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• The coupling of nonlocal interaction and damping has better arrest behavior during the stable crack growth and reduce the vibration amplitude in the oscillation region of energy release ratio. • The magnitude of additional energy barrier in the stable region caused by nonlocal interactions can be changed by damping. • Finite element simulation and experiment have good agreement, which can support the theoretical prediction. In this study, the arrest behavior of locally resonant structure with nonlocal interaction and damping are analyzed. Based on the Wiener-Hopf method, the energy release ratio G 0 / G which denotes the arrest property is derived. The effects of nonlocal interaction and damping parameters on the oscillation and stability regions during the crack growth are discussed. The arrest characteristics of three locally resonant structures are compared. In order to support the theoretical calculation, both the finite element simulation and fracture experiment are performed. Results show that the locally resonant structure with nonlocal interaction and damping has smaller energy release ratio G 0 / G. It indicates that the coupling of both nonlocal interaction and damping can significantly enhance the propagation resistance of crack propagation. [ABSTRACT FROM AUTHOR]

Wave invisibility in confined space has been proved practical significance in mechanical engineering and military fields. In this work, a flexural wave cloak of a corner-domain target in a metamaterial plate with proportional integral (PI) active control circuit is proposed. According to the double reflection principle and mechanical characteristic at the boundary, wave fields for a corner-domain target are defined as a collection of incident, scattering and three mirror domains. The unknown scattering mode coefficients are determined by the image method and boundary conditions. The dynamic stress concentration, scattering amplitude and scattering cross-section for the corner-domain target are obtained. The cloaking configuration is composed of multiple equally spaced concentric layers, which are filled with piezoelectric (PZT) patches. In addition, these PZT patches are connected to the active control circuit with proportional integral (PI) control module. The results indicate that the flexural wave cloak can reduce the dynamic stress concentration, scattering amplitude and scattering cross-section in corner domain. Compared to the original structure without PI active control, the effective frequency range of the active cloak can be extended by 20%. • A flexural wave cloak of a corner-domain target in a metamaterial plate with proportional integral (PI) active control circuit is proposed. • The unknown scattering mode coefficients are determined by the image method and boundary conditions. • The flexural wave cloak can reduce the dynamic stress concentration, scattering amplitude and scattering cross-section in corner domain. [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]

• 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]

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 nonreciprocal phenomenon appears in nonlinear acoustic metamaterial which are composed of a linear phononic crystal and a nonlinear layer. Based on the nonlinear characteristics, the acoustic waves can pass in one direction and are prohibited in reverse. Naturally, people will wonder whether the nonreciprocal phenomenon can be found in nonlinear elastic wave metamaterial. Because of the coupling of the multi-displacements, this problem becomes more complicated but interesting for waves in solid. Motivated by this enlightenment, we will discuss the band gap and transmission properties of elastic waves in both linear and nonlinear periodic systems. The fundamental and double frequency waves can be generated by the interaction between SH waves and the nonlinearity of materials. According to continuity conditions of incident SH wave, the transfer matrices are derived. The stop band and transmission coefficient are obtained by Bloch's law. This research is expected to be helpful to develop new elastic wave metamaterial devices. [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]

In the present work, the nonlinear internal resonance of double-walled nanobeams under the external parametric load is studied. The nonlocal continuum theory is applied to describe the nano scale effects and the nonlinear governing equations are derived by the multiple scale method. The parametric internal resonance is considered and the relation between the frequency and amplitude is discussed. From the numerical simulation, it can be observed that small scale effects are more obvious for short structures. Three different nonlinear cases can be found. The gap between the stable and instable regions is reduced by the van der Walls (vdW) interaction but enhanced by the excitation amplitude. Moreover, the dynamical motions of double-walled nanobeams are sensitive to the initial condition and excitation frequency. [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]

In order to predict the effective properties of multiferroic composite materials, the effective material constants of multiferroic composites with the coated inclusion and imperfect interface are investigated. Based on the generalized self-consistent theory, the closed-form solutions of the effective material constants are derived. For the composites with piezomagnetic inclusion, piezoelectric coating and polymer matrix, numerical calculations are performed to present the influences of the imperfect interface cooperating with the coating on the effective material constants. From the results, it can be observed that the effective constants can be enhanced by the coating but reduced by the imperfect interface. Moreover, the coating has the shielding effects on the imperfect interface for the composite structures with its higher filling ratio. [ABSTRACT FROM AUTHOR]

Structures under parametric load can be induced to the parametric instability in which the excitation frequency is located the instability region. In the present work, the parametric instability of double-walled carbon nanotubes is studied. The axial harmonic excitation is considered and the nonlocal continuum theory is applied. The critical equation is derived as the Mathieu form by the Galerkin's theory and the instability condition is presented with the Bolotin's method. Numerical calculations are performed and it can be seen that the van der Waals interaction can enhance the stability of double-walled nanotubes under the parametric excitation. The parametric instability becomes more obvious with the matrix stiffness decreasing and small scale coefficient increasing. The parametric instability is going to be more significant for higher mode numbers. For the nanosystem with the soft matrix and higher mode number, the small scale coefficient and the ratio of the length to the diameter have obvious influences on the starting point of the instability region. [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]

In this work, it is focused on the problems that the influences of the remanent polarization and Maxwell stress in the surrounding medium on a moving anti-plane interfacial crack between two dissimilar piezoelectric materials. By the Fourier and its inverse transforms, it is converted to two pairs of dual integral equations. The closed-form solutions of the intensity factors of the stress and electric displacement are derived. It can be observed that the difference between the moving crack and static case can be reduced by the remanent polarization. Influences of the Maxwell stress become more obvious for the systems with larger remanent polarizations. The fracture properties of the moving interfacial crack between two dissimilar piezoelectric solids can be obviously changed by the remanent polarization and Maxwell stress. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear free vibration of the nanotube with damping effects is studied. Based on the nonlocal elastic theory and Hamilton principle, the governing equation of the nonlinear free vibration for the nanotube is obtained. The Galerkin method is employed to reduce the nonlinear equation with the integral and partial differential characteristics into a nonlinear ordinary differential equation. Then the relation is solved by the multiple scale method and the approximate analytical solution is derived. The nonlinear vibration behaviors are discussed with the effects of damping, elastic matrix stiffness, small scales and initial displacements. From the results, it can be observed that the nonlinear vibration can be reduced by the matrix damping. The elastic matrix stiffness has significant influences on the nonlinear vibration properties. The nonlinear behaviors can be changed by the small scale effects, especially for the structure with large initial displacement. [ABSTRACT FROM AUTHOR]

Abstract: Based on the nonlocal continuum theory, the nonlinear primary resonance of nano beam with the axial initial load is investigated. The amplitude–frequency response for the primary resonance is derived with the multiple scale method and the stability is analyzed. The nonlinear primary resonance of nano beam is discussed with the influences of small scale effect, axial initial load, mode number, Winkler foundation modulus and the ratio of the length to the diameter. From the results, the typical hardening nonlinearity can be observed. Moreover, some significant and interesting nonlinear phenomena can be found for the primary resonance of nano beam. This work is expected to be useful for the design and analysis for the nonlinear dynamic behaviors of structures at nano scales. [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]

Abstract: In this paper, the bending behaviors of the nanoplate with small scale effects are investigated by the nonlocal continuum theory. The governing equations for the nonlocal Mindlin and Kirchhoff plate models are derived. The expressions of the bending displacement are presented analytically. The difference between the two models is discussed and bending properties of the nanoplate are illustrated. It can be observed that the small scale effects are obvious for bending properties of the nanoplate. The half wave numbers, width ratios and elastic matrix properties also have significant influence on bending behaviors. [Copyright &y& Elsevier]

Abstract: In this paper, the thermal effects on the vibration properties of the double-layered nanoplates are studied. Based on the nonlocal continuum theory, the governing equations are derived and the expressions of the natural frequencies are presented. The axial stress caused by the thermal effects is considered. The influences of the small scale coefficient, the room or low temperature, the high temperature, the half wave numbers, the temperature change and the ratio of plate widths are discussed. Numerical results show that the small scale effects are significant for larger half wave numbers. The vibration properties can be obviously tuned by the thermal effects, the ratio of the nanoplate widths and the half wave numbers. The influences on the vibration behaviors are usually different for mode I and mode II. [Copyright &y& Elsevier]

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: The three-dimensional periodic piezoelectric composites are composed of the spheres embedded in matrix materials with the face center cubic arrangement. The electric fields are approximated as quasi-static. By the plane-wave expansion method, the band structures of BaTiO3/polymer and polymer/BaTiO3 composites are calculated. The expression of generalized eigenvalue equation is derived. The results show that it is more easily to generate the wave band gaps for piezoelectric spheres in polymer matrix than the reverse structures. The location and width of band gaps can be changed by piezoelectricity. The piezoelectric constants can influence the degenerate relation for the two lowest acoustic branches. [Copyright &y& Elsevier]

Abstract: In this paper, the elastic wave propagation in phononic crystals with piezoelectric and piezomagnetic inclusions is investigated taking the magneto-electro-elastic coupling into account. The electric and magnetic fields are approximated as quasi-static. The band structures of three kinds of piezoelectric/piezomagnetic phononic crystals—CoFe2O4/quartz, BaTiO3/CoFe2O4 and BaTiO3–CoFe2O4/polymer periodic composites are calculated using the plane-wave expansion method. The piezoelectric and piezomagnetic effects on the band structures are analyzed. The numerical results show that in CoFe2O4/quartz structures, only one narrow band gap exists along the Γ–X direction for the coupling of xy-mode and z-mode for the filling fraction f being 0.4; while in BaTiO3/CoFe2O4 composites, only one narrow band gap exists along the Γ–X direction forxy-mode and no band gap exists for z-mode as the filling friction f is 0.5. Moreover, for the new type of magneto-electro-elastic phononic crystal—BaTiO3–CoFe2O4/polymer periodic composite, the band gap characteristics are more superior in the whole considered frequency regions due to the big contrast of the material properties in the two constituents and the effects of the piezoelectricity and piezomagneticity on the band gap structures are remarkable. [Copyright &y& Elsevier]

Abstract: Two-dimensional in-plane wave propagation and localization in the disordered layered piezoelectric phononic crystals with material 6mm are investigated taking the electromechanical coupling into account. The electric field is approximated as quasi-static. The analytical solutions of elastic waves are obtained. The 6×6 transfer matrix between two consecutive unit cells is obtained by means of the mechanical and electrical continuity conditions. The expressions of the localization factor and localization length in the disordered periodic structures are presented by regarding the variables of the mechanical and electrical fields as the elements of the state vector. The numerical results of the localization factors and localization lengths are presented for two kinds of disordered piezoelectric phononic crystals, i.e. ZnO–PZT–5H and PVDF–PZT–5H piezocomposites. It is seen from the results that the incident angle of elastic waves and the thickness of the piezoelectric ceramics have significant effects on the wave localization characteristics. For different piezoelectric phononic crystals, the effects of the incident angle are very different. Moreover, with the increase of the disorder degree, the localization phenomenon is strengthened. [Copyright &y& Elsevier]

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]

• 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]

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]

• The incremental harmonic balance (IHB) method is improved to study the propagation behaviors of the elastic wave metamaterials with the strongly nonlinear characteristics. • The band gap and the nonreciprocal transmission are presented to realize the diode phenomenon of the strongly nonlinear elastic wave. • Both the numerical calculations and experiments are performed to demonstrate the theoretical predictions. Based on the granular diatomic lattice chain model, the band gap properties and nonreciprocal transmission of elastic wave metamaterials with the nonlinearity are studied. Extending the incremental harmonic balance (IHB) method to the nonlinear elastic wave, the traditional approach for the nonlinear periodic structures is improved. The influences on the band gap properties are discussed and the diode phenomenon can be observed. Then the nonreciprocal transmission of elastic wave metamaterials is realized. Both the theoretical and numerical results are presented to show the band gap structure and nonreciprocal phenomenon. And the experiments are performed to support these predictions. This study is expected to extend the applications of phononic crystals and elastic wave metamaterials with nonlinear properties. [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 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]

Highlights: [•] Band gap behaviors of sandwich panels with corrugated cores are studied. [•] Frequency responses of sandwich panels are effectively computed using the SEM. [•] Vibration distributions of sandwich panels in stop and pass bands are displayed. [•] Influences of some parameters on vibration isolation abilities are studied. [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]

• Microplastic-induced changes affect soil function and soil microbial communities. • The effects of microplastics on soil or soil organisms depend on particle types, concentration and exposure time. • Consumption of microplastics can cause mechanical damage, chemical responses and disrupt gut microbial communities. • Microplastics have potential effects on plant growth and may accumulate and transport in plants. • Some bacteria biodegrade microplastics could be used for soil bioremediation. Microplastics are emerging contaminants and their presence in water and soil ecosystems has recently drawn considerable attention because they pose a great threat to entire ecosystems. Recent researches have focused on the detection, occurrence, characterization, and toxicology of microplastics in marine and freshwater ecosystems; however, our understanding of the ecological effects of microplastics in soil ecosystems is still limited compared with that in aquatic ecosystems. Here, we have compiled literature, studying the sources, migration of microplastics in soil, negative impacts on soil health and function, trophic transfer in food chains, and the corresponding adverse effects on soil organisms in order to address the potential ecological and human health risks caused by microplastics in soil. This review aims to address gaps in knowledge, shed light on the ecological effects of microplastics in soil, and propose future studies on microplastic pollution and the resultant soil ecotoxicity. Furthermore, this review is focused on limiting microplastics in soil and establishing management and remediation measures to mitigate the risks posed by microplastic pollution. [ABSTRACT FROM AUTHOR]