Absolute Band Gaps in Two-Dimensional Phononic Crystal Plates

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.

scholarly journals Using PWE/FE Method to Calculate the Band Structures of the Semi-Infinite PCs: Periodic in x–y Plane and Finite in z -direction

2017 ◽  
Vol 42 (4) ◽  
pp. 735-742 ◽  
Author(s):  
Denghui Qian ◽  
Zhiyu Shi
Keyword(s):  
Finite Element ◽  
Band Structure ◽  
Plane Wave ◽  
Composite Structures ◽  
Phononic Crystal ◽  
Plane Wave Expansion ◽  
Fe Method ◽  
Band Structures ◽  
Wave Expansion ◽  
Elastic Composite

Abstract This paper introduces the concept of semi-infinite phononic crystal (PC) on account of the infinite periodicity in x-y plane and finiteness in z-direction. The plane wave expansion and finite element methods are coupled and formulized to calculate the band structures of the proposed periodic elastic composite structures based on the typical geometric properties. First, the coupled plane wave expansion and finite element (PWE/FE) method is applied to calculate the band structures of the Pb/rubber, steel/epoxy and steel/aluminum semi-infinite PCs with cylindrical scatters. Then, it is used to calculate the band structure of the Pb/rubber semi-infinite PC with cubic scatter. Last, the band structure of the rubbercoated Pb/epoxy three-component semi-infinite PC is calculated by the proposed method. Besides, all the results are compared with those calculated by the finite element (FE) method implemented by adopting COMSOL Multiphysics. Numerical results and further analysis demonstrate that the proposed PWE/FE method has strong applicability and high accuracy.

Elastic band structures of two-dimensional solid phononic crystal with negative Poisson's ratios

2012 ◽  
Vol 407 (21) ◽  
pp. 4186-4192 ◽  
Author(s):  
Tian-Xue Ma ◽  
Yue-Sheng Wang ◽  
Xiao-Xing Su ◽  
Yan-Feng Wang
Keyword(s):  
Phononic Crystal ◽  
Two Dimensional ◽  
Elastic Band ◽  
Band Structures ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Tunable Band Gaps of Acoustic Waves in Two-Dimensional Phononic Crystals With Reticular Band Structures

2009 ◽  
Author(s):  
Zi-Gui Huang ◽  
Yunn-Lin Hwang ◽  
Pei-Yu Wang ◽  
Yen-Chieh Mao
Keyword(s):  
Acoustic Waves ◽  
Composite Structures ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Sound Insulation ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Elastic Band ◽  
Band Structures ◽  
Elastic Band Gaps

The excellent applications and researches of so-called photonic crystals raise the exciting researches of phononic crystals. By the analogy between photon and phonon, repetitive composite structures that are made up of different elastic materials can also prevent elastic waves of some certain frequencies from passing by, i.e., the frequency band gap features also exist in acoustic waves. In this paper, we present the results of the tunable band gaps of acoustic waves in two-dimensional phononic crystals with reticular band structures using the finite element method. Band gaps variations of the bulk modes due to different thickness and angles of reticular band structures are calculated and discussed. The results show that the total elastic band gaps for mixed polarization modes can be enlarged or reduced by adjusting the orientation of the reticular band structures. The phenomena of band gaps of elastic or acoustic waves can potentially be utilized for vibration-free, high-precision mechanical systems, and sound insulation.

ACOUSTIC BAND GAPS TUNED BY TRANSLATION GROUP SYMMETRY IN TWO-DIMENSIONAL PERIODIC COMPOSITES

2009 ◽  
Vol 23 (13) ◽  
pp. 1687-1694 ◽  
Author(s):  
ZHONGFEI MU ◽  
FUGEN WU
Keyword(s):  
Cross Section ◽  
Band Gaps ◽  
Group Symmetry ◽  
Two Dimensional ◽  
Translation Group ◽  
Plane Wave Expansion ◽  
Periodic Arrays ◽  
Periodic Composites ◽  
Super Cell ◽  
The Cross

The acoustic band structures of two kinds of acoustic crystals (two-dimensional periodic arrays of rigid solid rods embedded in air with two different configurations) have been studied by the plane-wave expansion (PWE) method based on super cell calculation. The translation group symmetry of the acoustic crystal is changed by changing the area of the cross section of adjacent rods. We found that by changing the translation group symmetry, one can effectively adjust the acoustic band gaps (ABGs). In the case that the cross section of scattering rods is square without any rotation, the decrease of translation group symmetry is advantaged to form ABGs. But when the cross section of scattering rods is square with a rotation of 45°, the decrease of translation group symmetry is disadvantaged to form ABGs.

Tuning Band Structures of Two-Dimensional Phononic Crystals With Biasing Fields

2014 ◽  
Vol 81 (9) ◽  
Author(s):  
Y. Huang ◽  
C. L. Zhang ◽  
W. Q. Chen
Keyword(s):  
Electric Field ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Two Dimensional ◽  
Plane Wave Expansion ◽  
Band Structures ◽  
Biasing Fields ◽  
Small Fields ◽  
Electric Field Change ◽  
Repulsion Effect

The control of band structures of 2D phononic crystals (PCs) composed of piezoelectric inclusions and elastic isotropic matrix with mechanical/electrical biasing fields is theoretically investigated. The theory for small fields superposed on biasing fields and the plane wave expansion (PWE) method is employed to compute the band structures of the PCs under different biasing fields, including the initial shear/normal stress and the initial electric field. We find that the initial shear stress breaks the symmetry of the material. In consequence, the two bands associated with the level repulsion effect are opened near the apparent crosspoint and form a local band gap. On the other hand, the normal initial stress and the biasing electric field change the effective stiffness and shift the positions of band gaps. The observed phenomena show that the biasing fields can be flexibly used to tune the PC devices.

scholarly journals Enhanced plane wave expansion analysis for the band structure of bulk modes in two-dimensional high-contrast solid–solid phononic crystals

2014 ◽  
Vol 12 (5) ◽  
pp. 487-492 ◽  
Author(s):  
Mohammadhosein Ghasemi Baboly ◽  
Yasser Soliman ◽  
Mehmet F. Su ◽  
Charles M. Reinke ◽  
Zayd C. Leseman ◽  
...  
Keyword(s):  
Band Structure ◽  
Plane Wave ◽  
Phononic Crystals ◽  
Two Dimensional ◽  
High Contrast ◽  
Plane Wave Expansion ◽  
Wave Expansion

Band structures in a two-dimensional phononic crystal with rotational multiple scatterers

2017 ◽  
Vol 31 (06) ◽  
pp. 1750038 ◽  
Author(s):  
Ailing Song ◽  
Xiaopeng Wang ◽  
Tianning Chen ◽  
Lele Wan
Keyword(s):  
Sound Pressure ◽  
Phononic Crystal ◽  
Low Frequency ◽  
Electrical Circuit ◽  
Frequency Noise ◽  
Transmission Spectra ◽  
Two Dimensional ◽  
Band Structures ◽  
Unit Cells ◽  
Circuit Analogy

In this paper, the acoustic wave propagation in a two-dimensional phononic crystal composed of rotational multiple scatterers is investigated. The dispersion relationships, the transmission spectra and the acoustic modes are calculated by using finite element method. In contrast to the system composed of square tubes, there exist a low-frequency resonant bandgap and two wide Bragg bandgaps in the proposed structure, and the transmission spectra coincide with band structures. Specially, the first bandgap is based on locally resonant mechanism, and the simulation results agree well with the results of electrical circuit analogy. Additionally, increasing the rotation angle can remarkably influence the band structures due to the transfer of sound pressure between the internal and external cavities in low-order modes, and the redistribution of sound pressure in high-order modes. Wider bandgaps are obtained in arrays composed of finite unit cells with different rotation angles. The analysis results provide a good reference for tuning and obtaining wide bandgaps, and hence exploring the potential applications of the proposed phononic crystal in low-frequency noise insulation.

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