Active elastic metamaterials for subwavelength wave propagation control

Recent research activities in elastic metamaterials demonstrate a significant potential for subwavelength wave propagation control owing to their interior locally resonant mechanism. The growing technological developments in electro/magnetomechanical couplings of smart materials have introduced a controlling degree of freedom for passive elastic metamaterials. Active elastic metamaterials could allow for a fine control of material physical behavior and thereby induce new functional properties that cannot be produced by passive approaches. In this paper, two types of active elastic metamaterials with shunted piezoelectric materials and electrorheological elastomers are proposed. Theoretical analyses and numerical validations of the active elastic metamaterials with detailed microstructures are pre- sented for designing adaptive applications in band gap structures and extraordinary waveguides. The active elastic metamaterial could provide a new design methodology for adaptive wave filters, high signal-to-noise sensors, and structural health monitoring applications.

Reconfigurable mechanism-based metamaterials for ternary-coded elastic wave polarizers and programmable refraction control

Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic waves.However,most of them rely on the resonant structural components,and thus are frequency-dependent and unchangeable.Here,we present a reconfigurable 2D mechanism-based metamaterial which possesses transformable and frequency-independent elastic properties.Based on the proposed mechanism-based metamaterial,interesting functionalities,such as ternarycoded elastic wave polarizer and programmable refraction,are demonstrated.Particularly,unique ternary-coded polarizers,with 1-trit polarization filtering and 2-trit polarization separating of longitudinal and transverse waves,are first achieved.Then,the strong anisotropy of the proposed metamaterial is harnessed to realize positive-negative bi-refraction,only-positive refraction,and only-negative refraction.Finally,the wave functions with detailed microstructures are numerically verified.

Wave control of a flexible space tether based on elastic metamaterials

This study proposes a spider‐web elastic metamaterial to suppress vibrations in space slender structures,such as flexible space tethers.The metamaterial consists of unit cells that are periodically distributed on the space tether to obtain band gaps.The finite element model of the unit cell is established by employing the absolute nodal coordinate formulation(ANCF)due to the large deformation of the structure.The eigenfrequencies and corresponding vibration modes of the unit cell are obtained by ANCF.Moreover,the band gap of the unit cell is calculated based on the phonon crystal theory.The relationship between the vibration modes and the band gaps is analyzed.Finally,an experiment is conducted to verify the vibration transmission characteristics of finite period cells.The results show the effectiveness of the spider‐web elastic metamaterial for vibration suppression of a flexible tether.This study provides insights into the use of elastic metamaterials for vibration isolation in space tether systems.

Modeling and analysis of gradient metamaterials for broad fusion bandgaps

A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap.First,three local resonators with linearly increasing stiffness are periodically attached to the spring-mass chain to construct the gradient metamaterial.The dispersion relation is then derived based on Bloch's theorem to reveal the fusion bandgap theoretically.The dynamic characteristic of the finite spring-mass chain is investigated to validate the fusion of multiple bandgaps.Finally,the effects of the design parameters on multiple bandgaps are discussed.The results show that the metamaterial with a non-uniform stiffness gradient pattern is capable of opening a broad fusion bandgap and effectively attenuating the longitudinal waves within a broad frequency region.

Elastic twisting metamaterial for perfect longitudinal-torsional wave mode conversion

In this work,we design a twisting metamaterial for longitudinal-torsional(L-T)mode conversion in pipes through exploring the theory of perfect transmodal FabryPerot interference(TFPI).Assuming that the axial and radial motions in pipes can be decoupled,we find that the metamaterial can be designed in a rectangular coordinate system,which is much more convenient than that in a cylindrical system.Numerical calculation with detailed microstructures shows that an efficient L-T mode conversion can be obtained in pipes with different radii.In addition,we fabricate mode-converting microstructures on an aluminum pipe and conduct ultrasonic experiments,and the results are in good agreement with the numerical calculations.We expect that the proposed LT mode-converting metamaterial and its design methodology can be applied in various ultrasonic devices.

A low-frequency pure metal metamaterial absorber with continuously tunable stiffness

To address the incompatibility between high environmental adaptability and deep subwavelength characteristics in conventional local resonance metamaterials,and overcome the deficiencies in the stability of existing active control techniques for band gaps,this paper proposes a design method of pure metal vibration damping metamaterial with continuously tunable stiffness for wideband elastic wave absorption.We design a dual-helix narrow-slit pure metal metamaterial unit,which possesses the triple advantage of high spatial compactness,low stiffness characteristics,and high structural stability,enabling the opening of elastic flexural band gaps in the low-frequency range.Similar to the principle of a sliding rheostat,the introduction of continuously sliding plug-ins into the helical slits enables the continuous variation of the stiffness of the metamaterial unit,achieving a continuously tunable band gap effect.This successfully extends the effective band gap by more than ten times.The experimental results indicate that this metamaterial unit can be used as an additional vibration absorber to absorb the low-frequency vibration energy effectively.Furthermore,it advances the metamaterial absorbers from a purely passive narrowband design to a wideband tunable one.The pure metal double-helix metamaterials retain the subwavelength properties of metamaterials and are suitable for deployment in harsh environments.Simultaneously,by adjusting its stiffness,it substantially broadens the effective band gap range,presenting promising potential applications in various mechanical equipment operating under adverse conditions.

A new tunable elastic metamaterial structure for manipulating band gaps/wave propagation

A one-dimensional mechanical lattice system with local resonators is proposed as an elastic metamaterial model,which shows negative mass and negative modulus under specific frequency ranges.The proposed representative units,consisting of accurately arranged rigid components,can generate controllable translational resonance and achieve negative mass and negative modulus by adjusting the local structural parameters.A shape memory polymer is adopted as a spring component,whose Young’s modulus is obviously affected by temperature,and the proposed metamaterials’tunable ability is achieved by adjusting temperature.The effect of the shape memory polymer’s stiffness variation on the band gaps is investigated detailedly,and the special phenomenon of intersecting dispersion curves is discussed,which can be designed and controlled by adjusting temperature.The dispersion relationship of the continuum metamaterial model affected by temperature is obtained,which shows great tunable ability to manipulate wave propagation.

Collision enhanced hyper-damping in nonlinear elastic metamaterial

Nonlinear elastic metamaterial,a topic which has attracted extensive attention in recent years,can enable broadband vibration reduction under relatively large amplitude.The combination of damping and strong nonlinearity in metamaterials may entail extraordinary effects and offer the capability for low-frequency and broadband vibration reduction.However,there exists a clear lack of proper design methods as well as the deficiency in understanding properties arising from this concept.To tackle this problem,this paper numerically demonstrates that the nonlinear elastic metamaterials,consisting of sandwich damping layers and collision resonators,can generate very robust hyper-damping effect,conducive to efficient and broadband vibration suppression.The collision-enhanced hyper damping is persistently presented in a large parameter space,ranging from small to large amplitudes,and for small and large damping coefficients.The achieved robust effects greatly enlarge the application scope of nonlinear metamaterials.We report the design concept,properties and mechanisms of the hyper-damping and its effect on vibration transmission.This paper reveals new properties offered by nonlinear elastic metamaterials,and offers a robust method for achieving efficient low-frequency and broadband vibration suppression.

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.

Design of quasi-zero-stiffness elastic diodes for low-frequency nonreciprocity through machine learning

Elastic diodes with nonreciprocity have the potential to enable unidirectional modulation of elastic waves.However,it is a challenge to achieve nonreciprocity at low frequencies(<100 Hz)using existing elastic diodes.This paper proposes a quasizero-stiffness(QZS)elastic diode to resolve such a tough issue and fulfill high-quality low-frequency nonreciprocity.The proposed elastic diode is invented by combining a QZS locally resonant metamaterial with a linear one,where the beneficial nonlinearity of the QZS metamaterial facilitates opening an amplitude-dependent band gap at very low frequencies.Firstly,the dispersion relation of the QZS metamaterial is derived theoretically based on the harmonic balance method(HBM).Then,the transmissibility of the QZS elastic diode in both the forward and backward directions is calculated through theoretical analyses and numerical simulations.Additionally,the influences of system parameters on the low-frequency nonreciprocal effect are discussed.The results indicate that considerable nonreciprocity is observed at a quite low frequency(e.g.,9 Hz),which is achieved by amplitude-dependent local resonance combined with interface reflection.Finally,a machine learning-based design optimization is introduced to evaluate and enhance the nonreciprocal effect of the QZS elastic diode.With the aid of machine learning(ML),the computational cost of predicting nonreciprocal effects during design optimization can be significantly reduced.Through design optimization,the nonreciprocal frequency bandwidth can be broadened while maintaining considerable isolation quality at low frequencies.

Optimization of Band Gap of 1D Elastic Metamaterial Under Impact Load by Regulating Stiffness

Designing materials that mitigate impacts effectively are crucial for protecting people and structures.Here,a single-resonator metamaterial with negative mass characteristics is proposed for impact mitigation,and numerical analysis of wave propagation shows explicitly how the spring stiffness and number of unit cells influence that mitigation.The results show clearly that a metamaterial with differing microstructural stiffness is better at mitigating the effect of a shock wave than one with a unique stiffness.Also,there is a critical number of unit cells beyond which the shock wave is not attenuated further,but the fabrication complexity increases.In the 40 groups of microstructural regions in this example,the attenuation effect no longer increases when there are more than 35 groups.This work offers guidance for microstructure designs in metamaterials and provides new ideas for using metamaterials to mitigate shock waves.

Active feedback control of sound radiation in elastic wave metamaterials immersed in water with fluid-solid coupling

Due to their potential properties unlike traditional materials and structures,elastic wave metamaterials have received significant interests in recent years.With the coupling between the acoustic and vibration,their mechanical characteristics can be tuned by the active feedback control system at low frequency ranges in which the traditional passive control is limited.This work illustrates that the superior performances of the effective mass density and sound pressure level(SPL)of an elastic wave metamaterial can be significantly changed by the active control,in which the periodic array of local resonators and orthogonal stiffeners are included.Significantly,based on the locally resonant mechanism,the negative density occurs over a frequency range.Due to the effects of lattice constant,structural damping and other parameters,the SPL with the function of fluid-solid coupling are illustrated and discussed.

Bandgap characteristics of the two-dimensional missing rib lattice structure

In this paper,the bandgap characteristics of a missing rib lattice structure composed of beam elements are investigated by using the Floquet-Bloch theorem.The tuning of the width and position of the bandgap is achieved by changing the local structural parameters,i.e.,the rotation angle,the short beam length,and the beam thickness.In order to expand the regulation of the bandgap,the influence of the material parameters of the crossed long beams inside the structure on the bandgap is analyzed.The results show that the mass density and stiffness of the structure have significant effects on the bandgap,while Poisson’s ratio has no effect on the bandgap.By analyzing the first ten bands of the reference unit cell,it can be found that the missing rib lattice structure generates multiple local resonance bandgaps for vibration reduction,and these bandgap widths are wider.The modal analysis reveals that the formation of the bandgap is due to the dipole resonance of the lattice structure,and this dipole resonance originates from the coupling of the bending deformation of the beam elements.In the band structure,the vibrational mode of the 9th band with a negative slope corresponds to a rotational resonance,which is different from that with the conventional negative slope formed by the coupling of two resonance modes.This study can provide a theoretical reference for the design of simple and lightweight elastic metamaterials,as well as for the regulation of bandgaps and the suppression of elastic waves.

A Novel Application of Multi-Resonant Dissipative Elastic Metahousing for Bearings

Bearing as an important machine element is widely used for industrial and automotive applications.At certain operational speed,bearings induce disturbing vibrations and noises that affect machine service life,productivity and passenger comfort in case of vehicle applications.Dissipative elastic metamaterials have caught considerable attention of scientific community due to their effective medium properties and peculiar dynamic characteristics including frequency bandgaps that can be effectively applied to attenuate and control undesirable vibration and noises.Although a substantial amount of theoretical work for effective medium characteristics and dynamic properties of acoustic/elastic metamaterials has been reported,the practical design and application of these composite structures for real-life engineering problems still remain unexplored.The present study intends to investigate a potential application of dissipative elastic metamaterials in controlling the bearing-generated vibration and noises over an ultrawide frequency range.The study is based on a simple analytical model together with rigorous finite element numerical simulations.It has been established that the dissipative characteristic of resonant system caused by larger material mismatch broadens the local resonance bandgaps beyond the bounding resonance frequency at the cost of wave transmission.In order to achieve broadband vibration and noise control,multi-resonant composite structures are embedded inside the bearing housing in five different layers.The reported results revealed the presence of broadband wave attenuation zone distributed from 3 to 52 kHz with consideration of material damping.The bearing-generated vibration and noises lying inside the wave attenuation zone will be mitigated.This feasibility study provides a new concept for the design and application of acoustic/elastic metamaterials in the bearing industry to improve machine service life and to enhance productivity and passenger comfort.

Sound Transmission Comparisons of Active Elastic Wave Metamaterial Immersed in External Mean Flow

Using the active feedback control system on the elastic wave metamaterial,this research concentrates on the sound transmission with the dynamic effective model.The metamaterial is subjected to an incident pressure and immersed in the external mean flow.The elastic wave metamaterial consists of double plates and the upper and lower four-link mechanisms are attached inside.The vertical resonator is attached by the active feedback control system and connected with two four-link mechanisms.Based on the dynamic equivalent method,the metamaterial is equivalent as a single-layer plate by the dynamic effective parameter.With the coupling between the fluid and structure,the expression of the sound transmission loss(STL)is derived.This research shows the influence of effective mass density on sound transmission properties,and the STL in both modes can be tuned by the acceleration and displacement feedback constants.In addition,the dynamic response and the STL are also changed obviously by different values of structural damping,incident angle(i.e.,the elevation and azimuth angles)and Mach number of the external fluid with the mean flow property.The results for sound transmission by two methods are compared,i.e.,the virtual work principle for double plates and the dynamic equivalent method corresponding to a single one.This paper is expected to be helpful for understanding the sound transmission properties of both pure single-and double-plate models.

A Design of Tunable Band Gaps in Anti-tetrachiral Structures Based on Shape Memory Alloy

Benefitted from the properties of band gaps,elastic metamaterials(EMs)have attracted extensive attention in vibration and noise reduction.However,the width and position of band gaps are fixed once the traditional structures are manufactured.It is difficult to adapt to complex and changeable service conditions.Therefore,research on intelligent tunable band gaps is of great importance and has become a hot issue in EMs.To achieve smart control of band gaps,a design of tunable band gaps in anti-tetrachiral structures based on shape memory alloy(SMA)is proposed in this paper.By governing the phase transition process of SMA,the geometric configuration and material properties of structures can be changed,resulting in tunable band gaps.Therein,the energy band structures and generation mechanism of tunable band gaps in different states are studied,realizing intelligent manipulation of elastic waves.In addition,the influence of different geometric parameters on band gaps is investigated,and the desired bandgap position can be customized,making bandgap control more flexible.In summary,the proposed SMA-based anti-tetrachiral metamaterial provides valuable reference for the application of SMA materials and the development of EMs.

Machine-learning-driven on-demand design of phononic beams

The development of phononic crystals, especially their interaction with topological insulators, allows exploration of the anomalous properties of acoustic/elastic waves for various applications. However, rapidly and inversely exploring the geometry of specific targets remains a major challenge. In this work, we show how machine learning can address this challenge by studying phononic crystal beams using two different inverse design schemes. We first develop the theory of phononic beams using the transfer matrix method. Then, we use the reinforcement learning algorithm to effectively and inversely design the structural parameters to maximize the bandgap width. Furthermore, we employ the tandem-architecture neural network to solve the training-difficulty problem caused by inconsistent data and complete the task of inverse structure design with the targeted topological properties. The two inverse-design schemes have different adaptabilities, and both are characterized by high efficiency and stability. This work provides deep insights into the combination of machine learning, topological property,and phononic crystals and offers a reliable platform for rapidly and inversely designing complex material and structure properties.