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.

scholarly journals Phononic band gaps of elastic periodic structures: A homogenization theory study

2007 ◽  
Vol 75 (5) ◽  
Author(s):  
Ying-Hong Liu ◽  
Chien C. Chang ◽  
Ruey-Lin Chern ◽  
C. Chung Chang
Keyword(s):  
Periodic Structures ◽  
Band Gaps ◽  
Homogenization Theory ◽  
Phononic Band Gaps

Locally resonant periodic structures with low-frequency band gaps

2013 ◽  
Vol 114 (3) ◽  
pp. 033532 ◽  
Author(s):  
Zhibao Cheng ◽  
Zhifei Shi ◽  
Y. L. Mo ◽  
Hongjun Xiang
Keyword(s):  
Frequency Band ◽  
Periodic Structures ◽  
Low Frequency ◽  
Band Gaps

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.

Multilayer-split-tube resonators with low-frequency band gaps in phononic crystals

2014 ◽  
Vol 116 (10) ◽  
pp. 103514 ◽  
Author(s):  
Li Jing ◽  
Jiu Hui Wu ◽  
Dong Guan ◽  
Nansha Gao
Keyword(s):  
Frequency Band ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Band Gaps

Multi-cavity coupling acoustic metamaterials with low-frequency broad band gaps based on negative mass density

2016 ◽  
Vol 30 (23) ◽  
pp. 1650317
Author(s):  
Chuanhui Yang ◽  
Jiu Hui Wu ◽  
Songhua Cao ◽  
Li Jing
Keyword(s):  
Band Gap ◽  
Mass Density ◽  
Resonant Cavity ◽  
Broad Band ◽  
Low Frequency ◽  
Band Gaps ◽  
Acoustic Metamaterials ◽  
Negative Mass ◽  
Closed Cavity ◽  
Cavity Coupling

This paper studies a novel kind of low-frequency broadband acoustic metamaterials with small size based on the mechanisms of negative mass density and multi-cavity coupling. The structure consists of a closed resonant cavity and an open resonant cavity, which can be equivalent to a homogeneous medium with effective negative mass density in a certain frequency range by using the parameter inversion method. The negative mass density makes the anti-resonance area increased, which results in broadened band gaps greatly. Owing to the multi-cavity coupling mechanism, the local resonances of the lower frequency mainly occur in the closed cavity, while the local resonances of the higher frequency mainly in the open cavity. Upon the interaction between the negative mass density and the multi-cavity coupling, there exists two broad band gaps in the range of 0–1800 Hz, i.e. the first-order band gap from 195 Hz to 660 Hz with the bandwidth of 465 Hz and the second-order band gap from 1157 Hz to 1663 Hz with the bandwidth of 506 Hz. The acoustic metamaterials with small size presented in this paper could provide a new approach to reduce the low-frequency broadband noises.

Three-Dimensional Sonic Band Gaps Tunned by Material Parameters

2010 ◽  
Vol 29-32 ◽  
pp. 1797-1802 ◽  
Author(s):  
Xiao Zhou Zhou ◽  
Yue Sheng Wang ◽  
Chuan Zeng Zhang
Keyword(s):  
Bulk Modulus ◽  
Mass Density ◽  
Density Ratio ◽  
Three Dimensional ◽  
Expansion Method ◽  
Small Mass ◽  
Band Gaps ◽  
Face Centered Cubic ◽  
Modulus Ratio ◽  
Material Parameters

In this paper, band gaps tunned by material parameters in three-dimensional fluid-fluid sonic crystals are studied. From the basic wave equation, it is found that the material parameters directly determining the three-dimensional sonic band gaps are the mass density ratio and bulk modulus ratio. The calculation of the sonic band gaps is completed by the plane-wave expansion method. The effects of these parameters on sonic band gaps are discussed in details for the simple-cubic (sc), face-centered cubic (fcc) and body-centered cubic (bcc) lattices. The results show that the first potential sonic band gap easily appears at both small mass density ratio and bulk modulus ratio, and becomes wider with both of these two parameters decreasing. The bulk modulus ratio plays a more important role than the mass density ratio in tuning the sonic band gaps. The present analysis can be applied to artificially design band gaps.

Shielding performance of T-shaped periodic barrier for surface waves in transversely isotropic soil

2021 ◽  
pp. 146442072110130
Author(s):  
De-Xin Ji ◽  
Gui-Lan Yu
Keyword(s):  
Finite Element Method ◽  
Surface Waves ◽  
Floquet Theory ◽  
Vibration Isolation ◽  
Mass Density ◽  
Density Ratio ◽  
Transversely Isotropic ◽  
Band Gaps ◽  
Modulus Ratio ◽  
Material Parameters

Aiming at the vibration isolation in transversely isotropic soil, a T-shaped partially embedded periodic barrier for surface waves is proposed, and its shielding performance is explored by using finite element method combined with Bloch-Floquet theory. Seven independent dimensionless material parameters are derived and their influences on band gaps are discussed numerically. The results show that the band gaps exhibit strong sensitivity to the three parameters out of seven, and the band gaps are far wider in transversely isotropic soils than that in the isotropic. The mass density ratio and the shear modulus ratio of the barrier to the soil, as well as the length ratio of the barrier above the ground to that below, can be used to adjust band gaps effectively to meet the shielding requirements for different frequency ranges under different anisotropic soils. As a case of study, the El Centro seismic wave is considered and found that it can be considerably attenuated by the designed periodic barrier.

Sign in / Sign up

Export Citation Format

Share Document