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.

Locally resonant effective phononic crystals for subwavelength vibration control of torsional cylindrical waves

2021 ◽  
pp. 1-30
Author(s):  
Ignacio Arretche ◽  
Kathryn Matlack
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Effective Properties ◽  
Equations Of Motion ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Unit Cell ◽  
Periodic Coefficients ◽  
Bloch Theorem ◽  
Plane Wave Propagation

Abstract Locally resonant materials allow for wave propagation control in the sub-wavelength regime. Even though these materials do not need periodicity, they are usually designed as periodic systems since this allows for the application of the Bloch theorem and analysis of the entire system based on a single unit cell. However, geometries that are invariant to translation result in equations of motion with periodic coefficients only if we assume plane wave propagation. When wave fronts are cylindrical or spherical, a system realized through tessellation of a unit cell does not result in periodic coefficients and the Bloch theorem cannot be applied. Therefore, most studies of periodic locally resonant systems are limited to plane wave propagation. In this paper, we address this limitation by introducing a locally resonant effective phononic crystal composed of a radially-varying matrix with attached torsional resonators. This material is not geometrically periodic but exhibits effective periodicity, i.e. its equations of motion are invariant to radial translations, allowing the Bloch theorem to be applied to radially propagating torsional waves. We show that this material can be analyzed under the already developed framework for metamaterials. To show the importance of using an effectively periodic system, we compare its behavior to a system that is not effectively periodic but has geometric periodicity. We show considerable differences in transmission as well as in the negative effective properties of these two systems. Locally resonant effective phononic crystals open possibilities for subwavelength elastic wave control in the near field of sources.

Modeling and Analysis of Nonlinear Wave Propagation in One-Dimensional Phononic Structures

2017 ◽  
Author(s):  
Mao Liu ◽  
W. D. Zhu
Keyword(s):  
Wave Propagation ◽  
Periodic Structures ◽  
Phononic Crystals ◽  
Nonlinear Wave Propagation ◽  
Linear Dispersion ◽  
Modeling And Analysis ◽  
Nonlinear Properties ◽  
Lagrange Strain ◽  
Nonlinear Regimes ◽  
Good Support

Different from elastic waves in linear periodic structures, those in phononic crystals with nonlinear properties can exhibit more interesting phenomena. Linear dispersion relations cannot predict band-gap variations due to intensity of wave motion; creating nonlinear phononic crystals remains challenging and few examples have been studied. Recent studies in the literature mainly focus on discrete chain-like structures and consider weak nonlinear regimes; they cannot accurately obtain some relations between wave propagation characteristics and nonlinearities. Our models are based on exact Green-Lagrange strain relations for a structure using the B-spline wavelet on the interval (BSWI) finite element method. Numerical examples show that the proposed method performs well for band structure problems with general nonlinearities. This study can provide good support for engineering applications, such as sound and vibration control using tunable band gaps of nonlinear phononic crystals.

Characteristics of Band Gap and Low-frequency Wave Propagation of Mechanically Tunable Phononic Crystals with Scatterers in Periodic Porous Elastomeric Matrices

2021 ◽  
pp. 1-34
Author(s):  
Shaowu Ning ◽  
Dongyang Chu ◽  
Fengyuan Yang ◽  
Heng Jiang ◽  
Zhanli Liu ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Coupling Effect ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Dynamic Responses ◽  
Acoustic Metamaterials ◽  
Frequency Wave ◽  
Strong Coupling Effect ◽  
The Matrix

Abstract The characteristics of passive responses and fixed band gaps of phononic crystals (PnCs) limit their possible applications. For overcoming this shortcoming, a class of tunable PnCs comprised of multiple scatterers and soft periodic porous elastomeric matrices are designed to manipulate the band structures and directionality of wave propagation through the applied deformation. During deformation, some tunable factors such as the coupling effect of scatterer and hole in the matrix, geometric and material nonlinearities, and the rearrangement of scatterer are activated by deformation to tune the dynamic responses of PnCs. The roles of these tunable factors in the manipulation of dynamic responses of PnCs are investigated in detail. The numerical results indicate that the tunability of the dynamic characteristic of PnCs is the result of the comprehensive function of these tunable factors mentioned above. The strong coupling effect between the hole in the matrix and the scatterer contributes to the formation of band gaps. The geometric nonlinearity of matrix and rearrangement of scatterer induced by deformation can simultaneously tune the band gaps and the directionality of wave propagation. However, the matrix's material nonlinearity only adjusts the band gaps of PnCs and does not affect the directionality of wave propagation in them. The research extends our understanding of the formation mechanism of band gaps of PnCs and provides an excellent opportunity for the design of the optimized tunable PnCs and acoustic metamaterials.

Analysis of an Ultra-Low Frequency and Ultra-Broadband Phononic Crystals Silencer with Small Size

2019 ◽  
Vol 27 (02) ◽  
pp. 1850026 ◽  
Author(s):  
Jiangwei Liu ◽  
Dianlong Yu ◽  
Jihong Wen ◽  
Zhenfang Zhang
Keyword(s):  
Wave Propagation ◽  
Periodic Structures ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Frequency Noise ◽  
Duct System ◽  
Frequency Range ◽  
Expansion Chamber ◽  
Band Formation ◽  
Low Frequencies

Existing research shows that acoustic BG in a certain frequency range can be realized by installing an expansion chamber on duct system, but the problems of broadband and size limitations at low frequencies remain to be researched. The study of acoustic and elastic wave propagation in artificial periodic structures has received increasing attention for many decades, and the presence of bandgap (BG) in phononic crystals (PCs), which inhibits elastic/acoustic wave propagation within the BG’ frequency range, supplies a new way to control noise and vibrations in duct system. Based on PC theory, a duct silencer backed with a gas–liquid expansion chamber is proposed to enhance the acoustic performance of low-frequency noise attenuation. The transfer matrix method (TMM) is used to investigate the acoustic BG properties. The influences on the BG properties of some key parameters are analyzed, and the band formation mechanism is revealed by the law of energy conservation. The results show that silencers with a small size can effectively attenuate ultra-low frequencies and ultra-broad bands.

scholarly journals Plane and Surface Acoustic Waves Manipulation by Three-Dimensional Composite Phononic Pillars with 3D Bandgap and Defect Analysis

Acoustics ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 25-41
Author(s):  
Muhammad ◽  
C.W. Lim ◽  
Andrew Y. T. Leung
Keyword(s):  
Acoustic Waves ◽  
Wave Attenuation ◽  
Numerical Technique ◽  
Surface Acoustic Waves ◽  
Three Dimensional ◽  
Phononic Crystals ◽  
Defect State ◽  
Two Dimensional ◽  
Defect Analysis ◽  
Acoustic Metamaterials

The current century witnessed an overwhelming research interest in phononic crystals (PnCs) and acoustic metamaterials (AMs) research owing to their fantastic properties in manipulating acoustic and elastic waves that are inconceivable from naturally occurring materials. Extensive research literature about the dynamical and mechanical properties of acoustic metamaterials currently exists, and this maturing research field is now finding possible industrial and infrastructural applications. The present study proposes a novel 3D composite multilayered phononic pillars capable of inducing two-dimensional and three-dimensional complete bandgaps (BGs). A phononic structure that consisted of silicon and tungsten layers was subjected to both plane and surface acoustic waves in three-dimensional and two-dimensional periodic systems, respectively. By frequency response study, the wave attenuation, trapping/localization, transmission, and defect analysis was carried out for both plane and surface acoustic waves. In the bandgap, the localized defect state was studied for both plane and surface acoustic waves separately. At the defect state, the localization of both plane and surface acoustic waves was observed. By varying the defect size, the localized frequency can be made tailorable. The study is based on a numerical technique, and it is validated by comparison with a reported theoretical work. The findings may provide a new perspective and insight for the designs and applications of three-dimensional phononic crystals for surface acoustic wave and plane wave manipulation, particularly for energy harvesting, sensing, focusing and waves isolation/attenuation purposes.

Acoustic Metamaterials

MRS Bulletin ◽  
2008 ◽  
Vol 33 (10) ◽  
pp. 931-934 ◽  
Author(s):  
Lee Fok ◽  
Muralidhar Ambati ◽  
Xiang Zhang
Keyword(s):  
Materials Science ◽  
Periodic Structures ◽  
Phononic Crystals ◽  
Acoustic Metamaterials ◽  
Design Development ◽  
Materials Properties ◽  
The Future ◽  
Basic Physics ◽  
Negative Materials

AbstractThe field of engineered materials with designed properties is expected to continue to grow in the future, and metamaterials are instrumental in allowing this freedom of design. Metamaterials, particularly acoustic, are still in the stage of infancy. Acoustic metamaterials are being explored theoretically, but there has been little headway on the experimental front. The design, development, and characterization of acoustic metamaterials will offer many opportunities in materials science. In this article, we review the basic physics of different kinds of acoustic periodic structures with special emphasis on locally resonant acoustic metamaterials. We first survey phononic crystals and then discuss localized resonances in intrinsic and inertial resonating structures of acoustic metamaterials. Finally, we present the ongoing efforts in realizing acoustic metamaterials with negative materials properties and discuss the implications of acoustic metamaterials.

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