Negative Effective Mass Density Research Articles

A novel multi-resonator honeycomb metamaterial with enhanced impact mitigation

Local resonant metamaterials show significant promise in applications involving the attenuation of impact waves. This paper introduces a honeycomb metamaterial featuring a circular distribution of multiple mass-beam resonators designed to enhance impact mitigation by broadening low frequency bandgaps. The bandgaps of unit cells with different number of mass-beam resonators (MBR) are calculated. It is found that the unit cell with circularly distributed resonators (C-MBR) has strong low frequency local resonance in all directions, thus opening a complete wide bandgap in about 500–1200Hz. Then, a method of equivalent stiffness reduction related to the corresponding mode shapes is used to research the negative effective mass density characteristic, explaining the generation of the low frequency bandgaps. Subsequently, the impact protection capacity of local resonant metamaterial is compared with that of ordinary honeycomb metamaterial through experiment and simulation. Interestingly, the maximum acceleration values under the impact load of local resonant metamaterial are about 45% lower than that of honeycomb metamaterial, and the reaction force under the blast load is about 80% reduction. Besides, by analyzing the acceleration curve waveform and transmission spectrum, the local resonant metamaterial is found to exhibit continuous short period vibration, which blocks the wave in low frequency band. Finally, the energy dissipation performance of the local resonant metamaterial explains that it converts more impact energy into the kinetic energy of the core with resonators, thereby reducing the energy transferred to the bottom panel. These results underscore the potential application of the proposed metamaterial with multi-resonators in impact mitigation and energy dissipation.

Wave transmission through acoustic lossy barrier by using non-Hermitian complementary metamaterial

Complementary metamaterials (CMMs), characterized by negative effective mass density and moduli within a specific frequency range, hold the promise of significantly enhancing wave energy transmission across acoustic barriers. These materials operate by acoustically counteracting the barrier, thus offering an efficient conduit for wave propagation. However, when the intrinsic loss factor of the acoustic barrier is considered, the transmission performance of CMMs experiences a marked decrease. This decrement is notably severe, surpassing the theoretical expectations based solely on acoustic dissipation within the barrier. Delving into the depth of this issue, our research scrutinizes the far-reaching implications of the loss factor on wave transmission and takes a critical step forward by extending the effective properties of the complementary metamaterials from real to complex domain, an approach embodying the concept of non-Hermitian physics. Subsequently, we introduce a non-Hermitian CMM, a groundbreaking solution that maintains high transmittance despite the barrier's loss. It adeptly reconciles the impedance mismatch between the lossy barrier and the background medium, ultimately enabling perfect transmission.

Lightweight soundproofing meta-panel for two separate broadband noises

We propose a lightweight soundproofing meta-panel, with a multi-scale lattice structure sandwiched between thin membranes, effectively suppressing two separate broadband noises. By adjusting the geometrical parameters, the meta-panel is designed to induce negative effective mass density and negative effective bulk modulus for two distinct target frequency bands: 100–500 Hz and 1000–1500 Hz, thereby achieving high transmission loss that outperforms the mass density law. A meta-panel sample is fabricated via 3D printing technology and we evaluate its sound insulation performance by measuring transmission loss and insertion loss in an impedance tube and an anechoic chamber. Experimental measurements show that the meta-panel can exhibit excellent insulation performance while being significantly lighter in weight (about 5%) compared to a steel plate, and furthermore, it effectively suppresses low-frequency road noise and high-frequency motor noise from an actual electric car.

Estimating effective acoustic properties of various configuration of perforated panels

Acoustic metamaterial attains uncommon material properties over natural material such as negative effective mass density, negative effective bulk modulus, or both. To start with, the present research demonstrates and establishes robust method to estimate and measure acoustic metamaterial properties of a Helmholtz resonator analytically using transfer matrix (TM) method and experimentally in detail. The proposed method extracts the reflection and transmission coefficients from corresponding TM to evaluate the effective acoustic metamaterial properties. For a single Helmholtz resonator, the effective bulk modulus has been observed negative; however, the effective density remains positive. In order to attain double negative material properties, the perforated panel (PP) and microperforated panel (MPP) have been introduced in parallel to resonator. The 1D electro-acoustic modeling has been carried out for all configurations to estimate effective properties analytically. Successively, the experiments have been conducted to measure the effective properties from acoustic metamaterial prospective. The analytical and experimental investigations on five different cases reveal that one can attain negative effective compressibility and effective density by cascading two PPs or MPPs with a finite duct. Moreover, by backing a Helmholtz resonator from both sides with two PPs or MPPs in parallel, one can attain double negative properties comparatively higher than earlier configuration in low-frequency zone in broadband. In total, eight different configurations have been investigated analytically and experimentally, where it has been demonstrated that the proposed compact model is more effective than a finite array of same Helmholtz resonators.

Temperature effects on wave attenuation properties of metamaterials: Bandgap drift

The bandgap properties of phononic crystals and acoustic metamaterials have been investigated far and wide due to their potential application in vibration and noise reduction devices. The factors affecting the bandgaps including the material parameters and structural parameters were widely discussed, while there are few papers about the effect of temperature on the bandgap properties. In this paper, the influence of temperature on bandgap characteristics of metamaterial devices is studied theoretically and numerically. Since the elastic constants of some materials are affected by temperature, the bandgap drift phenomenon caused by temperature is displayed visually in the one-dimensional spring-mass system. Based on one-dimensional spring-mass metamaterials, the temperature-dependent theoretical formulations for calculating the dispersion relationships are derived and the effective mass equations related to temperature are also deduced to illustrate the negative effective mass density properties. Finally, the vibration attenuation properties and the directional transmission characteristics of two metastructures at different temperatures are performed to manipulate elastic wave field by temperature. This study could provide some insight into the use of acoustic metamaterials in extreme environments and provides a new approach for elastic wave field manipulation.

Nonlinear Ultrasonic Detection Enhanced by 3-D Printed Phononic Crystals

Nonlinear ultrasonic methods are a novel non-destructive testing and evaluation technology due to their high sensitivity to micro-defects. However, the inherent nonlinearity of ultrasonic equipment hinders the feature extraction with micro-defects information and limits the full-scale use of nonlinear ultrasonic NDT techniques. In this work, we propose a material-enabled filter using phononic crystals (PCs) as functional units to eliminate the unapplicable inherent nonlinearity component. The PCs composed of mass blocks and connective layers symmetrical about the host plate, are simultaneously processed by melting deposition of PLA. The finite element method with Bloch–Floquet boundary condition is implemented to obtain the bandgap at 100 kHz. Based on the mass-spring model, the mechanism of bandgap formation is proved to be attributed to the negative effective mass density band induced by the local resonance of mass block. The PCs successfully opens a propagation wave transmission gap and eliminates the inherent nonlinearity to improve the nonlinear detection of micro-defects in the aluminum plate. This work provides a useful methodology for the wide application of PC-based nonlinear detection methods in the non-destructive testing field.

Auxetics and Other Systems with Unusual Characteristics

Auxetics and Other Systems with Unusual Characteristics

Multiple Re‐Entrant Star‐Shaped Honeycomb with Double Negative Parameters and Bandgap Properties

Achieving bandgaps and double negative properties with single‐phase metamaterial in the low‐frequency range remains a challenge. Currently, acoustic metamaterials with double negative parameters are made of different materials, which can limit their application and design. Herein, a single‐phase multiple re‐entrant star‐shaped honeycomb (MRSSH) is designed and the double negative parameters and bandgaps are simulated. The numerical results show that the MRSSH exhibits three bandgaps and double negative characteristics (negative effective mass density and negative effective modulus) within a certain frequency range. The formation mechanics of bandgaps are investigated by analyzing the vibration modes. Moreover, the effects of geometry parameters such as internal concave angle and re‐entrant on the bandgaps and vibration modes of the MRSSH are investigated. By adjusting the geometry parameters, the dispersion curves and bandgap distribution can be tuned simultaneously. This study provides a new idea for designing a single‐phase lightweight metamaterial that can apply to noised reduction, vibration control, and super‐resolution imaging.

Topologically customized and surface-mounted meta-devices for Lamb wave manipulation

Lamb waves inside thin-walled structures have received extensive attention due to their great promise in applications such as structural health monitoring. Applications point at the common need for effective conditioning and manipulation of the wave propagation in terms of both frequency content and mode components. In this work, the concept of metamaterials is exploited to construct functional meta-devices (MDs). The MDs are designed to deliver prescribed functionalities after they are surface-mounted onto a structure conveying Lamb waves. To this end, a unified inverse-design scheme based on topology optimization is proposed and applied to achieve multifold functions such as frequency filtering, single-mode transmission and wave filtering at the subwavelength scale. Configuration features of the optimized MDs are extracted to reveal the mechanism governing the generation of broad Bragg scattering bandgaps. Analyses on negative effective mass density and the polarized mode explain the directional locally resonant bandgaps which exhibit strong anisotropic density. A representative MD with a finite number of unit cells is examined through finite element simulations. Temporal signals and their transmission spectra confirm the expected band features. An experiment is carried out to confirm the prescribed wave manipulation functions of the designed MD in terms of achieving selective frequency and wave mode transmission. This work provides a universal approach for topologically customizing MDs for the precise and tactic control of Lamb wave propagation.

Active multifunctional composite metamaterials with negative effective mass density and negative effective modulus

In this paper, a new composite metamaterial structure with negative effective mass density, negative effective modulus, and an ultralarge Poisson’s ratio is designed for vibration isolation, wave filtering, programmable construction of waveguides and negative refraction. This metamaterial can achieve vibration isolation in different frequency ranges using the shunting circuits. In two-dimensional metamaterial plate, a negative longitudinal modulus can be achieved by designing a model with an ultralarge Poisson’s ratio. This metamaterial can serve as wave filter when both shear and longitudinal waves are presented simultaneously. Wave propagation in the metamaterial can be controlled by switching of the shunting circuits. In this way, waveguides can be created programmatically. The phenomenon of negative refraction is also achieved in this metamaterial. Through control of the shunting circuits, this multifunctional metamaterial can be applied to vibration isolation, wave filtering, programmable waveguide construction, and negative refraction without changing its geometric structure.

Bandgap mechanism and vibration reduction property of wave-resistance sleeper with negative effective mass density

Based on the capability of controlling low-frequency elastic waves in solids with subwavelength size, locally resonant phononic crystals have potential applications in track vibration reduction. By periodically embedding 3D locally resonant unit cells (LRUCs) in a concrete matrix, a wave-resistance sleeper with a negative effective mass density is proposed, and the generation mechanism of the bandgap and parameter sensitivity are studied. Furthermore, the vibration mitigation performance of the wave-resistance sleeper applied to the ballastless track is analyzed. The results show that the local resonance of the LRUC results in negative responses in the wave-resistance sleeper to the vibration excitation, and a bandgap is generated in this frequency range. By changing the elastic modulus of the coating or the core density, the boundary frequencies of the bandgap of the wave-resistance sleeper can be effectively adjusted, and the bandwidth can be expanded by increasing the ratio of core radius to coating thickness, or by increasing the filling fraction, and adopting a thinner steel spherical shell. The bandgap of the wave-resistance sleeper was verified by test results. Based on the local resonance mechanism, the wave-resistance sleeper can effectively prohibit vibrations at multiple design frequencies from transmitting to the track bed.

Research on Design and Mechanism of Sound Insulating Structure Based on Acoustic Metamaterials

In view of the difficult problems of low-frequency noise reduction, based on the clamping boundary-type acoustic metamaterial theory with negative effective mass density, a structure combining membrane-type and clamping boundary-type is designed, which can realize good sound insulation performance in the low-frequency region, and the theoretical calculation and numerical simulation are in good agreement. At the same time, the transmission property of the structure at zero refractive index and impedance matching is studied. The research suggests that the structure has good low-frequency broadband sound insulation performance, and can achieve high transmission performance of sound waves through structural regulation.

Acoustic Metasurface-Aided Broadband Noise Reduction in Automobile Induced by Tire-Pavement Interaction

The primary noise sources of the vehicle are the engine, exhaust, aeroacoustic noise, and tire–pavement interaction. Noise generated by the first three factors can be reduced by replacing the combustion engine with an electric motor and optimizing aerodynamic design. Currently, a dominant noise within automobiles occurs from the tire–pavement interaction over a speed of 70–80 km/h. Most noise suppression efforts aim to use sound absorbers and cavity resonators to narrow the bandwidth of acoustic frequencies using foams. We demonstrate a technique utilizing acoustic metasurfaces (AMSes) with high reflective characteristics using relatively lightweight materials for noise reduction without any change in mechanical strength or weight of the tire. A simple technique is demonstrated that utilizes acoustic metalayers with high reflective characteristics using relatively lightweight materials for noise reduction without any change in mechanical strength or weight of the tire. The proposed design can significantly reduce the noise arising from tire–pavement interaction over a broadband of acoustic frequencies under 1000 Hz and over a wide range of vehicle speeds using a negative effective dynamic mass density approach. The experiment demonstrated that the sound transmission loss of AMSes is 2–5 dB larger than the acoustic foam near the cavity mode, at 200–300 Hz. The proposed approach can be extended to the generalized area of acoustic and vibration isolation.

Metastructures with double-spiral resonators for low-frequency flexural wave attenuation

This study introduces a novel framework for local resonant systems to low bandgap frequencies without greatly increasing spatial penalties in grid structures. The proposed double-spiral resonator (DSR) consists of a pair of spiral spring-like structures and a rigid plate acting as the “mass” of the oscillating system, which can serve as an effective mechanical filter. A rapid and accurate calculation based on the stiffness matrix method is proposed to precisely predict the fundamental resonant frequency of the resonator. Periodic installation of these resonators in a grid-like beam structure can lead to the formation of a new type of metastructure that possesses negative effective properties. Investigations on the bandgap characteristics of the proposed metastructure are conducted using the finite element method. It is found that a low-frequency resonant-type bandgap is present in such a structure. Changing the thickness of the central mass or the number of parasitic beam segments enables the manipulation of the bandgap location. The validity of the analytical results is evaluated via comparison with the finite element results and experimental measurements. By using multiple resonators with similar resonance frequencies, the attenuation bandwidth can be effectively broadened. The physics behind wave attenuation can be realized by introducing a negative effective mass density. The results demonstrate that the proposed structure exhibiting unique dynamic characteristics can successfully attenuate undesired structural vibrations at low frequencies. It may be concluded that this DSR can be used as an alternative to current vibration filtering systems.

Design of cylindrical honeycomb sandwich meta-structures for vibration suppression

In this study, a lightweight cylindrical honeycomb sandwich structure with low-frequency vibration attenuation ability is designed. An analytical model based on Love shell theory is established to investigate the dispersion relations of an orthotropic cylindrical shell with local resonators. The low-frequency band gaps and the presence of negative effective mass density are confirmed analytically. Subsequently, the influences of curvature and orthotropy on wave propagation behavior are discussed and the prediction formula for band gaps is defined for engineering design. To verify the feasibility of the design method, a real cylindrical honeycomb sandwich meta-structure is first designed and fabricated by introducing local resonators into a square honeycomb structure. The forced vibration response of the proposed cylindrical meta-structure is studied using both numerical simulations and experimental validation. Furthermore, a cylindrical meta-structure with a plate inside is studied numerically and experimentally, which confirms its excellent vibration suppression performance in actual applications. This study is of great significance in promoting the application of local resonance meta-structures in engineering field.

Negative Effective Mass in Plasmonic Systems.

We report the negative effective mass (density) metamaterials based on the electro-mechanical coupling exploiting plasma oscillations of a free electron gas. The negative mass appears as a result of the vibration of a metallic particle with a frequency of ω, which is close the frequency of the plasma oscillations of the electron gas relative to the ionic lattice . The plasma oscillations are represented with the elastic spring , where is the plasma frequency. Thus, the metallic particle vibrated with the external frequency ω is described by the effective mass , which is negative when the frequency approaches from above. The idea is exemplified with two conducting metals, namely Au and Li.

The influence of design parameters of engineered aggregate in metaconcrete on bandgap region

Metaconcrete is a new type of concrete made of partially replaced locally resonant engineered aggregates for providing enhanced blast and impact resistance. The engineered aggregate consists of solid core coated with a relatively soft material to activate the resonant behaviours of inclusion at the desired frequencies. The resonant aggregates could trigger the negative effective mass density (NEMD) of the system interacting with the applied dynamic loadings thus attenuate stress wave propagation. This unique attenuation behavior occurs only if the designed resonant frequency of engineered aggregates ( f0) is within the frequency spectrum of the applied loading. To help design metaconcrete with the desirable attenuation range for structure protection against blast loads, the frequency ranges of different blast scenarios with the scaled distance ranging from 1 m/kg1/3 to 10 m/kg1/3 are numerically investigated, the interested frequency range is found up to 50 kHz. In this study, the tunable properties of metaconcrete containing various aggregate configurations are numerically investigated by using finite element software COMSOL Multiphysics. The numerical model is calibrated first by using the results from a previous study on three-dimensional locally resonant metamaterial. With the calibrated numerical model, the frequency ranges of the NEMD of metaconcrete containing engineered aggregates in four geometric shapes are analysed. The effect of the parameters such as the aggregate shape, size, volume fraction, and material properties on the region of the NEMD are investigated. The sensitivity of the factors influencing the region of the NEMD is evaluated and discussed. The results can be used for designing engineered aggregates for better structural protections.

Thermal tuning of negative effective mass density in a two-dimensional acoustic metamaterial with hexagonal lattice

The unique characteristics like periodic and locally resonant behaviors of acoustic metamaterials result in an anomalous response to the wave propagation and exhibit complete elastic wave bandgaps. However, these unusual properties arise from the geometry of the artificially designed metastructure and can be significantly affected under the exposure of the thermal environment. In this paper, we present a thermally tunable two-dimensional acoustic metamaterial with a hexagonal lattice. The numerical results demonstrated that by adjusting the externally applied temperature to the structure and imposing several different load conditions like thermal deformation and thermal stress, a tunable effective mass density of the metamaterial could be obtained. The proposed concept further extends the ongoing research in the field of tunable acoustic metamaterials.

Editorial: Multiscale Lattices and Composite Materials: Optimal Design, Modeling and Characterization

The Research Topic “Multiscale lattices and composite materials:” (MLCM) is focused on the optimal design, modeling, and characterization of novel lattices, composite materials, and structures at different scales, through the control of the internal architecture of the system. A fundamental goal of this article collection is the study of mechanical metamaterials that are able to form next-generation-generation cellular solids; lattice materials, multiscale composites; and structural-scale systems. The collection took inspiration from the peculiar behaviors exhibited by structured materials at multiple scales (Bosia et al., 2018). The latter include, for example, high stiffness, strength, and toughness at extremely low densities (Meza et al., 2014), phononic band-gaps (Lu et al., 2009), sound control ability (Cummer et al., 2016); negative effective mass density (Liu et al., 2000); localized confined waves (Theocharis et al., 2013), to name but a few examples. The research reported devoted special attention to the creation of complex mechanical systems with properties derived mainly from their geometric design rather than their chemical composition (Cummer et al., 2016; Bertoldi et al., 2017). Also investigated was the use of multiscale lattices to optimally design reinforcing elements for novel composite materials (Fleck et al., 2010; Li et al., 2014). The chosen modeling and experimental approaches were able to predict and characterize the intrinsically complex mechanical behavior of the analyzed systems through multiscale techniques.

Demonstration of effective acoustic properties of different configurations of Helmholtz resonators

Acoustic metamaterial attains uncommon material properties over natural material such as negative effective mass density or negative effective bulk modulus or both. The effective bulk modulus of a classical acoustic reactive filter such as Helmholtz resonator has been observed negative, using lumped element model, at resonance point, which desires further investigations. Present research demonstrates and establishes robust method to estimate and measure acoustic metamaterial properties of a Helmholtz resonator analytically, numerically and experimentally in detail. The proposed numerical technique simulates ASTM-2611 standard of measurement to extract corresponding reflection and transmission coefficients to evaluate the effective acoustic metamaterial properties. The subsequent investigations have been carried out by taking eight different configurations of Helmholtz resonators such as parallel and series using similar and dissimilar resonators. Performance of each configuration has been investigated analytically, numerically and validated experimentally. At last, a finite array of Helmholtz resonators has been investigated. From investigations, it has been observed that five configurations of Helmholtz resonators and finite array have negative effective mass density and effective bulk modulus. Summarizing, the present research endeavors analytical, numerical and experimental investigations of different configurations of Helmholtz resonators in detail, which is first in its own kind.