Research on the band gaps of the two-dimensional Sierpinski fractal phononic crystals

2015 ◽  
Vol 29 (23) ◽  
pp. 1550134 ◽  
Author(s):  
Nansha Gao ◽  
Jiu Hui Wu ◽  
Li Jing
Keyword(s):  
Rotation Angle ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Transmission Spectra ◽  
Two Dimensional ◽  
Bragg Scattering ◽  
Frequency Range ◽  
Displacement Fields ◽  
First Time

In this paper, we study the band gaps (BGs) of the two-dimensional (2D) Sierpinski fractal phononic crystals (SFPGs) embedded in the homogenous matrix. The BGs structure, transmission spectra and displacement fields of eigenmodes of the proposed structures are calculated by using finite element method (FEM). Due to the simultaneous mechanisms of the Bragg scattering, the structure can exhibit low-frequency BGs, which can be effectively shifted by changing the inclusion rotation angle. The initial stress values can compress the BGs is proposed for the first time. Through the calculation, it is shown that, in the 2D solid–solid SFPG, the multi-frequency BGs exist. The whole BGs would incline to the low-frequency range with the increase of the fractal dimension. The SFPGs with different shape inclusions, can modulate the number, width and location of BGs. The study in this paper is relevant to the design of tuning BGs and isolators in the low-frequency range.

Low-frequency bandgaps of two-dimensional phononic crystal plate composed of asymmetric double-sided cylinder stubs

2016 ◽  
Vol 30 (07) ◽  
pp. 1650029 ◽  
Author(s):  
Ailing Song ◽  
Xiaopeng Wang ◽  
Tianning Chen ◽  
Ping Jiang ◽  
Kai Bao
Keyword(s):  
Phononic Crystal ◽  
Low Frequency ◽  
Resonant Mode ◽  
Dispersion Relations ◽  
Transmission Spectra ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Frequency Range ◽  
Displacement Fields ◽  
Band Structures

In this paper, we theoretically investigate the propagation characteristics of Lamb wave in a two-dimensional (2D) asymmetric phononic crystal (PC) plate composed of cylinder stubs of different radius deposited on both sides of a thin homogeneous plate. The dispersion relations, transmission spectra and displacement fields of the eigenmodes are calculated by using the finite element method (FEM). Two complete bandgaps (BGs) can be found in low-frequency range and the transmission spectra coincide with the band structures. We investigate the evolution of dispersion relations with the decrease of the upper stub radius. The physical mechanism of the upper stub radius effect is also studied with the displacement fields of the unit cell. Numerical results show that the symmetry of the stub radius can remarkably influence the band structures and the asymmetric double-sided plate exhibits a new bandgap (BG) in lower frequency range due to the coupling between the lower stub’s resonant mode and the plate’s Lamb mode becomes weak and the adjacent bands separate. Moreover, we further investigate the effect of the stub height on the dispersion relations and find that the BGs shift to lower frequency regions with the increase of the stub height. In addition, the BGs’ sensitivity to the upper stub radius and the stub height is discussed. The low-frequency BGs in the proposed PC plate can potentially be used to control and insulate vibration in low frequency range.

scholarly journals Research on the Band Gap Characteristics of Two-Dimensional Phononic Crystals Microcavity with Local Resonant Structure

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mao Liu ◽  
Pei Li ◽  
Yongteng Zhong ◽  
Jiawei Xiang
Keyword(s):  
Band Gap ◽  
Phononic Crystal ◽  
Engineering Application ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Wave Band ◽  
Two Dimensional ◽  
Frequency Range ◽  
Gap Characteristics

A new two-dimensional locally resonant phononic crystal with microcavity structure is proposed. The acoustic wave band gap characteristics of this new structure are studied using finite element method. At the same time, the corresponding displacement eigenmodes of the band edges of the lowest band gap and the transmission spectrum are calculated. The results proved that phononic crystals with microcavity structure exhibited complete band gaps in low-frequency range. The eigenfrequency of the lower edge of the first gap is lower than no microcavity structure. However, for no microcavity structure type of quadrilateral phononic crystal plate, the second band gap disappeared and the frequency range of the first band gap is relatively narrow. The main reason for appearing low-frequency band gaps is that the proposed phononic crystal introduced the local resonant microcavity structure. This study provides a good support for engineering application such as low-frequency vibration attenuation and noise control.

Large band gaps in two-dimensional phononic crystals with self-similarity structure

2015 ◽  
Vol 29 (04) ◽  
pp. 1550017 ◽  
Author(s):  
Nansha Gao ◽  
Jiu Hui Wu ◽  
Lie Yu
Keyword(s):  
Great Influence ◽  
Low Frequency ◽  
Phononic Crystals ◽  
The Self ◽  
Band Gaps ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Self Similarity ◽  
Displacement Fields ◽  
Similarity Structure

In this paper, we study the band gaps (BGs) of two-dimensional (2D) phononic crystals (PCs) composed of self-similarity shape inclusions embedded in the homogenous matrix. The dispersion relations, transmission spectra, and displacement fields of eigenmodes of the proposed structures are calculated by use of finite element method. Due to the simultaneous mechanisms of the Bragg scattering, the structure can exhibit low-frequency BGs, which can be effectively shifted by changing the geometries and degree of the self-similarity structure. The BGs are significantly dependent upon the geometrical parameters and degree of the self-similarity structure. It is concluded that, the PCs with self-similarity structure, can modulate the location and width of BGs. But it must be pointed out, the shape of self-similarity inclusion exercises a great influence on the BGs. The study in this paper is relevant to the design of tuning BGs and isolators in the low-frequency range.

Research on the large band gaps in multilayer radial phononic crystal structure

2016 ◽  
Vol 30 (10) ◽  
pp. 1650108 ◽  
Author(s):  
Nansha Gao ◽  
Jiu Hui Wu ◽  
Dong Guan
Keyword(s):  
Crystal Structure ◽  
Finite Element Method ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Transmission Spectra ◽  
Intermediate Mass ◽  
Displacement Fields ◽  
Vibration Coupling ◽  
Single Material

In this paper, we study the band gaps (BGs) of new proposed radial phononic crystal (RPC) structure composed of multilayer sections. The band structure, transmission spectra and eigenmode displacement fields of the multilayer RPC are calculated by using finite element method (FEM). Due to the vibration coupling effects between thin circular plate and intermediate mass, the RPC structure can exhibit large BGs, which can be effectively shifted by changing the different geometry values. This study shows that multilayer RPC can unfold larger and lower BGs than traditional phononic crystals (PCs) and RPC can be composed of single material.

Low frequency phononic band structures in two-dimensional arc-shaped phononic crystals

2012 ◽  
Vol 376 (33) ◽  
pp. 2256-2263 ◽  
Author(s):  
Zhenlong Xu ◽  
Fugen Wu ◽  
Zhongning Guo
Keyword(s):  
Low Frequency ◽  
Phononic Crystals ◽  
Two Dimensional ◽  
Band Structures

scholarly journals “Fuzzy Band Gaps”: A Physically Motivated Indicator of Bloch Wave Evanescence in Phononic Systems

Crystals ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 66
Author(s):  
Connor D. Pierce ◽  
Kathryn H. Matlack
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Quantitative Measure ◽  
Bloch Wave ◽  
Phononic Crystals ◽  
Wave Transmission ◽  
Band Gaps ◽  
Dissipative Systems ◽  
Frequency Range ◽  
Wave Modes

Phononic crystals (PCs) have been widely reported to exhibit band gaps, which for non-dissipative systems are well defined from the dispersion relation as a frequency range in which no propagating (i.e., non-decaying) wave modes exist. However, the notion of a band gap is less clear in dissipative systems, as all wave modes exhibit attenuation. Various measures have been proposed to quantify the “evanescence” of frequency ranges and/or wave propagation directions, but these measures are not based on measurable physical quantities. Furthermore, in finite systems created by truncating a PC, wave propagation is strongly attenuated but not completely forbidden, and a quantitative measure that predicts wave transmission in a finite PC from the infinite dispersion relation is elusive. In this paper, we propose an “evanescence indicator” for PCs with 1D periodicity that relates the decay component of the Bloch wavevector to the transmitted wave amplitude through a finite PC. When plotted over a frequency range of interest, this indicator reveals frequency regions of strongly attenuated wave propagation, which are dubbed “fuzzy band gaps” due to the smooth (rather than abrupt) transition between evanescent and propagating wave characteristics. The indicator is capable of identifying polarized fuzzy band gaps, including fuzzy band gaps which exists with respect to “hybrid” polarizations which consist of multiple simultaneous polarizations. We validate the indicator using simulations and experiments of wave transmission through highly viscoelastic and finite phononic crystals.

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.

scholarly journals Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals

2008 ◽  
Vol 45 (14-15) ◽  
pp. 4203-4210 ◽  
Author(s):  
Yi-Ze Wang ◽  
Feng-Ming Li ◽  
Wen-Hu Huang ◽  
Xiaoai Jiang ◽  
Yue-Sheng Wang ◽  
...  
Keyword(s):  
Phononic Crystals ◽  
Band Gaps ◽  
Wave Band ◽  
Two Dimensional

scholarly journals Phononic Band Gaps of Elastic Periodic Structures: A Homogenization Theory Study

2007 ◽  
Author(s):  
Ying-Hong Liu ◽  
Chien C. Chang ◽  
Ruey-Lin Chern ◽  
C. Chung Chang
Keyword(s):  
Elastic Constants ◽  
Periodic Structures ◽  
Mass Density ◽  
Density Ratio ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Homogenization Theory ◽  
Dominant Factor ◽  
Phononic Band Gaps

In this study, we investigate band structures of phononic crystals with particular emphasis on the effects of the mass density ratio and of the contrast of elastic constants. The phononic crystals consist of arrays of different media embedded in a rubber or epoxy. It is shown that the density ratio rather than the contrast of elastic constants is the dominant factor that opens up phononic band gaps. The physical background of this observation is explained by applying the theory of homogenization to investigate the group velocities of the low-frequency bands at the center of symmetry Γ.

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