Applicability of Dynamic Homogenization for Acoustic Metamaterials

2014 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Negative Refraction ◽  
Effective Properties ◽  
Dynamic Properties ◽  
Low Frequency ◽  
Bloch Wave ◽  
Acoustic Metamaterials ◽  
Infinite Domain ◽  
True Negative ◽  
Periodic Composite ◽  
Frequency Regime

Dynamic homogenization seeks to define frequency dependent effective properties for heterogeneous composites for the purpose of studying wave propagation in them. These properties can be used to predict and design for metamaterial behavior. However, there is an approximation involved in replacing a heterogeneous composite with its homogenized equivalent. In this paper we propose a quantification to this approximation. By way of explicit examples we show that a comprehensive homogenization scheme proposed in earlier papers is applicable in a finite composite setting and in the low frequency regime. We also show that there exist good arguments for considering the second branch of a locally resonant composite a true negative branch. Furthermore, we note that infinite-domain homogenization is more applicable to finite cases of locally resonant metamaterial composites than it is to 2-phase composites. We also study the effect of the interface location on the applicability of homogenization. The results open intriguing questions regarding the effects of replacing a semi-infinite periodic composite with its Bloch-wave (infinite domain) dynamic properties on such phenomenon as negative refraction.

Effective Dynamic Properties of Microstructured Heterogeneous Materials

2012 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Wave Propagation ◽  
Explicit Form ◽  
Constitutive Equations ◽  
Effective Properties ◽  
Dynamic Properties ◽  
Effective Property ◽  
Bloch Wave ◽  
Periodic Composites ◽  
Effective Dynamic ◽  
Dynamic Effective Properties

Central to the idea of metamaterials is the concept of dynamic homogenization which seeks to define frequency dependent effective properties for Bloch wave propagation. While the theory of static effective property calculations goes back about 60 years, progress in the actual calculation of dynamic effective properties for periodic composites has been made only very recently. Here we discuss the explicit form of the effective dynamic constitutive equations. We elaborate upon the existence and emergence of coupling in the dynamic constitutive relation and further symmetries of the effective tensors.

scholarly journals Research Progress of Locally Resonance Acoustic Metamaterials

2021 ◽  
Vol 248 ◽  
pp. 01041
Author(s):  
Du Zhehua
Keyword(s):  
Sound Wave ◽  
Negative Refraction ◽  
Low Frequency ◽  
Research Progress ◽  
Frequency Noise ◽  
Bragg Scattering ◽  
Acoustic Metamaterials ◽  
Low Frequency Noise ◽  
Phonon Crystal ◽  
Developed Surface

Bragg scattering phonon crystal and locally resonant acoustic metamaterials were introduced. In order to generate noise reduction, the lattice constant of Bragg scattering phonon crystal should be of the same order of magnitude as the wave length of the sound wave, therefore, its application field is limited. Locally resonant acoustic metamaterials consume sound energy by coupling its own resonant frequencies with those of sound waves at close range. Its size is two orders of magnitude smaller than the wavelength of sound wave; thus, the control of low-frequency noise by small-size acoustic metamaterials is realized. Locally resonant acoustic metamaterials have some extraordinary physical characteristic in the conventional medium for their special acoustic structural units, such as negative refraction and negative mass density. Especially in low frequency band, they have acoustic forbidden band in which the sound wave transmission is prohibited. Acoustic structural unit having resonant characteristics has been developed. Surface-mounted resonant element plate structures and thin film acoustic metamaterials are the normal types of locally resonant acoustic metamaterials. Their research and development provide a new method for low-frequency noise control.

scholarly journals Overall dynamic properties of three-dimensional periodic elastic composites

2011 ◽  
Vol 468 (2137) ◽  
pp. 269-287 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Effective Properties ◽  
Dynamic Properties ◽  
Mass Density ◽  
Three Dimensional ◽  
Linear Momentum ◽  
Three Dimensions ◽  
Theoretical Treatment ◽  
Periodic Composite ◽  
Constitutive Parameters ◽  
Elastic Composites

This article presents a method for the homogenization of three-dimensional periodic elastic composites. It allows for the evaluation of the averaged overall frequency-dependent dynamic material constitutive tensors relating the averaged dynamic field variable tensors of velocity, strain, stress and linear momentum. Although the form of the dynamic constitutive relation for three-dimensional elastodynamic wave propagation has been known, this is the first time that explicit calculations of the effective parameters (for three dimensions) are presented. We show that for three-dimensional periodic composites, the overall compliance (stiffness) tensor, as produced directly by our formulation, is Hermitian, regardless of whether the corresponding unit cell is geometrically or materially symmetric. Overall, mass density is shown to be a tensor and, like the overall compliance tensor, always Hermitian. The average strain and linear momentum tensors are, however, coupled, and the coupling tensors are shown to be each others' Hermitian transpose. Finally, we present a numerical example of a three-dimensional periodic composite composed of elastic cubes periodically distributed in an elastic matrix. The presented results corroborate the predictions of the theoretical treatment illustrating the frequency dependence of the constitutive parameters. We also show that the effective properties calculated in this paper satisfy the dispersion relation of the composite.

scholarly journals Making waves round a structured cloak: lattices, negative refraction and fringes

2013 ◽  
Vol 469 (2157) ◽  
pp. 20130218 ◽  
Author(s):  
D. J. Colquitt ◽  
I. S. Jones ◽  
N. V. Movchan ◽  
A. B. Movchan ◽  
M. Brun ◽  
...  
Keyword(s):  
Electromagnetic Waves ◽  
Negative Refraction ◽  
Lattice Structure ◽  
Low Frequency ◽  
Plane Shear ◽  
Wide Range ◽  
Out Of Plane ◽  
Frequency Regime ◽  
The Stability

Using the framework of transformation optics, this paper presents a detailed analysis of a non-singular square cloak for acoustic, out-of-plane shear elastic and electromagnetic waves. Analysis of wave propagation through the cloak is presented and accompanied by numerical illustrations. The efficacy of the regularized cloak is demonstrated and an objective numerical measure of the quality of the cloaking effect is provided. It is demonstrated that the cloaking effect persists over a wide range of frequencies. As a demonstration of the effectiveness of the regularized cloak, a Young's double slit experiment is presented. The stability of the interference pattern is examined when a cloaked and uncloaked obstacle are successively placed in front of one of the apertures. This novel link with a well-known quantum mechanical experiment provides an additional method through which the quality of cloaks may be examined. In the second half of the paper, it is shown that an approximate cloak may be constructed using a discrete lattice structure. The efficiency of the approximate lattice cloak is analysed and a series of illustrative simulations presented. It is demonstrated that effective cloaking may be obtained by using a relatively simple lattice structure, particularly, in the low-frequency regime.

scholarly journals Band Gaps and Vibration Isolation of a Three-dimensional Metamaterial with a Star Structure

Materials ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 3812 ◽  
Author(s):  
Heng Jiang ◽  
Mangong Zhang ◽  
Yu Liu ◽  
Dongliang Pei ◽  
Meng Chen ◽  
...  
Keyword(s):  
Band Gap ◽  
Vibration Isolation ◽  
Dynamic Properties ◽  
Structural Parameters ◽  
Mass Density ◽  
Three Dimensional ◽  
Low Frequency ◽  
Band Gaps ◽  
Acoustic Metamaterials ◽  
Star Structure

Elastic metamaterials have promising applications in wave control and vibration isolation, due to their extraordinary characteristics, e.g., negative Poisson ratio, band gaps, effective negative mass density and effective negative modulus. How to develop new functional metamaterials using a special structure has always been a hot topic in this field. In this study, a three-dimensional (3D) star structure is designed to construct metamaterials with both negative static and dynamic properties. The results show that the 3D star structure formed a wide band gap at lower frequency and had a negative Poisson’s ratio. Different from conventional acoustic metamaterials, the main physical mechanism behind the low-frequency band gap of the 3D star structure is the resonance mode formed by the bending deformation of each rib plate, which made it easier to achieve effective isolation of low-frequency elastic waves with a low mass density. In addition, many structural parameters of the 3D star structure can be modulated to effectively adjust the band gap frequency by changing the angle between the concave nodes and aspect ratio. This study provides a new way to design the 3D acoustic metamaterials and develop the lightweight vibration isolation devices.

Analytical approach of membrane-type acoustic metamaterial with ring masses

2018 ◽  
Vol 14 (5) ◽  
pp. 828-836 ◽  
Author(s):  
Hongyan Tian ◽  
Ding Tong ◽  
Yourui Tao
Keyword(s):  
Analytical Approach ◽  
Transmission Loss ◽  
Low Frequency ◽  
Ring Structure ◽  
Acoustic Metamaterials ◽  
Acoustic Response ◽  
Content Type ◽  
Frequency Regime ◽  
Geometrical Effects ◽  
Membrane Type

Purpose Membrane-type acoustic metamaterials (MAMs) recently have been emerged to display useful sound attenuation properties in a low-frequency regime. The purpose of this paper is to present an analytical approach to investigate the transmission loss (TL) of a square membrane-ring structure of MAM. The geometrical effects of ring mass on the TL peak and dip frequencies of the MAM are obtained and discussed. Design/methodology/approach In this paper, based on the wave propagation and vibration theory, considering the effects of ring mass and acoustic pressure on the membrane, an analytical model is presented to analyze acoustic response of MAM. Findings Multiple peak frequencies and wide bandwidth appear in the membrane-ring structure, and they can be tuned by changing the location or numbers of the ring mass on the membrane. It is a useful method for designing such type of metamaterial. Originality/value In this paper, an analytical method is presented to evaluate the effects of ring geometric on the TL performance of square membrane-type locally resonant metamaterial. It is proved that achieving broadband and multi-peak TL profile in a single cell can indeed happen by increasing additional ring mass. The TL and frequency bandwidth can be tuned by changing the location, adding numbers and varying mass distribution of the ring masses on the membrane.

scholarly journals Study on broadband low-frequency sound insulation of multi-channel resonator acoustic metamaterials

AIP Advances ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 045321
Author(s):  
Chi Xu ◽  
Hui Guo ◽  
Yinghang Chen ◽  
Xiaori Dong ◽  
Hongling Ye ◽  
...  
Keyword(s):  
Low Frequency ◽  
Sound Insulation ◽  
Acoustic Metamaterials ◽  
Frequency Sound

Tunable underwater acoustic metamaterials via quasi-Helmholtz resonance: From low-frequency to ultra-broadband

2021 ◽  
Vol 118 (7) ◽  
pp. 071904
Author(s):  
Mingyu Duan ◽  
Chenlei Yu ◽  
Fengxian Xin ◽  
Tian Jian Lu
Keyword(s):  
Low Frequency ◽  
Acoustic Metamaterials ◽  
Underwater Acoustic ◽  
Helmholtz Resonance

scholarly journals Research Progress and Development Trends of Acoustic Metamaterials

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 4018
Author(s):  
Hao Song ◽  
Xiaodong Ding ◽  
Zixian Cui ◽  
Haohao Hu
Keyword(s):  
Doppler Effect ◽  
Negative Refraction ◽  
Development Trend ◽  
Atomic Clusters ◽  
Research Progress ◽  
Acoustic Metamaterials ◽  
Development Trends ◽  
Related Research ◽  
The Past ◽  
Anomalous Doppler Effect

Acoustic metamaterials are materials with artificially designed structures, which have characteristics that surpass the behavior of natural materials, such as negative refraction, anomalous Doppler effect, plane focusing, etc. This article mainly introduces and summarizes the related research progress of acoustic metamaterials in the past two decades, focusing on meta-atomic acoustic metamaterials, metamolecular acoustic metamaterials, meta-atomic clusters and metamolecule cluster acoustic metamaterials. Finally, the research overview and development trend of acoustic metasurfaces are briefly introduced.

scholarly journals Influence of Li2CO3 addition on electrical and magnetic properties of Ni0.6Mg0.4Fe2O4

2020 ◽  
Vol 10 (03) ◽  
pp. 2050003
Author(s):  
M. R. Hassan ◽  
M. T. Islam ◽  
M. N. I. Khan
Keyword(s):  
Magnetic Properties ◽  
Single Phase ◽  
Low Frequency ◽  
Solid State Reaction Method ◽  
Charge Carriers ◽  
X Ray Diffraction ◽  
X Ray ◽  
Electrical And Magnetic Properties ◽  
Frequency Regime ◽  
Xrd Patterns

In this research, influence of adding Li2CO3 (at 0%, 2%, 4%, 6%) on electrical and magnetic properties of [Formula: see text][Formula: see text]Fe2O4 (with 60% Ni and 40% Mg) ferrite has been studied. The samples are prepared by solid state reaction method and sintered at 1300∘C for 6[Formula: see text]h. X-ray diffraction (XRD) patterns show the samples belong to single-phase cubic structure without any impurity phase. The magnetic properties (saturation magnetization and coercivity) of the samples have been investigated by VSM and found that the higher concentration of Li2CO3 reduces the hysteresis loss. DC resistivity increases with Li2CO3 contents whereas it decreases initially and then becomes constant at lower value with temperature which indicates that the studied samples are semiconductor. The dielectric dispersion occurs at a low-frequency regime and the loss peaks are formed in a higher frequency regime, which are due to the presence of resonance between applied frequency and hopping frequency of charge carriers. Notably, the loss peaks are shifted to the lower frequency with Li2CO3 additions.

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