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.

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 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 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.

Effective Dynamic Properties and Multi-Resonant Design of Acoustic Metamaterials

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
R. Zhu ◽  
G. L. Huang ◽  
G. K. Hu
Keyword(s):  
Dynamic Properties ◽  
Wave Dispersion ◽  
Wave Band ◽  
Energy Transfer Mechanism ◽  
Acoustic Metamaterials ◽  
Multiple Wave ◽  
Reflection And Transmission ◽  
Acoustic Metamaterial ◽  
Effective Dynamic ◽  
The Difference

In the study, a retrieval approach is extended to determine the effective dynamic properties of a finite multilayered acoustic metamaterial based on the theoretical reflection and transmission analysis. The accuracy of the method is verified through a comparison of wave dispersion curve predictions from the homogeneous effective medium and the exact solution. A multiresonant design is then suggested for the desirable multiple wave band gaps by using a finite acoustic metamaterial slab. Finally, the band gap behavior and kinetic energy transfer mechanism in a multilayered composite with a periodic microstructure are studied to demonstrate the difference between the Bragg scattering mechanism and the locally resonant mechanism.

Physical modeling and analysis of P-wave attenuation anisotropy in transversely isotropic media

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. D1-D7 ◽  
Author(s):  
Yaping Zhu ◽  
Ilya Tsvankin ◽  
Pawan Dewangan ◽  
Kasper van Wijk
Keyword(s):  
Attenuation Coefficient ◽  
Symmetry Axis ◽  
Wave Attenuation ◽  
Transversely Isotropic ◽  
P Wave ◽  
Velocity Variation ◽  
Ratio Method ◽  
Fracture Detection ◽  
Wide Range ◽  
Attenuation Anisotropy

Anisotropic attenuation can provide sensitive attributes for fracture detection and lithology discrimination. This paper analyzes measurements of the P-wave attenuation coefficient in a transversely isotropic sample made of phenolic material. Using the spectral-ratio method, we estimate the group (effective) attenuation coefficient of P-waves transmitted through the sample for a wide range of propagation angles (from [Formula: see text] to [Formula: see text]) with the symmetry axis. Correction for the difference between the group and phase angles and for the angular velocity variation help us to obtain the normalized phase attenuation coefficient [Formula: see text] governed by the Thomsen-style attenuation-anisotropy parameters [Formula: see text] and [Formula: see text]. Whereas the symmetry axis of the angle-dependent coefficient [Formula: see text] practically coincides with that of the velocity function, the magnitude of the attenuation anisotropy far exceeds that of the velocity anisotropy. The quality factor [Formula: see text] increases more than tenfold from the symmetry axis (slow direction) to the isotropy plane (fast direction). Inversion of the coefficient [Formula: see text] using the Christoffel equation yields large negative values of the parameters [Formula: see text] and [Formula: see text]. The robustness of our results critically depends on several factors, such as the availability of an accurate anisotropic velocity model and adequacy of the homogeneous concept of wave propagation, as well as the choice of the frequency band. The methodology discussed here can be extended to field measurements of anisotropic attenuation needed for AVO (amplitude-variation-with-offset) analysis, amplitude-preserving migration, and seismic fracture detection.

Study on dynamic effective parameters of bilayer perforated thin-plate acoustic metamaterials

2020 ◽  
pp. 2150048
Author(s):  
Yicai Xu ◽  
Jiu Hui Wu ◽  
Yongqing Cai
Keyword(s):  
Thin Plate ◽  
Thin Plates ◽  
Formation Mechanisms ◽  
Acoustic Metamaterials ◽  
Effective Parameters ◽  
Retrieval Method ◽  
Acoustic Metamaterial ◽  
Resonance Frequencies ◽  
Wave Normal ◽  
Mass Type

In this paper, dynamic effective parameters of mass-type and stiffness-type bilayer perforated thin-plate acoustic metamaterials (MBPM and SBPM) are investigated by simulations and experiments. Dynamic effective parameters are calculated by the retrieval method, and formation mechanisms of special effective parameters are analyzed by simulated fields. Divergent effective parameters are produced by anti-resonances of coupled perforations or coupled perforated thin-plates, zero effective parameters are produced by resonances of coupled perforated thin-plates. The impacts of perforation parameters on dynamic effective parameters for symmetric and asymmetric BPMs are systemically studied, the simulated and experimental results both show that variation trends of resonance and anti-resonance frequencies of mass-type bilayer perforated thin-plate acoustic metamaterial (MBPM) are different from stiffness-type bilayer perforated thin-plate acoustic metamaterial (SBPM), because perforations mainly change system mass in MBPM and system stiffness in SBPM, respectively. Dynamic effective parameters are bi-anisotropic in asymmetric BPM, and doubly negative effective parameters are achieved by coupled perforations when plan wave normal incident from the side with smaller perforation parameters. A modified retrieval method is proposed to calculate unified effective parameters for the asymmetric BPM, and the unified effective parameters equal to averaged effective parameters of two symmetric BPMs. This work systematically studies dynamic effective parameters of bilayer perforated structures, which has a great guiding significance in design of perforated acoustic devices.

Efficient wave-mode separation in vertical transversely isotropic media

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. C35-C47 ◽  
Author(s):  
Yang Zhou ◽  
Huazhong Wang
Keyword(s):  
Transversely Isotropic ◽  
Wave Mode ◽  
Phase Changes ◽  
Isotropic Case ◽  
Conservation Of Energy ◽  
Mode Separation ◽  
Isotropic Media ◽  
Curl Operators ◽  
Vti Media ◽  
Poynting Vectors

Wave-mode separation can be achieved by projecting elastic wavefields onto mutually orthogonal polarization directions. In isotropic media, because the P-wave’s polarization vectors are consistent with wave vectors, the isotropic separation operators are represented by divergence and curl operators, which are easy to realize. In anisotropic media, polarization vectors deviate from wave vectors based on local anisotropic strength and separation operators lose their simplicity. Conventionally, anisotropic wave-mode separation is implemented either by direct filtering in the wavenumber domain or nonstationary filtering in the space domain, which are computationally expensive. Moreover, in conventional anisotropic separation, correcting for amplitude and phase changes of waveforms by applying separation operators is also more difficult than in an isotropic case. We have developed new operators for efficient wave-mode separation in vertical transversely isotropic (VTI) media. Our separation operators are constructed by local rotation of wave vectors to directions where the quasi-P (qP) wave is polarized. The deviation angles between the wave vectors and the qP-wave’s polarization vectors are explicitly estimated using the Poynting vectors. Obtaining polarization directions by rotating wave vectors yields separation operators in VTI media with the same forms as divergence and curl operators, except that the spatial derivatives are now rotated to implement wavefield projections in accurate polarization directions. The main increase in computational cost relative to isotropic separation operators is the estimation of the Poynting vectors, which is relatively small within elastic-wave extrapolation. As a result, applying the proposed operators is efficient. In the meantime, the waveforms corrections for divergence and curl operators can be directly extended for our new operators due to the similarities between these operators. By numerical exercises, we have determined that wave modes can be well-separated with small numerical cost using the present separation operators. The conservation of energy in wave-mode separation by applying waveform corrections was also verified.

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