Bloch-Theory-Based Analysis of Damped Phononic Materials

2011 ◽  
Author(s):  
Michael J. Frazier ◽  
Mahmoud I. Hussein
Keyword(s):  
Band Structure ◽  
Wave Attenuation ◽  
Effective Properties ◽  
The Novel ◽  
Acoustic Metamaterials ◽  
Mass Model ◽  
Acoustic Metamaterial ◽  
Optical Branch ◽  
Lumped Parameter ◽  
Impact Vibration

In this paper, we combine Bloch theory with familiar techniques of structural dynamics to study the effects of energy dissipation (i.e., damping) in an acoustic metamaterial. The formulation we present has the novel feature of incorporating a temporal component to wave attenuation in addition to the standard spatial component. The frequency band structure reflects the metamaterial response to the damping intensity. In the context of a lumped parameter nested mass model, increasing the magnitude of damping is shown to cause the band structure to descend the frequency range and reveal an intriguing phenomenon: branch overtaking. This effect occurs as dissipation causes the optical branch to descend below the acoustical branch. The resulting decrease in the width of the band gap would impact vibration minimization and isolation. We also examine the effective properties of the metamaterial, specifically, the effective mass and effective stiffness, and the conditions for these quantities to become negative. Finally, the aforementioned material results are shown to be related to their finite counterpart. For ease of exposition, we consider a special form of Rayleigh damping in which the damping is proportional to the stiffness. The intrinsic presence of dissipation in acoustic metamaterials and the limited scientific literature addressing damped wave propagation in periodic media in general motivates our present study.

scholarly journals Reduced Linear Constrained Elastic and Viscoelastic Homogeneous Cosserat Media as Acoustic Metamaterials

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 521
Author(s):  
Elena F. Grekova ◽  
Alexey V. Porubov ◽  
Francesco dell’Isola
Keyword(s):  
Wave Attenuation ◽  
Pure Shear ◽  
Transversely Isotropic ◽  
Isotropic Case ◽  
Acoustic Metamaterials ◽  
Wave Localization ◽  
Acoustic Metamaterial ◽  
Dissipation Parameter ◽  
Material Behaviors ◽  
Mixed Wave

We consider the reduced constrained linear Cosserat continuum, a particular type of a Cosserat medium, for three different material behaviors or symmetries: the isotropic elastic case, a special type of elastic transversely isotropic case, and the isotropic viscoelastic case. Such continua, in which stresses do not work on rates of microrotation gradients, behave as acoustic metamaterials for the (pure) shear waves and also for one branch of the mixed wave in the considered anisotropic material case. In elastic media, those waves do not propagate for frequencies exceeding a certain threshold, whence these media exhibit a single negative acoustic metamaterial behavior in this range. In the isotropic viscoelastic case, dissipation destroys the bandgap and favors wave propagation. This curious effect is, probably, due to the fact that the bandgap is associated not with the dissipation, but with the wave localization which can be destroyed by the viscosity. The dispersion curve is now decreasing in some part of the former bandgap, above a certain frequency, whence the medium is a double negative acoustic metamaterial. We prove the existence of a boundary wavenumber in the viscoelastic case and estimate its value. Below the characteristic frequency corresponding to the boundary of the elastic bandgap, the wave attenuation (logarithmic decrement) is a growing function of the viscous dissipation parameter. Above this frequency, the attenuation decreases as the viscosity increases.

scholarly journals A Review of Tunable Acoustic Metamaterials

2018 ◽  
Vol 8 (9) ◽  
pp. 1480 ◽  
Author(s):  
Shuang Chen ◽  
Yuancheng Fan ◽  
Quanhong Fu ◽  
Hongjing Wu ◽  
Yabin Jin ◽  
...  
Keyword(s):  
Acoustic Wave ◽  
Acoustic Impedance ◽  
Acoustic Waves ◽  
Recent Progress ◽  
The Novel ◽  
Acoustic Metamaterials ◽  
Practical Application ◽  
Acoustic Metamaterial ◽  
Modulation Techniques ◽  
Narrow Frequency Band

Acoustic metamaterial science is an emerging field at the frontier of modern acoustics. It provides a prominent platform for acoustic wave control in subwavelength-sized metadevices or metasystems. However, most of the metamaterials can only work in a narrow frequency band once fabricated, which limits the practical application of acoustic metamaterials. This paper highlights some recent progress in tunable acoustic metamaterials based on various modulation techniques. Acoustic metamaterials have been designed to control the attenuation of acoustic waves, invisibility cloaking, and acoustic wavefront engineering, such as focusing via manipulating the acoustic impedance of metamaterials. The reviewed techniques are promising in extending the novel acoustics response into wider frequency bands, in that tunable acoustic metamaterials may be exploited for unusual applications compared to conventional acoustic devices.

scholarly journals Hybrid Bandgaps in Mass-coupled Bragg Atomic Chains: Generation and Switching

2021 ◽  
Vol 8 ◽  
Author(s):  
Shao-Feng Xu ◽  
Zhu-Long Xu ◽  
Kuo-Chih Chuang
Keyword(s):  
Structural Parameters ◽  
Dynamic Stiffness ◽  
Detailed Examination ◽  
Acoustic Metamaterials ◽  
Acoustic Metamaterial ◽  
Chain System ◽  
Different Types ◽  
Atomic Chains ◽  
Amplification System ◽  
Three Degree Of Freedom

In this work, without introducing mass-in-mass units or inertial amplification mechanisms, we show that two Bragg atomic chains can form an acoustic metamaterial that possesses different types of bandgaps other than Bragg ones, including local resonance and inertial amplification-like bandgaps. Specifically, by coupling masses of one monatomic chain to the same masses of a diatomic or triatomic chain, hybrid bandgaps can be generated and further be switched through the adjustment of the structural parameters. To provide a tuning guidance for the hybrid bandgaps, we derived an analytical transition parameter (p-value) for the mass-coupled monatomic/diatomic chain and analytical discriminants for the mass-coupled monatomic/triatomic chain. In our proposed mass-coupled monatomic/triatomic chain system, each set of analytical discriminants determines a hybrid bandgap state and a detailed examination reveals 14 different bandgap states. In addition to bandgap switching, the analytical p-value and discriminants can also be used as a guide for designing the coupled-chain acoustic metamaterials. The relations between the mass-coupled monatomic/triatomic chain system and a three-degree-of-freedom (DOF) inertial amplification system further indicate that the band structure of the former is equivalent to that of the latter through coupling masses by negative dynamic stiffness springs.

Adjustable sound insulation frequency band through the combination of membrane-type acoustic metamaterial array

2021 ◽  
Vol 263 (1) ◽  
pp. 5869-5877
Author(s):  
Xiang Wu ◽  
TengLong Jiang ◽  
JianWang Shao ◽  
GuoMing Deng ◽  
Chang Jin
Keyword(s):  
Thin Films ◽  
Frequency Band ◽  
Transmission Loss ◽  
Structural Parameters ◽  
Sound Insulation ◽  
Acoustic Metamaterials ◽  
Additional Mass ◽  
Acoustic Metamaterial ◽  
Material Parameters ◽  
Membrane Type

Membrane-type acoustic metamaterials are thin films or plates composed of periodic units with small additional mass. A large number of studies have shown that these metamaterials exhibit tunable anti-resonance, and their transmission loss values are much higher than the corresponding quality laws. At present, most researches on membrane-type acoustic metamaterials focus on the unit cell, and the sound insulation frequency band can only be adjusted by adjusting the structural parameters and material parameters. In this paper, two kinds of acoustic metamaterials with different structures are designed, which are the center placement of the mass and the eccentric placement of the mass.The two structures have different sound insulation characteristics. By designing different array combinations of acoustic metamaterials, the sound insulation peaks of different frequency bands are obtained. This paper studies the corresponding combination law, and effectively realizes the adjustable sound insulation frequency band.

scholarly journals Gradient index phononic crystals and metamaterials

Nanophotonics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 685-701 ◽  
Author(s):  
Yabin Jin ◽  
Bahram Djafari-Rouhani ◽  
Daniel Torrent
Keyword(s):  
Refractive Index ◽  
Wave Propagation ◽  
Acoustic Waves ◽  
Effective Properties ◽  
Periodic Structures ◽  
Phononic Crystals ◽  
Ray Theory ◽  
Acoustic Metamaterials ◽  
Propagation Of Waves ◽  
At Will

AbstractPhononic crystals and acoustic metamaterials are periodic structures whose effective properties can be tailored at will to achieve extreme control on wave propagation. Their refractive index is obtained from the homogenization of the infinite periodic system, but it is possible to locally change the properties of a finite crystal in such a way that it results in an effective gradient of the refractive index. In such case the propagation of waves can be accurately described by means of ray theory, and different refractive devices can be designed in the framework of wave propagation in inhomogeneous media. In this paper we review the different devices that have been studied for the control of both bulk and guided acoustic waves based on graded phononic crystals.

scholarly journals Hybrid acoustic metamaterial as super absorber for broadband low-frequency sound

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Yufan Tang ◽  
Shuwei Ren ◽  
Han Meng ◽  
Fengxian Xin ◽  
Lixi Huang ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Absorption Coefficient ◽  
Sound Absorption ◽  
Low Frequency ◽  
Functional Materials ◽  
Theoretical Method ◽  
Acoustic Metamaterials ◽  
Mechanical Stiffness ◽  
Acoustic Metamaterial ◽  
Frequency Sound

Abstract A hybrid acoustic metamaterial is proposed as a new class of sound absorber, which exhibits superior broadband low-frequency sound absorption as well as excellent mechanical stiffness/strength. Based on the honeycomb-corrugation hybrid core (H-C hybrid core), we introduce perforations on both top facesheet and corrugation, forming perforated honeycomb-corrugation hybrid (PHCH) to gain super broadband low-frequency sound absorption. Applying the theory of micro-perforated panel (MPP), we establish a theoretical method to calculate the sound absorption coefficient of this new kind of metamaterial. Perfect sound absorption is found at just a few hundreds hertz with two-octave 0.5 absorption bandwidth. To verify this model, a finite element model is developed to calculate the absorption coefficient and analyze the viscous-thermal energy dissipation. It is found that viscous energy dissipation at perforation regions dominates the total energy consumed. This new kind of acoustic metamaterials show promising engineering applications, which can serve as multiple functional materials with extraordinary low-frequency sound absorption, excellent stiffness/strength and impact energy absorption.

The band gap properties of the three-component semi-infinite plate-like LRPC by using PWE/FE method

2018 ◽  
Vol 32 (16) ◽  
pp. 1850173
Author(s):  
Denghui Qian ◽  
Jianchun Wang
Keyword(s):  
Finite Element ◽  
Band Structure ◽  
Band Gap ◽  
Phononic Crystal ◽  
Infinite Plate ◽  
Frequency Range ◽  
Fe Method ◽  
Mass Model ◽  
Rubber Layer ◽  
The Matrix

This paper applies coupled plane wave expansion and finite element (PWE/FE) method to calculate the band structure of the proposed three-component semi-infinite plate-like locally resonant phononic crystal (LRPC). In order to verify the accuracy of the result, the band structure calculated by PWE/FE method is compared to that calculated by the traditional finite element (FE) method, and the frequency range of the band gap in the band structure is compared to that of the attenuation in the transmission power spectrum. Numerical results and further analysis demonstrate that a band gap is opened by the coupling between the dominant vibrations of the rubber layer and the matrix modes. In addition, the influences of the geometry parameters on the band gap are studied and understood with the help of the simple “base-spring-mass” model, the influence of the viscidity of rubber layer on the band gap is also investigated.

Active Control of Wind-Induced Building Vibration Using a Linear Coupling Strategy

2001 ◽  
Author(s):  
S. Mohammad Hashemi ◽  
M. F. Golnaraghi
Keyword(s):  
Control System ◽  
Active Control ◽  
Lumped Parameter Model ◽  
Test Bed ◽  
Lumped Mass ◽  
Mass Model ◽  
Linear Coupling ◽  
Lumped Parameter ◽  
Coupling Strategy ◽  
Lumped Mass Model

Abstract The active control of building vibration is addressed. The aeroelastic lumped mass model of a building is designed to be used as the test bed for the active control system. The five story lumped parameter model was modeled as a cantilever beam exhibiting planar vibration. A Linear Coupling Control (LCC) strategy was implemented to eliminate the vibrations. An active (moving) mass damper (AMD) was first designed and experimentally implemented to control the first mode vibration of the system. An alternative pendulum control system was then designed and implemented. The proposed pendulum, having three times smaller mass than the AMD, was found to be more effective in reducing the building vibrations.

Determination of effective properties and effective thickness of resonant acoustic metamaterial

2006 ◽  
Vol 119 (5) ◽  
pp. 3388-3388
Author(s):  
Vladimir Fokin ◽  
Muralidhar Ambati ◽  
Cheng Sun ◽  
Xiang Zhang
Keyword(s):  
Effective Properties ◽  
Effective Thickness ◽  
Acoustic Metamaterial
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