The Calculation of the Band Structure in 3D Phononic Crystal with Hexagonal Lattice

AbstractIn this article, the propagation of acoustic waves in the phononic crystals (PCs) of three dimensions with the hexagonal (HEX) lattice is studied theoretically. The PCs are constituted of nickel (Ni) spheres embedded in epoxy. The calculations of the band structure and the density of states are performed using the plane wave expansion (PWE) method in the irreducible part of the Brillouin zone (BZ). In this study, we analyse the dependence of the band structures inside (the complete band gap width) on c/a and filling fraction in the irreducible part of the first BZ. Also, we have analysed the band structure of the ALHA and MLHKM planes. The results show that the maximum width of absolute elastic band gap (AEBG) (0.045) in the irreducible part of the BZ of HEX lattice is formed for c/a=6 and filling fraction equal to 0.01. In addition, the maximum of the first and second AEBG widths are 0.0884 and 0.0474, respectively, in the MLHKM plane, and the maximum of the first and second AEBG widths are 0.0851 and 0.0431, respectively, in the ALHA plane.

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Full Band-Gap Silicon Phononic Crystals for Surface Acoustic Waves

Noise Control and Acoustics ◽

10.1115/imece2006-16227 ◽

2006 ◽

Cited By ~ 1

Author(s):

Saeed Mohammadi ◽

Abdelkrim Khelif ◽

Ryan Westafer ◽

Eric Massey ◽

William D. Hunt ◽

...

Keyword(s):

Band Gap ◽

Acoustic Waves ◽

Phononic Crystal ◽

Surface Acoustic Waves ◽

Hexagonal Lattice ◽

Phononic Crystals ◽

Bulk Wave ◽

Filling Fraction ◽

Phononic Band Gap ◽

Wide Range

Periodic elastic structures, called phononic crystals, show interesting frequency domain characteristics that can greatly influence the performance of acoustic and ultrasonic devices for several applications. Phononic crystals are acoustic counterparts of the extensively-investigated photonic crystals that are made by varying material properties periodically. Here we demonstrate the existence of phononic band-gaps for surface acoustic waves (SAWs) in a half-space of two dimensional phononic crystals consisting of hexagonal (honeycomb) arrangement of air cylinders in a crystalline Silicon background with low filling fraction. A theoretical calculation of band structure for bulk wave using finite element method is also achieved and shows that there is no complete phononic band gap in the case of the low filling fraction. Fabrication of the holes in Silicon is done by optical lithography and deep Silicon dry etching. In the experimental characterization, we have used slanted finger interdigitated transducers deposited on a thin layer of Zinc oxide (sputtered on top of the phononic crystal structure to excite elastic surface waves in Silicon) to cover a wide range of frequencies. We believe this to be the first reported demonstration of phononic band-gap for SAWs in a hexagonal lattice phononic crystal at such a high frequency.

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Evidence of a large elastic band gap in a one-dimensional phononic crystal

2016 IEEE International Ultrasonics Symposium (IUS) ◽

10.1109/ultsym.2016.7728683 ◽

2016 ◽

Author(s):

Etienne Coffy ◽

Sebastien Euphrasie ◽

Pascal Vairac ◽

Abdelkrim Khelif

Keyword(s):

Band Gap ◽

Phononic Crystal ◽

Elastic Band ◽

One Dimensional

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

Modern Physics Letters B ◽

10.1142/s0217984918501737 ◽

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.

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Flexural Vibration Band Gaps in a Ternary Phononic Crystal Thin Plate

Materials Science Forum ◽

10.4028/www.scientific.net/msf.675-677.1085 ◽

2011 ◽

Vol 675-677 ◽

pp. 1085-1088

Author(s):

Zong Jian Yao ◽

Gui Lan Yu ◽

Jian Bao Li

Keyword(s):

Band Gap ◽

Thin Plate ◽

Mass Density ◽

Phononic Crystal ◽

Flexural Vibration ◽

Expansion Method ◽

Band Gaps ◽

Physical Parameters ◽

Vibration Band ◽

Filling Fraction

The band structures of flexural waves in a ternary locally resonant phononic crystal thin plate are studied using the improved plane wave expansion method. And the thin concrete plate composed of a square array of steel cylinders hemmed around by rubber is considered here. Absolute band gaps of flexural vibration with low frequency are shown. The calculation results show that the band gap width is strongly dependent on the filling fraction, the radius ratio, the mass density and the Young’s modulus contrasts between the core and the coating. So by changing these physical parameters, the required band gap could be obtained.

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Acoustic Waves in Two-Dimensional Phononic Crystals With Reticular Geometric Structures

Journal of Vibration and Acoustics ◽

10.1115/1.4003201 ◽

2011 ◽

Vol 133 (3) ◽

Cited By ~ 10

Author(s):

Zi-Gui Huang ◽

Zheng-Yu Chen

Keyword(s):

Band Gap ◽

Acoustic Waves ◽

Phononic Crystals ◽

Band Gaps ◽

Sound Insulation ◽

Two Dimensional ◽

Elastic Band ◽

Geometric Structures ◽

2D And 3D ◽

Elastic Band Gaps

Previous studies on photonic crystals raise the exciting topic of phononic crystals. This paper presents the results of tunable band gaps in the acoustic waves of two-dimensional phononic crystals with reticular geometric structures using the 2D and 3D finite element methods. This paper calculates and discusses the band gap variations of the bulk modes due to different sizes of reticular geometric structures. Results show that adjusting the orientation of the reticular geometric structures can increase or decrease the total elastic band gaps for mixed polarization modes. The band gap phenomena of elastic or acoustic waves can potentially be utilized to achieve vibration-free, high-precision mechanical systems, and sound insulation.

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Absolute Band Gaps in Two-Dimensional Phononic Crystal Plates

Noise Control and Acoustics ◽

10.1115/imece2006-13353 ◽

2006 ◽

Author(s):

Je´roˆme Vasseur ◽

Pierre A. Deymier ◽

Bahram Djafari-Rouhani ◽

Yan Pennec

Keyword(s):

Band Structure ◽

Phononic Crystal ◽

Plate Thickness ◽

Two Dimensional ◽

Plane Wave Expansion ◽

Elastic Band ◽

Band Structures ◽

Super Cell ◽

Order Of Magnitude ◽

Crystal Dispersion

The elastic band structures of two-dimensional phononic crystal plates are computed with the help of a super-cell plane wave expansion (PWE) method. These band structures strongly differ from the infinite 2D phononic crystal dispersion curves. In particular, these band structures exhibit surface modes and guided modes. The influence of the constituent materials, of the plate thickness and of the geometry of the array on the band structure is investigated. We focus more specifically on determining the thicknesses of the plate for which absolute forbidden bands exist. Namely, we show that absolute forbidden bands occur in the band structure if the thickness of the plate is of the same order of magnitude as the periodicity of the array of inclusions.

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Flexural Vibration in a Binary Phononic Crystal Thick Plate with a Point Defect

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.168-170.1577 ◽

2010 ◽

Vol 168-170 ◽

pp. 1577-1580

Author(s):

Zong Jian Yao ◽

Gui Lan Yu ◽

Yue Sheng Wang ◽

Jian Bao Li

Keyword(s):

Frequency Response ◽

Point Defect ◽

Band Gap ◽

Response Function ◽

Frequency Response Function ◽

Thick Plate ◽

Phononic Crystal ◽

Flexural Vibration ◽

Rubber Matrix ◽

Filling Fraction

Based on the finite element method, the propagation of flexural vibration in a binary phononic crystal thick plate with a point defect is studied. The plate is composed of a square array of concrete cylinders embedded in the rubber matrix. Complete band structure and frequency response function of this perfect thick plate indicates the existence of low-frequency absolute band gap. Detailed investigations have been carried out to study the dependence of the width of absolute band gap on both structural and material parameters. For the point defect, the defect modes are localized around the defect, and the frequency and the number of the defect bands are significantly dependent on the filling fraction, the size and the mass density of the defect cylinder. To better support the statement of the defect band structures, we also represent the frequency response function of the propagation of flexural vibration in the thick plate with a point defect. Based on the detailed investigations, both the absolute band gap and the defect bands of a binary thick plate could be modulated with appropriate parameters. It may be useful to vibration control in engineering structure.

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Experimental study of guiding and filtering of acoustic waves in a two dimensional ultrasonic crystal

Zeitschrift für Kristallographie - Crystalline Materials ◽

10.1524/zkri.2005.220.9-10.836 ◽

2005 ◽

Vol 220 (9-10) ◽

Cited By ~ 7

Author(s):

Abdelkrim Khelif ◽

Abdelkrim Choujaa ◽

Sarah Benchabane ◽

Bahram Djafari-Rouhani ◽

Vincent Laude

Keyword(s):

Band Gap ◽

Acoustic Waves ◽

Theoretical Study ◽

Phononic Crystal ◽

Wide Frequency Range ◽

Two Dimensional ◽

Full Band ◽

Side Walls ◽

Difference Time ◽

Good Agreement

AbstractWe present a combined experimental and theoretical study of the guiding, bending and filtering of acoustic waves in an ultrasonic crystal. The crystal consists of a two-dimensional periodical array of steel rods immersed in water, for wich a complete acoustic band gap extending from 240 to 325 kHz is found experimentally. Waveguides for acoustic waves are further created by removing a line defect, on which stubs can be added by removing rods from the side-walls of the waveguide. Full transmission is observed for a one-period-wide straight waveguide within the full-band-gap of the perfect phononic crystal, i.e. for a waveguide aperture smaller than one acoustic wavelength. Waveguiding over a wide frequency range is also obtained for a one-period-wide waveguide with two sharp 90° bends. Finite-difference time-domain computations are found to be in good agreement with the measurements in all experimental configurations.

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Influence of Point Defects on Band Gaps of Fe-Epoxy in Two-Dimensional Phononic Crystal

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.652-654.1377 ◽

2013 ◽

Vol 652-654 ◽

pp. 1377-1382

Author(s):

Jiao He ◽

Guang Hui Fan ◽

De Xun Zhao ◽

Ying Kai Liu

Keyword(s):

Point Defect ◽

Band Gap ◽

Nearest Neighbor ◽

Phononic Crystal ◽

Expansion Method ◽

Band Gaps ◽

Two Dimensional ◽

Defect States ◽

Filling Fraction ◽

Nearest Neighbor Coupling

The band gap of a new two-dimensional phononic crystal was studied by the plane-wave expansion method. The two-dimensional phononic crystal is formed by square-shape array geometry of iron cylinders with square cross section inserted in an epoxy resin. The band gaps of different structures were calculated such as defect-free, single cavity crystal point defect states, crystal point defect states with (10) direction coupling, crystal point defect states with (10) direction next-nearest-neighbor coupling, and crystal point defect states with (11) direction next-nearest-neighbor coupling. Compared with that of defect-free, it is conclude that point defect is beneficial to the production of band gaps. The bandwidth of point defect is about 5 times larger than that of the defect-free crystal with the filling fraction F=0.4. In addition, the maximum number of band gap is in the crystal point defect states with (10) direction next-nearest-neighbor coupling. It will provide a theoretical reference for the manufacture of phononic crystal.

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