Elastic Wave Metamaterials Research Articles

Arrest behavior of local resonators connected by nonlocal interaction in elastic wave metamaterials with machine learning prediction

Arrest behavior of local resonators connected by nonlocal interaction in elastic wave metamaterials with machine learning prediction

Nonlinear soliton spiral induces coupled multimode dynamics in multi-stable dissipative metamaterials

With the robust and self-trapped properties, recent advances about soliton dynamics in multi-stable mechanical metamaterials have led to many innovative techniques from signal processing to robotics. This work proposes a multi-stable mechanical metamaterial driven by nonlinear dissipative solitons, in which the coupling and decoupling of multiple locomotion modes can be achieved. Based on a cylinder network with asymmetric energy landscape, the uniform field model of Landau theory is developed. During the theoretical calculation, the analytical solutions of several dissipative solitons are derived, which allow multiple special behaviors of solitary waves, such as wave velocity gaps, directional propagation and spiral phase transition. By incorporating such effects into robotic designs, a variety of complex movements can be achieved by a single structure, including hopping, rolling, rotating, swinging, bending and translational components. In particular, as excitation positions change, the mechanical metamaterial can flexibly switch multiple locomotion modes without changing configurations, e.g., spinning and spin-less, straight and oblique as well as coupled multimode movements. This work wishes to provide some new inspirations for the applications of nonlinear elastic wave metamaterials and phase transition theory in robotics.

Negative Refraction of Mixing Waves in Nonlinear Elastic Wave Metamaterials

Negative Refraction of Mixing Waves in Nonlinear Elastic Wave Metamaterials

Dual-band topological states in actively convertible metamaterials with parallel platforms

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.

Active control on topological interface states of elastic wave metamaterials with double coupled chains.

Topological elastic wave metamaterials have shown significant advantages in manipulating wave propagation and realizing localized modes. However, topological properties of most mechanical metamaterials are difficult to change because of structural limitations. This work proposes the elastic wave metamaterials with double coupled chains and active control, in which band inversion and topological interface modes can be achieved by flexibly tuning negative capacitance circuits. Finite element simulations and experiments are performed to demonstrate the topological interface modes, which show good agreements with the theoretical results. This research seeks to provide effective strategies for the design and application of topological elastic wave metamaterials.

Orthotropic metamaterials with freely tailorable elastic constants

To control mechanical waves and structural vibrations, an important method is to design metamaterials with tailored elastic constants, but it is very difficult. In this paper, a simple and universal metamaterial design method is proposed. This orthotropic metamaterial is composed of elements arrayed periodically in space. The element includes two cuboid structures. The first structure is the basic structure of the element, and the second structure is the transformation of the first structure of the element. The first structure of the element is a cuboid structure composed of 24 bars connected by 8 nodes, and the second structure of the element is a cuboid structure composed of 36 bars connected by 14 nodes. This metamaterial has six independent elastic constants, so there is a large degree of freedom in the material design. Therefore, it has great application value in the fields of mechanical metamaterials, elastic wave metamaterials, acoustic metamaterials, and seismic metamaterials, and has also laid the foundation for realizing the dream of controlling mechanical waves and structural vibrations.

Characteristics of band gaps of a metamaterial plate with membrane-type resonators based on the energy approach

Local resonance metamaterials have garnered substantial interest in recent years due to their potential to effectively control low-frequency noise and vibration. This study proposes a new metamaterial plate with double mass membrane-type resonators (DMMRs). Combining polynomial fitting and virtual spring method, the natural characteristics of the resonator and the dispersion surfaces of the metamaterial plate are obtained. Results show the proposed metamaterial plate exhibits multiple band gaps, resulting from the cancellation of shear forces in the plate by the reaction forces generated by the first two resonances of the resonators. Parametric analysis is performed to obtain the variation patterns of the band gaps, where approximate models of the resonator are adopted to explain the effects of the parameters. It is found that the occurrence and width of the two band gaps are closely related to the mass ratio between the masses on the resonator and the substrate plate. Furthermore, finite element analysis is conducted to verify the effectiveness of the theoretical derivation, as well as the suppression effect of the metamaterial plate. The findings demonstrate the advantages of the metamaterial plate in vibration control and band gap tuning. The study provides guidance for the design and analysis of elastic wave metamaterials.

Nonlocal interactions on dynamic growth of an inclusion in locally resonant elastic wave metamaterials

Nonlocal interactions on dynamic growth of an inclusion in locally resonant elastic wave metamaterials

Nonlocal topological states in elastic wave metamaterials with active feedback control

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.

Diode behaviors of curved elastic wave metamaterials with a nonlinear granular chain

Diode behaviors of curved elastic wave metamaterials with a nonlinear granular chain

Second-order topological corner states in two-dimensional elastic wave metamaterials with nonsymmorphic symmetries

This paper investigates the higher-order topological behavior of elastic wave metamaterials composed of L-shaped pillars attached to a plate. In this system, the multi-dimensional topological transitions can be developed for physical transfer among the corner, edge, and bulk elastic wave modes by tuning the rotation angle of the L-shaped pillars. Different from the four degenerate corner states in the symmorphic system, these corner states in this metamaterial evolve into two doublets because of the lack of mirror symmetries. With the energy highly trapped at the corners, it thus can immediately realize elastic resonators/sensors with high-quality factors. Besides, the coupling effect between corner and edge states is analyzed in the multi-dimensional topological system. The edge–corner coupling effect could be applied to relevant fields, such as high-sensitive detection, elastic energy harvesting, and optomechanical sensing.

Sound transmission of active elastic wave metamaterial with double locally resonant substructures surrounded by external mean flow

The elastic wave metamaterial with active feedback control is presented to discuss its dynamic effective parameter and sound transmission properties. Both studies are initiated from the local resonance with the active feedback control and dynamic structural response. The acoustic-structure coupling of the metamaterial with resonators and orthogonal stiffeners are analyzed with effects of the external mean flow. Different analytical methods are used to derive the effective mass density and sound transmission loss (STL) of the elastic wave metamaterial. The effective density is obtained by the dynamic effective medium method firstly. And the second one applies the spatial harmonic expansion method with the principle of virtual work for the STL based on the Bloch–Floquet theorem and Poisson summations. The effective mass density shows frequency-dependent properties and appears positive and negative values in a certain frequency region simultaneously. This research also illustrates both characteristics can be tuned by the active feedback control with the acceleration and displacement feedback control actions. Numerical results of coupled structures show that the changes of transmission characteristics in the certain frequency region are consistent with the effective mass density properties of uncoupled unit cell structure. In addition, influences of the lattice constants, incident angles and Mach number on the STL are illustrated and discussed.

Nonreciprocal Transmission of Non-collinear Mixing Wave in Nonlinear Elastic Wave Metamaterial

Nonreciprocal Transmission of Non-collinear Mixing Wave in Nonlinear Elastic Wave Metamaterial

A review of elastic plate wave metamaterials

超材料指具有超越天然材料性能的人工材料，因其独特的物理性质及广泛的应用领域受到人们的关注。固体中的弹性波被广泛应用于无损检测、无线通讯、无源传感等领域，具有重要的应用价值。不同于流体声波，固体中的弹性波由于存在纵波与横波的耦合及模式转换，更难进行精确操纵，这就给超材料的应用提供了很好的舞台。本文以弹性波中极具代表性的板波作为焦点，较为系统地回顾了板波超材料的发展历史、主要研究进展及其在未来信息功能器件发展方向的潜力。

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

In this work, the three-dimensional (3D) 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 quasi-longitudinal (qP) and quasi-shear (qS1 and qS2) 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 vibration isolators by using the Bragg scattering and local resonance band gaps in a layered honeycomb meta-structure

In this study, a vibration isolator is designed using the Bragg scattering and local resonance band gaps in a layered honeycomb meta-structure. Various studies have been conducted on the noise and vibration problems of engineering structures by utilizing the band gaps in phononic crystal meta-materials. However, no study on the application of phononic crystal meta-materials to the design of vibration isolators has been published due to the large lattice constant and narrow band gap. To overcome the difficulties of realization in vibration isolators, a layered honeycomb meta-structure is proposed in this study. The proposed meta-structure consists of a layered square honeycomb structure and a local resonator placed inside the honeycomb core. A transfer matrix model based on the effective mass is developed to comprehend the mechanism of band gap formation. Furthermore, a strategy for designing an ultra-wide low-frequency coupled band gap is established analytically. Then, a four-layer honeycomb meta-structure is designed and fabricated based on the proposed design strategy. Experimental results demonstrate the successful realization of an ultra-wide coupled band gap with the introduction of the resonators with meticulously selected parameters. Finally, the designed meta-structure is applied to a vibration isolator, and the vibration isolation performance is verified experimentally. This work has broad engineering application prospects and is of high significance for promoting the implementation of elastic wave meta-materials in the engineering field.

Discrete scattering and meta-arrest of locally resonant elastic wave metamaterials with a semi-infinite crack

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.

Transient Invisibility and Cloak of Impact Elastic Wave in Piezoelectric/Piezomagnetic Metamaterials

Based on the scattering cancellation technique, a piezoelectric cloaking is designed, which can make the piezomagnetic cylinder invisible to transient elastic waves. Following the Laplace transform, the piezoelectric cloaking mechanism is presented and dynamic stress concentration factor (DSCF) is derived by the plane wave expansion method. The numerical method of the inverse Laplace transformation is used to show the cloaking behavior that besides the invisible phenomenon, the DSCF is also reduced by the cloak. The piezoelectric parameter plays a positive role on enhancing the object invisibility and improving the stress distribution. These results can offer the fundamental design and application of elastic wave metamaterials.

PIEZOELECTRIC METAMATERIALS AND WAVE CONTROL: STATUS QUO AND PROSPECTS

Elastic wave metamaterial is a kind of artificially designed periodic structure. It has received extensive attention due to its special mechanical properties and has shown valuable and unique application prospects in both military and civilian fields. Actively or passively controlling the characteristics of elastic wave metamaterials according to the needs can endow them with stronger applicability. There are lots of tuning ways, among which using piezoelectric materials is a convenient, fast, high-precision, small-sized and low-cost method. In this article, we first briefly introduced the basic aspects of elastic wave metamaterials, tunable metamaterials, piezoelectric materials and several commonly used shunt circuits. Then, according to the different application forms of piezoelectric materials in elastic wave metamaterials, they are divided into two categories: in the first category, the piezoelectric material constitutes the major structure or acts as a part of the major structure; in the second category, the piezoelectric material is used in the form of a spring or a patch attached to the surface of the major structure or embedded in the structure, acting as an actuator or/and a sensor. We elaborated on the research topics and the development history of the two categories of piezoelectric elastic wave metamaterials, related to band gap regulation, waveguide, negative refraction, super transmission, topological state, cloak as well as shunt circuits. Finally, we summarized the research deficiencies of piezoelectric elastic wave metamaterials and outlined corresponding future research prospects.

Electro-mechanical coupling diode of elastic wave in nonlinear piezoelectric metamaterials.

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.