obtained using the nonlocal elastic theory. The phase velocity and the group velocity are derived, respectively. The dispersion relation is analyzed with different wave numbers and scale coefficients. It can be observed from the results that the dispersion properties of the longitudinal wave are induced by the small scale effects, which will disappear in local continuous models. The dispersion degree can be strengthened by increasing the scale coefficient and the wave number. Furthermore, the characteristics for the group velocity of the longitudinal wave in nanoplates can also be tuned by these factors. [Copyright &y& Elsevier]

In this work, the symmetric transmission is broken in the system with a linear half–space combined by a nonlinear one with a corrugated interface. The interaction between nonlinear materials and elastic waves can generate second harmonics, so the non–symmetric transmission is realized. With the corrugation effects, irregularly reflected and transmitted waves are generated for both fundamental and second harmonics during the incident SH mode across the corrugated interface. Based on the Fourier series expansion method for the interface, the solution with the first order approximation of reflection and transmission coefficients are derived and the effects of the interface corrugation are discussed. The non–symmetric transmission is proved by both theoretical analysis and experiments. It is found that the reflected and transmitted waves are different when the fundamental wave incidents from the opposite direction. Compared with the positive incidence, there is no second harmonic in the linear half–space for the negative case and the generation of second harmonics in the nonlinear half–space is weaker. • The non–symmetric transmission is proved by both theoretical analysis and experiments. • Irregularly waves are generated for both fundamental and second harmonics at the corrugated interface. • Compared with the positive incidence, there is no second harmonics in the linear half–space for the negative case. [ABSTRACT FROM AUTHOR]

• The effective mass density is derived and the dynamic responses are presented by the dynamic effective medium method. • The sound transmission loss (STL) is obtained based on the principle of virtual work. • The negative mass density and STL in the lower frequencies can be adjusted by the active feedback control. With the active feedback control system on elastic wave metamaterials, this research is concentrated on the effective mass density and sound transmission by a harmonic incident sound pressure. The elastic wave metamaterials consist of double plates which are attached by the upper and lower four-link mechanisms being bonded with four lateral resonators. The vertical resonator in every unit cell is jointed by the active feedback control system which is connected by two four-link mechanisms. Using the dynamic effective medium method, the expressions of the effective mass density are obtained and the dynamic responses are presented. Based on the Bloch–Floquet theorem and Poisson summation formula, the sound transmission loss (STL) of this elastic wave metamaterial is shown by the principle of virtual work. This research also shows that the characteristics of the effective mass density and STL can be tuned by the acceleration and displacement feedback in the active control system. Furthermore, it is found that the dynamic response and STL are also changed obviously by different incident angles (including the elevation and azimuth angles), the periodicity spacing of local resonators and the structural damping. [Display omitted] Composite Figure: Elastic wave metamaterials is presented in this work as shown in (a) the structure with local resonators attached to the active feedback control systems. The effective mass density is derived and the dynamic responses are presented by the dynamic effective medium method, there are two modes and appear two negative density regions in the double plates model, (b) in-phase and (c) anti-phase modes of the dynamic effective mass density. Based on the incident sound pressure wave, the sound transmission loss (STL) is obtained by the principle of virtual work, the STL can be tuned in the lower frequency region by the active control, (d) influences of the positive acceleration and (e) the displacement feedback control on the STL. [ABSTRACT FROM AUTHOR]

The propagation of elastic waves in magnetoelectroelastic grid structures is studied. Band gap properties are presented and the effects of the magnetoelectroelastic coupling and initial stress are considered. Numerical calculations are performed using the plane-wave expansion method. The results show that the band gap width can be tuned by the initial stress. It is hoped that our results will be helpful for designing acoustic filters with magnetoelectroelastic materials and grid structures. [ABSTRACT FROM AUTHOR]

In this investigation, three-dimensional nonreciprocal transmission is realized by the combination of structural asymmetry and material nonlinearity. Analytical solutions of the coupled quasi-longitudinal (qP) and quasi-shear (qS 1 and qS 2) waves are derived. According to Bloch's law and the stiffness matrix method, we obtain the band gaps and the transmission coefficients of the fundamental and double frequency waves. We also discuss the effects of the incident azimuthal angle on the propagation behaviors in nonlinear phononic crystals and elastic wave metamaterials. This present work is expected to help design practical devices of nonreciprocal transmission with vector characteristics. • Three-dimensional nonreciprocal transmission is realized by material nonlinearities. • Analytical solutions of coupled quasi-longitudinal and quasi-shear waves are derived. • The effects of incident azimuthal angles on the propagation behaviors are discussed. [ABSTRACT FROM AUTHOR]

• A broadband flexural wave black hole equipment or concentrator is designed. • The piezoelectric transducer patches connected by external electrical circuits are used as the active components. • The experiments are performed to present the comparisons with the numerical simulations. The black hole equipment or concentrator plays an important role in harnessing the wave energy, which has the potential application in the energy collecting engineering. In this work, we propose a broadband flexural wave black hole equipment or concentrator which is designed by the coordinate transformation method and active control systems. The concentrator with 48 alternative sectorial layers has a good concentrating performance. The polydimethylsiloxane (PDMS) and piezoelectric transducer (PZT) patches connected by external electrical circuits are used as the active components of the flexural wave concentrating configuration. By finite element simulations and experiments, the results show that the effective frequency region of the flexural wave concentrator without the active control systems is from 800 Hz to 1500 Hz. In addition, a wider frequency region of the concentrating performance from 800 Hz to 2000 Hz can be obtained by the active control system connected with external resistors and negative capacitor circuits. Furthermore, experiments are performed to show the excellent agreement with the numerical predictions. The black hole or concentrator of flexural waves with the active control action. Image, graphical abstract [ABSTRACT FROM AUTHOR]

The propagation of in-plane waves in piezoelectric metamaterials involves the coupling of longitudinal (i.e. quasi–pressure), transverse (i.e. quasi–shear) and electric potential waves, which can result in different exotic phenomena. In this study, the stiffness matrix method is used to analyze the dispersion relation, which contains anomalous propagation characteristics. With the coupling of electric potential, the frequency spectrum of in–plane wave shows new characteristics. The exceptional point caused by non–Hermitian operator that does not exist before also appears when the vertical wave number is imaginary. The oblique incidence of the in–plane wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes which include the negative refraction. The normal mode decomposition is developed to study the in-plane incidence of piezoelectric metamaterial and then the averaged Poynting vector is applied to obtain the refraction angle. Moreover, the defect layer is introduced into the phononic crystals to study the transmission coefficients with two different symmetrical arrangements. When the balanced gain and loss are considered in the metamaterial, the Parity–Time symmetry appears and brings in pairs of exceptional points to achieve complete transmission with unidirectional zero reflection. • With the coupling of electric potential, the exceptional point caused by non–Hermitian operator that does not exist before appears when the vertical wave number is imaginary. • The oblique incidence of the in–plane wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes which include the negative refraction. • The defect layer is introduced to study the transmission coefficients with two different symmetrical arrangements. [ABSTRACT FROM AUTHOR]

Propagation of elastic waves along a direction has special interests in practical applications. These concerns generate the design of an elastic wave metamaterial with electrically switchable properties, which is studied in this work. The structure contains a T-shaped waveguide in a plate with the 3D printing technology; and the active control system is used to tune the propagation direction of the flexural wave. The piezoelectric patches which are connected by the negative capacitance circuits are applied to behave as the active control system. The finite element simulation is performed to give the theoretical prediction of the switchable waveguide and the tunable equivalent parameters are achieved by the electrical circuits. The active control experiments are finally carried out to support the numerical design. [ABSTRACT FROM AUTHOR]

• The band structures are obtained by the transfer matrix method and the transmission coefficients are achieved by the stiffness matrix method. • Experiments are performed for comparison with the theoretical results. • The nonreciprocal transmission of elastic waves is realized by enlightenment of an acoustic diode. In this investigation, the nonreciprocal transmission of elastic waves is realized by enlightenment of an acoustic diode. The phenomenon can be found in a nonlinear elastic wave metamaterial which consists of a linear phononic crystal attached by a nonlinear elastic medium. The structural asymmetry and material nonlinearity break the inherent reciprocity. The multi-displacements coupling of elastic waves in solids makes the problem more complicated in mathematics, but with showing interesting physical phenomenon. The elastic waves with the fundamental and double frequencies can be generated by the interaction between an incident longitudinal wave and the material nonlinearity. Based on the Bloch's law and continuity conditions, the band structures are obtained by the transfer matrix method and the transmission coefficients are achieved by the stiffness matrix method. Especially, experiments are performed for comparison with the theoretical results. This research may be helpful to design practical devices with nonreciprocal transmission of the elastic wave metamaterial. The transmission coefficient for the incident longitudinal wave from the left boundary, which shows the fundamental and double frequency waves are zero in the frequency region with nonreciprocal transmission. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• The energy release ratio which denotes the crack splitting resistance is derived and the corresponding radiated waves are discussed • The energy barrier before the stable propagates is larger, which means that the ability to resist the crack speed is enhanced • The lower energy release ratio in the subsonic and supersonic regions indicates that the elastic wave metamaterials with local resonators has a better crack resistance and shows the meta-arrest property. In this study, the dynamic effective mass and effects of local resonators on the crack growth are investigated. Based on Wiener-Hopf method and factorization using Cauchy-type integral, the energy release ratio which denotes crack splitting resistance is derived and the corresponding radiated waves are discussed. The results show that at variance with traditional periodic mass-spring lattice chain, the radiated energy of the present elastic wave metamaterial with local resonators is more sensitive to low crack speeds. The energy barrier before the stable propagates is larger, which means that the ability to resist the crack speed is enhanced. The lower energy release ratio in the subsonic and supersonic regions indicates that the elastic wave metamaterials with local resonators has better crack resistance and shows the meta-arrest property. The present results might have potential application to improve the crack resistance of advanced materials and structures. [ABSTRACT FROM AUTHOR]