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.

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.

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.

Theoretical and Experimental Study on Phononic Crystal Structures for Low-Frequency Noise Reduction in the Brake

2013 ◽  
Author(s):  
Li Shen ◽  
Jiu Hui Wu
Keyword(s):  
Noise Reduction ◽  
Phononic Crystal ◽  
Low Frequency ◽  
Equivalent Model ◽  
Frequency Noise ◽  
Steel Matrix ◽  
Two Dimensional ◽  
Low Frequency Noise ◽  
Frequency Range ◽  
Extremely Low Frequency

Phononic crystal is an artificial periodic structure in which elastic constants distribute periodically. In this paper, a two dimensional Bragg scattering phononic crystal was introduced into low-frequency noise reduction facility in the brake originally. Through the theoretical analysis by using Plane-wave Expansion Method to obtain the band diagram of a phononic crystal with holes periodically arranged in the 45 carbon steel plate and establishing the equivalent model in motion as the brake, we find an approximate bandgap between 0–5400Hz in the low-frequency range while the complete static bandgaps are distributed in the high-frequency range. It is believed that this kind of extremely low-frequency bandgap is due to the combination of the vibration of a single scatter and the interaction among scatters. In order to demonstrate the theory, contrastive experiment was taken. Noise spectrum diagram of the origin plate without holes was obtained in the first experiment. According to the equivalent model, the two dimensional air column/steel matrix phononic crystal structure in which filling rate was 40% was designed to apply in the test apparatus so that the frequency range (2050 to 2300Hz) of strong noise would be involved in this bandgap. Moreover, the noise in the whole frequency range (0–2550Hz) went down. This phenomenon proved that experiment result was coincident with theoretic consequence. The maximum decreasing amplitude of the noise reached as much as 25dB and the average decreasing amplitude was about 13dB from 2050 to 2300 Hz. In a word, this bandgap which is the combination effect of structure periodicity or the Mie scattering has an obvious extremely low-frequency characteristic in noise and vibration control in the brake.

TUNABLE BAND STRUCTURES OF 2D MULTI-ATOM ARCHIMEDEAN-LIKE PHONONIC CRYSTALS

2012 ◽  
Vol 01 (02) ◽  
pp. 1250016 ◽  
Author(s):  
Y. L. XU ◽  
C. Q. CHEN ◽  
X. G. TIAN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Two Dimensional ◽  
Primitive Cell ◽  
The Finite Element Method ◽  
Band Structures ◽  
Solid System

Two dimensional multi-atom Archimedean-like phononic crystals (MAPCs) can be obtained by adding "atoms" at suitable positions in primitive cells of traditional simple lattices. Band structures of solid-solid and solid-air MAPCs are computed by the finite element method in conjunction with the Bloch theory. For the solid-solid system, our results show that the MAPCs can be suitably designed to split and shift band gaps of the corresponding traditional simple phononic crystal (i.e., with only one scatterer inside a primitive cell). For the solid-air system, the MAPCs have more and wider band gaps than the corresponding traditional simple phononic crystal. Numerical calculations for both solid-solid and solid-air MAPCs show that the band gap of traditional simple phononic crystal can be tuned by appropriately adding "atoms" into its primitive cell.

Studies on Band Structures and Wave Localization Phenomenon of the Randomly Disordered Two-Dimensional Solid-Fluid Phononic Crystals

2011 ◽  
Vol 675-677 ◽  
pp. 639-642
Author(s):  
A Li Chen ◽  
Yue Sheng Wang ◽  
Chuan Zeng Zhang
Keyword(s):  
Phononic Crystal ◽  
Expansion Method ◽  
Two Dimensional ◽  
Wave Localization ◽  
Plane Wave Expansion Method ◽  
Displacement Fields ◽  
Band Structures ◽  
Water Matrix ◽  
Localization Phenomenon ◽  
Disorder Degree

The supercell based plane wave expansion method is used to study the effects of random disorders on the band structures of a two-dimensional (2D) solid-fluid phononic crystal. Phononic systems with steel scatterers embedded in a water matrix are calculated in detail. The radius disorder and location disorder are concerned. The influences of the disorder degree on the first band gap are investigated. The localization phenomenon is discussed by computing the displacement fields in the supercell.

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.

Hybrid radial plate-type elastic metamaterials for lowering and widening acoustic bandgaps

2018 ◽  
Vol 32 (26) ◽  
pp. 1850286
Author(s):  
Yinggang Li ◽  
Qingwen Zhou ◽  
Ling Zhu ◽  
Kailing Guo
Keyword(s):  
Phononic Crystal ◽  
Low Frequency ◽  
Geometrical Parameters ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
One Dimensional ◽  
Relative Bandwidth ◽  
Elastic Metamaterials ◽  
Plate Type ◽  
Radial Plate

In this paper, we present theoretical investigation on the wave propagation and acoustic bandgap characteristics in hybrid radial plate-type elastic metamaterials constituted of periodic double-sides composite stubs deposited on one-dimensional binary radial phononic crystal plate. The dispersion relations and the displacement fields of the eigenmodes are calculated by using the finite element method on the basis of two-dimensional axial symmetry models. Numerical results show that the proposed hybrid radial plate-type elastic metamaterial can generate lowering and widening acoustic bandgaps and yield a significant expansion of the relative bandwidth by a factor of 5 compared to the traditional radial plate-type elastic metamaterial with double-sided composite stubs. The displacement fields of the eigenmodes are applied to reveal the formation mechanism of lowering and widening acoustic bandgaps. In addition, the influences of the physical and geometrical parameters on the bandgaps are further performed. These low-frequency broadband acoustic bandgap properties in the radial plate-type elastic metamaterials can probably be applied to vibration and noise reduction in the rotary machines and structures.

scholarly journals Tunable characteristics of low-frequency bandgaps in two-dimensional multivibrator phononic crystal plates under prestrain

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hai-Fei Zhu ◽  
Xiao-Wei Sun ◽  
Ting Song ◽  
Xiao-Dong Wen ◽  
Xi-Xuan Liu ◽  
...  
Keyword(s):  
Phononic Crystal ◽  
Real Life ◽  
Low Frequency ◽  
Acoustic Vibration ◽  
Crystal Plate ◽  
Frequency Noise ◽  
Two Dimensional ◽  
The Matrix ◽  
Noise Frequency ◽  
Realtime Control

AbstractIn view of the influence of variability of low-frequency noise frequency on noise prevention in real life, we present a novel two-dimensional tunable phononic crystal plate which is consisted of lead columns deposited in a silicone rubber plate with periodic holes and calculate its bandgap characteristics by finite element method. The low-frequency bandgap mechanism of the designed model is discussed simultaneously. Accordingly, the influence of geometric parameters of the phononic crystal plate on the bandgap characteristics is analyzed and the bandgap adjustability under prestretch strain is further studied. Results show that the new designed phononic crystal plate has lower bandgap starting frequency and wider bandwidth than the traditional single-sided structure, which is due to the coupling between the resonance mode of the scatterer and the long traveling wave in the matrix with the introduction of periodic holes. Applying prestretch strain to the matrix can realize active realtime control of low-frequency bandgap under slight deformation and broaden the low-frequency bandgap, which can be explained as the multiple bands tend to be flattened due to the localization degree of unit cell vibration increases with the rise of prestrain. The presented structure improves the realtime adjustability of sound isolation and vibration reduction frequency for phononic crystal in complex acoustic vibration environments.

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