Acoustic Metamaterial With Fractal Coiling Up Space for Sound Blocking in a Deep Subwavelength Scale

Inspired by fractal photonic/phononic crystals, the self-similar fractal technique is applied to design acoustic metamaterial. By replacing the straight channel of coiling up space with a smaller coiling up space, a class of topological architectures with fractal coiling up space is developed. The significant effect of the fractal-inspired hierarchy on the band structure with fractal coiling up space is systematically investigated. Furthermore, sound wave propagation in the acoustic metamaterial with the fractal coiling up space is comprehensively highlighted. Our results show that the acoustic metamaterial with higher-order fractal coiling up space exhibits deep subwavelength bandgaps, in which the sound propagation will be well blocked. Thus, this work provides insights into the role of the fractal hierarchy in regulating the dynamic behavior of the acoustic metamaterial and provides opportunities for the design of a robust filtering device in a subwavelength scale.

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The role of the Coulomb gap in the self-consistent band structure of SmS

Journal of Physics C Solid State Physics ◽

10.1088/0022-3719/19/14/015 ◽

1986 ◽

Vol 19 (14) ◽

pp. 2485-2498 ◽

Cited By ~ 25

Author(s):

F Lopez-Aguilar ◽

J Costa-Quintana

Keyword(s):

Band Structure ◽

The Self ◽

Coulomb Gap ◽

Self Consistent

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Self-similar solution of laser-produced plasma expansion into vacuum with kappa-distributed electrons

Nukleonika ◽

10.1515/nuka-2016-0020 ◽

2016 ◽

Vol 61 (2) ◽

pp. 115-118

Author(s):

Djamila Bennaceur-Doumaz ◽

Djemai Bara

Keyword(s):

Hydrodynamic Model ◽

The Self ◽

Plasma Expansion ◽

Type Distribution ◽

Self Similar Solution ◽

Laser Produced Plasma ◽

Analytic Expressions ◽

Self Similar ◽

Kappa Distributed Electrons

Abstract The expansion of semi-infinite laser produced plasma into vacuum is analyzed with a hydrodynamic model for cold ions assuming electrons modeled by a kappa-type distribution. Self-similar analytic expressions for the potential, velocity, and density of the plasma have been derived. It is shown that nonthermal energetic electrons have the role of accelerating the self-similar expansion.

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On generalized-vortex boundary layers

Journal of Fluid Mechanics ◽

10.1017/s0022112072002745 ◽

1972 ◽

Vol 52 (4) ◽

pp. 753-780 ◽

Cited By ~ 29

Author(s):

R. J. Belcher ◽

O. R. Burggraf ◽

K. Stewartson

Keyword(s):

Boundary Layer ◽

Azimuthal Velocity ◽

Radial Component ◽

Similarity Solutions ◽

The Self ◽

Consistent Solution ◽

Self Similar ◽

Terminal Structure ◽

Boundary Radius

We define a generalized vortex to have azimuthal velocity proportional to a power of radiusr−n. The properties of the steady laminar boundary layer generated by such a vortex over a fixed coaxial disk of radiusaare examined. Though the boundary-layer thickness is zero a t the edge of the disk, reversals of the radial component of velocity u must occur, so that an extra boundary condition is needed at any interior boundary radiusrEto make the structure unique. Numerical integrations of the unsteady governing equations were carried out forn= − 1, 0, ½ and 1. Whenn= 0 and − 1 solutions of the self-similar equations are known for an infinite disk. Assuming terminal similarity to fix the boundary conditions atr=rEwhenur> 0, a consistent solution was found which agrees with those of the self-similar equations whenrEis small. However, ifn= ½ and 1, no similarity solutions are known, although the terminal structure forn= 1 was deduced earlier by the present authors. From the numerical integration forn= ½, we are able to deduce the limit structure forr→ 0 by using a combination of analytic and numerical techniques with the proviso of a consistent self-similar form asrE→ 0. The structure is then analogous to a ladder consisting of an infinite number of regions where viscosity may be neglected, each separated by much thinner viscous transitional regions playing the role of the rungs. This structure appears to be characteristic of all generalized vortices for which 0.1217 <n< 1.

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Ferroelectric based fractal phononic crystals: wave propagation and band structure

Ferroelectrics ◽

10.1080/00150193.2020.1713352 ◽

2020 ◽

Vol 557 (1) ◽

pp. 85-91

Author(s):

Selami Palaz ◽

Zafer Ozer ◽

Amirullah M. Mamedov ◽

Ekmel Ozbay

Keyword(s):

Wave Propagation ◽

Band Structure ◽

Cross Section ◽

Phononic Crystal ◽

Circular Cross Section ◽

Phononic Crystals ◽

Square Lattice ◽

Rubber Matrix ◽

Element Simulation ◽

Piezoelectric Inclusion

In this study, the band structure and transmission in multiferroic based Sierpinski carpet phononic crystal are investigated based on finite element simulation. In order to obtain the band structure of the phononic crystal (PnC), the Floquet periodicity conditions were applied to the sides of the unit cell. The square lattice PnC consists of various piezoelectric inclusion in a rubber matrix with square and circular cross section.

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Elastic Wave Propagation of Two-Dimensional Metamaterials Composed of Auxetic Star-Shaped Honeycomb Structures

Crystals ◽

10.3390/cryst9030121 ◽

2019 ◽

Vol 9 (3) ◽

pp. 121 ◽

Cited By ~ 4

Author(s):

Shu-Yeh Chang ◽

Chung-De Chen ◽

Jia-Yi Yeh ◽

Lien-Wen Chen

Keyword(s):

Wave Propagation ◽

Cross Sections ◽

Vibration Isolation ◽

Negative Refraction ◽

Phononic Crystal ◽

Phononic Crystals ◽

The Self ◽

The Finite Element Method ◽

Elastic Waveguide ◽

Potential Applications

In this paper, the wave propagation in phononic crystal composed of auxetic star-shaped honeycomb matrix with negative Poisson’s ratio is presented. Two types of inclusions with circular and rectangular cross sections are considered and the band structures of the phononic crystals are also obtained by the finite element method. The band structure of the phononic crystal is affected significantly by the auxeticity of the star-shaped honeycomb. Some other interesting findings are also presented, such as the negative refraction and the self-collimation. The present study demonstrates the potential applications of the star-shaped honeycomb in phononic crystals, such as vibration isolation and the elastic waveguide.

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