Three-Dimensional Trampolinelike Behavior in an Ultralight Elastic Metamaterial

Elastic and acoustic metamaterials are man-made structures designed to control and manipulate waves through band gaps. The generalized bandwidth of metamaterials with locally resonant (LR) band gaps is usually narrow, limiting their applications in noise and vibration control. On the other hand, nonlinear metamaterials with dipolar resonances can present a broad chaotic band with low amplitude resonances due to bridging coupling, which is only observed under sufficiently large excitation amplitudes. In this work, we show that bridging-coupling phenomenon can also be observed in linear metamaterials with dipolar resonance, producing a special pass band with low amplitude resonances at low frequencies without excitation amplitude dependence. Such phenomenon emerges in a modified resonant metachain with zigzag interconnections and is based on the isomerism of traditional metamaterials. Although this modified isomer preserves the static stiffness and mass density (i.e., static performance) of the original metamaterial, its dispersive behavior presents interesting properties (i.e., branches with negative mass features and overlapping of opposite group velocity), resulting in an overall negative effective mass between the LR band gaps that is responsible for the remote interaction and the enhanced wave performance. In addition to the theoretical discussions, the bridging coupling is experimentally observed in a three-dimensional printed elastic metamaterial rod supporting longitudinal waves. The design can be extended to elastic bending, acoustic and electromechanical media, as well as to systems with periodicity in two and three dimensions (i.e., plates and solids). Therefore, the findings of this work open avenues to investigate the bridging-coupling phenomenon in linear systems as well as to explore the properties of metamaterial isomers.

In this paper, inerter-based dynamic vibration absorbers (IDVAs) are applied in elastic metamaterials to broaden low-frequency band gaps. A discrete mass-spring lattice system and a distributed metamaterial beam carrying a periodic array of IDVAs are, respectively, considered. The IDVA consists of a spring and an inerter connected to a traditional mass-spring resonator. Compared to the traditional resonators, the special designed IDVAs generate two local-resonance (LR) band gaps for the discrete lattice system, a narrow low-frequency band gap and a wider high-frequency one. For the distributed IDVA-based metamaterial beam, in addition to the generated two separated LR band gaps, the Bragg band gap can also be significantly broadened and the three band gaps are very close to each other. Being able to amplify inertia, the IDVAs can be relatively light even operated for opening up low-frequency band gaps. When further introducing a dissipative damping mechanism into the IDVA-based metamaterials, the two close-split LR band gaps in the lattice system are merged into one wide band gap. As for the metamaterial beam with the dissipative IDVAs, an even wider band gap can be acquired due to the overlap of the adjacent LR and Bragg-scattering band gaps.

A novel lever-type elastic metamaterial model for low-frequency wave attenuation

This paper presents the modeling technique, design method, a new working mechanism and influence factors for elastic metamaterials (EMs) with parallel multi-resonators for broadband elastic vibration suppression. The general formula of the effective mass is deduced, and the effects of the relevant structural parameters on the frequency regions of the negative effective mass are illustrated in details. Subsequently, the dispersion relation and transmission spectrum of the EMs are studied. Based on the theoretical approach, the EMs plates were proposed, and the formation mechanism of the band gaps are analyzed by studying the displacement field of the eigenmodes at the band gaps edges. The related results well confirm that the novel EMs induces multi-frequency negative effective mass, and the number of the regions is equal to the number of the local resonators. The start frequencies of the band gaps are decided by the natural frequencies of each resonator, and the width of frequency band with negative effective mass can be broadened by enlarging the mass ratio of the local resonator. The EMs plate with the thickness of only 2.5 mm designed on the basis of theoretical research exhibits two flexural vibration band gaps (FVBGs) with the total width of 78.4 Hz below 200 Hz, which has been verified by the transmission testing experiments. For the formation mechanism of the FVBGs, the vibration is localized in the according resonator at the lower edge of each band gap, while at the upper edges the local resonance mass and the base plate vibrate in a reverse phase. Based on the theoretical and numerical analyses, the EMs with multiple parallel local resonators would be used in various fields, such as noise and vibration isolation, filters, and other renewed devices.

Low-frequency band gaps in quasi-zero stiffness locally resonant metamaterial shaft

Elastic metamaterials utilize locally resonant mechanical elements to onset band gap characteristics that are typically exploited in vibration suppression and isolation applications. The present work employs a comprehensive structural intensity analysis (SIA) to depict the structural power distribution and variations associated with band gap frequency ranges, as well as outside them along both dimensions of a two-dimensional (2D) metamaterial. Following a brief theoretical dispersion analysis, the actual mechanics of a finite metamaterial plate undergoing flexural loading and consisting of a square array of 100 cells is examined experimentally using a fabricated prototype. Scanning laser Doppler vibrometer (SLDV) tests are carried out to experimentally measure the deformations of the metamaterial in response to base excitations within a broad frequency range. In addition to confirming the attenuation and blocked propagation of elastic waves throughout the elastic medium via graphical visualizations of power flow maps, the SIA reveals interesting observations, which give additional insights into energy flow and transmission in elastic metamaterials as a result of the local resonance effects. A drastic reduction in power flow magnitudes to the bulk regions of the plate within a band gap is noticeably met with a large amplification of structural intensity around and in the neighborhood of the excitation source as a compensatory effect. Finally, the theoretical and experimentally measured streamlines of power flow are presented as an alternative tool to predict the structural power patterns and track vortices as well as confined regions of energy concentrations.

Photonic band structure and omnidirectional band gap in anisotropic superlattice

In order to achieve the attenuation of low‐frequency sound, in this paper, a hybrid metamaterial structure with a complete band gap below 500 Hz is proposed, which is subjected to second‐order fractal, series fusion, and whether the structure is framed or not to form 8 different structures. Based on the finite element method and Bloch's theorem, the bandgap and transport properties of all model structures are evaluated, and the bandgap and propagation properties of metamaterial structures with different fractal levels are elucidated in terms of band structure and group velocity. In addition, the third‐order fractal structure and the dependence of the band gap on the material are also studied. The results show that the structure has a superior band gap width, and the complete band gap of its tandem fusion structure accounts for up to 45.502% in the range of 500 Hz, and the second‐order fractal has a complete band gap of 45.588% in the range of 1000 Hz. Compared with other structures, it can produce lower and better band gap. The research in this paper provides a new strategy for realizing acoustic metamaterial structures with low frequency band gaps.

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.

Presented in this paper are study results of dispersion relationships of periodic structures composited of concrete and rubber, from which the frequency band gap can be found. Two models with fixed or free boundary conditions are proposed to approximate the bound frequencies of the first band gap. Studies are conducted to investigate the low-frequency and directional frequency band gaps for their application to engineering. The study finds that civil engineering structures can be designed to block harmful waves, such as earthquake disturbance.

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.

Over the past two decades, an extensive research effort has been devoted to elastic metamaterials, structured artificial materials at subwavelength scales, for elastic wave manipulations in solids. Due to the extreme values of material parameters, negative and/or positive, they achieved, the applications can range from wave and/or vibration attenuations, wave guiding and imaging, enhanced sensing, to invisible cloaking. However, conventional passive metamaterials have limitations, i.e. they can only be operated in narrow frequency regions and their functions are usually locked into space or with minor tunabilities once fabricated, lacking real time reconfigurabilities. Those limitations strongly hinder them from practical usages. With the rapid development of smart materials and structures, more and more intelligent elements are being introduced into wave propagation, vibration and sound control systems. The piezoelectric shunting technique is one well known method that receives considerable attention. In this dissertation, by leveraging the circuit control concept, both analog and digital, we propose some circuit controlled active/adaptive/hybrid/programmable metamaterials and metasurfaces for unprecedent elastic wave manipulations. Analytical, numerically and experimentally approaches are combined throughout the dissertation to illustrate design concepts, characterize wave propagation properties, and valid the designs. Specifically, active elastic metamaterials with tunable stiffness in local resonators are first designed for tunable wave and/or vibration mitigations. We then extend this concept to achieve super broadband wave attenuations with frequency-dependent stiffness elements. By introducing the variable stiffness elements to the host medium, a hybrid metamaterial is developed for switched ON/OFF wave propagations and broadband negative refractions. Based on a developed approximate transformation method, an active metamaterial is designed and placed on a plate to achieve spatially varying effective mass densities for broadband elastic trajectory control. Finally, a programmable metasurface with ultrathin-thickness is demonstrated for broadband, real-time and multifunctional wavefront manipulations in a plate. The active, adaptive, hybrid, and programmable elastic metamaterials and/or metasurfaces are still in their infant stages. The examples presented in the dissertation are transformable to different length and time scales and could serve as efficient and powerful tools in exploring some unconventional wave phenomenon in solid structures, i.e. by using concepts in quantum mechanics, where passive approaches are significantly limited. The designs could also immediately open new possibilities in elastic wave control devices including, but not limited to structural health monitoring, stealth technology, active noise control, as well as medical instrumentation and imaging.

Acoustic metamaterials have received much attention recently. In the past decades, countless structures have been studied for their novel physical phenomenon or potential applications. The goals of many of the works were to explore ways to enlarge the band gap, lower the band gap frequency, and/or generate greater attenuation of vibration. However, most of the work was limited to simulation, with experimental studies rarer. In this work, we would like to experimentally present the transmission spectrum of an acoustic metamaterial with a proposed structure called the coated double hybrid lattice (CDHL) [1]. The CDHL has both crystalline structure and local resonators, which provide high-frequency and low-frequency band gaps, respectively. A structure was fabricated and tested to experimentally determine the transmission spectrum. Both, a higher frequency band gap and a lower frequency band gap, were obtained. Vibration is clearly attenuated in the frequency range of 70–90 kHz. This is due to the Bragg scattering effect. At the same time, around the frequency of 4.8kHz, another band gap is observed which is attributed to local resonance. It turns out that our experimental results coincide with our previous simulation quite well.

In recent years, elastic metamaterials have become extremely fascinating to many researchers due to the bandgap characteristics. This study develops, a basic elastic metamaterial-based vibration isolation gasket that is capable of isolating low-frequency elastic waves. The elastic metamaterial based on local resonance has been numerically and experimentally investigated and discussed. The result shows that a wide low-frequency bandgap from 430 Hz to 1490 Hz appears for elastic waves. Although the elastic metamaterial is only made up of three unit cells, modeling and experimental findings demonstrate a significant attenuation impact. This work not only provides a new option to design elastic metamaterial for controlling elastic waves, but also provides a new design idea for vibration isolation gasket.

Bandgap properties of one-dimensional superconducting photonic crystals containing metamaterials are investigated by the transfer matrix method. It is shown that the low-frequency band gap can also be present in this superconducting photonic crystal similar to the usual superconducting photonic crystal containing dielectric materials. The low-frequency band gap can be widened considerably when the suitable structure parameters are chosen. However, in certain structural parameters, the low-frequency band gap can not be found in this superconducting photonic crystal just as in one-dimensional dielectric-dielectric photonic crystal. The polarization properties and the influences of the operating temperature and the structure parameters of superconducting photonic crystals on the photonic band gap are also investigated in this paper.