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.

Mechanically Tunable Solid/Solid Phononic Crystals Through the Rearrangement of Hard Scatterers Controlled by the Deformation of Periodic Elastomeric Matrixes

2020 ◽  
Vol 87 (10) ◽  
Author(s):  
Shaowu Ning ◽  
Chengcheng Luo ◽  
Fengyuan Yang ◽  
Zhanli Liu ◽  
Zhuo Zhuang
Keyword(s):  
Wave Propagation ◽  
Coupling Effect ◽  
Matrix Material ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Dynamic Responses ◽  
Two Phase ◽  
Elastomeric Matrix ◽  
The Matrix

Abstract The fixed band gap characteristic of passive phononic crystals (PCs) is possible to limit their applications in engineering. To overcome this shortcoming, inspired by the tunable mechanism of the spider silks, a new class of tunable PCs comprising periodic scatterers and periodic elastomeric matrix are proposed to effectively tune the band gaps and directionality of propagating waves. The orientation and arrangement of hard scatterers are controlled by the deformation of the periodic elastomeric matrix to enhance the tunability of their dynamic responses. According to this idea, PCs with differently shaped and arranged cylindroid scatterers are designed. Through introducing the multiple scatterers into the periodic elastomeric matrix, the scattering coupling effect between them is enhanced. The simulation results indicate that the orientation and arrangement of the scatterers could be altered continuously during deformation. During deformation, the number, position, and width of band gaps can be effectively tuned due to the geometric nonlinearity of the matrix and the rearrangement of multiple scatterers. The transmissibility of finite-sized structures without damping decreases significantly in the frequency ranges of band gaps. However, introducing the damping into the matrix material significantly enhances the ability to suppress elastic wave propagation but makes it difficult to identify the band gaps from the transmittance spectrum. The directionality of wave propagation can be also effectively tuned. In the low-frequency range, such as the first two phase constant surfaces, the phase and group velocity profiles and the anisotropy indexes are calculated and the results indicate that the deformation makes the wave propagation more isotropic. The schemes presented in this paper provide an effective approach to tune the band gaps of the solid/solid PCs and open avenues for the design of tunable PCs.

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.

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.

Wave propagation in acoustic metamaterials with resonantly shunted cross-shape piezos

2018 ◽  
Vol 29 (13) ◽  
pp. 2744-2753 ◽  
Author(s):  
Shengbing Chen
Keyword(s):  
Wave Propagation ◽  
Band Gap ◽  
Vibration Isolation ◽  
Band Gaps ◽  
Acoustic Metamaterials ◽  
Resonant Frequencies ◽  
Piezoelectric Patch ◽  
Transmission Properties ◽  
Gap Width ◽  
Band Gap Width

Cross-shape piezoelectric patches were originally proposed to improve the band-gap properties of acoustic metamaterials with shunting circuits. The dispersion curves are characterized through the application of finite element method. Also, the theoretical band-gap predictions are verified by simulation results obtained from COMSOL. The investigation results show that the proposed scheme distinguishes itself from the conventional square patches by broader band gaps, whose bandwidth is almost doubled. The inherent capacitance of the piezoelectric patch is strongly related to the boundary conditions, so the local resonant band gap is strongly affected by the shape of piezoelectric patches as well. As a result, the band-gap width and location of metamaterials with different shape patches are rather different, even with the same size patches. Also, negative modulus (NM) and Poisson’s ratio were observed around the resonant frequencies. The transmission properties of finite periods agree well with band-gap predictions. An obvious attenuation zone (AZ) is produced around the band-gap location, in which the wave propagation is decayed strongly. Similarly, the width of AZ of the proposed metamaterial is much larger than that of the conventional one. Hence, the proposed scheme demonstrates more advantages in the application to vibration isolation when compared with the conventional.

scholarly journals Gradient index phononic crystals and metamaterials

Nanophotonics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 685-701 ◽  
Author(s):  
Yabin Jin ◽  
Bahram Djafari-Rouhani ◽  
Daniel Torrent
Keyword(s):  
Refractive Index ◽  
Wave Propagation ◽  
Acoustic Waves ◽  
Effective Properties ◽  
Periodic Structures ◽  
Phononic Crystals ◽  
Ray Theory ◽  
Acoustic Metamaterials ◽  
Propagation Of Waves ◽  
At Will

AbstractPhononic crystals and acoustic metamaterials are periodic structures whose effective properties can be tailored at will to achieve extreme control on wave propagation. Their refractive index is obtained from the homogenization of the infinite periodic system, but it is possible to locally change the properties of a finite crystal in such a way that it results in an effective gradient of the refractive index. In such case the propagation of waves can be accurately described by means of ray theory, and different refractive devices can be designed in the framework of wave propagation in inhomogeneous media. In this paper we review the different devices that have been studied for the control of both bulk and guided acoustic waves based on graded phononic crystals.

Low-frequency tunable locally resonant band gaps in acoustic metamaterials through large deformation

2020 ◽  
Vol 35 ◽  
pp. 100623 ◽  
Author(s):  
Shaowu Ning ◽  
Fengyuan Yang ◽  
Chengcheng Luo ◽  
Zhanli Liu ◽  
Zhuo Zhuang
Keyword(s):  
Large Deformation ◽  
Low Frequency ◽  
Band Gaps ◽  
Acoustic Metamaterials ◽  
Frequency Tunable
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