Three-Dimensional Sonic Band Gaps Tunned by 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.

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

Proceedings of the Institution of Mechanical Engineers Part L Journal of Materials Design and Applications ◽

10.1177/14644207211013054 ◽

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.

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Effects of Material Parameters on Longitudinal Vibration Band Gaps in Thin Phononic Crystal Plates

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.654.16 ◽

2014 ◽

Vol 654 ◽

pp. 16-19

Author(s):

Hao Jiang Zhao ◽

Rong Qiang Liu ◽

Hong Wei Guo

Keyword(s):

Longitudinal Vibration ◽

Mass Density ◽

Phononic Crystal ◽

Density Ratio ◽

Young Modulus ◽

Expansion Method ◽

Band Gaps ◽

Square Lattice ◽

Vibration Band ◽

Material Parameters

The improved plane wave expansion method is used to investigate the effects of material parameters on the longitudinal vibration band gaps in thin phononic crystal plates. Both square lattice and graphite lattice are considered. Results show that the parameters playing the essential roles are the mass density ratio and the Young modulus ratio of the scatterers and the host materials.

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

Volume 10: Mechanics of Solids and Structures, Parts A and B ◽

10.1115/imece2007-43969 ◽

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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Study on band gap properties of two-dimensional phononic crystals based on generalized viscoelastic modeling

Modern Physics Letters B ◽

10.1142/s0217984919504037 ◽

2019 ◽

Vol 33 (32) ◽

pp. 1950403

Author(s):

Fengxiang Guo ◽

Hui Guo ◽

Pei Sun ◽

Tao Yuan ◽

Yansong Wang

Keyword(s):

Plane Waves ◽

Single Mode ◽

Expansion Method ◽

Maxwell Model ◽

Phononic Crystals ◽

Band Gaps ◽

Two Dimensional ◽

Band Structures ◽

Material Parameters ◽

Multi Mode

Viscoelastic materials can dissipate energy and hinder propagation for plane waves, which can adjust the band structures of phononic crystals (PCs). In this study, the wave propagation in a two-dimensional PC with a viscoelastic matrix is investigated. The Maxwell model is utilized to analyze the effect of material parameters on the frequency dependence of viscoelasticity. Material parameters include the relaxation time, the initial value and the final value of the shear modulus. Band structures of viscoelastic phononic crystals (VPCs) are solved by combining the plane wave expansion method and iterative algorithm based on Bloch theory. The effects of the viscoelasticity on the band structures are studied using the single-mode and multi-mode Maxwell models. Results reveal that the viscoelasticity of the materials not only extends the band gaps but also shifts the band gaps to lower frequencies. Furthermore, the viscoelasticity simulated by the multi-mode model can precisely adjust anyone of the band gaps of VPCs separately. Results provide insights into the design and applications of VPCs.

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Flexural Vibration Band Gaps in a Ternary Phononic Crystal Thin Plate

Materials Science Forum ◽

10.4028/www.scientific.net/msf.675-677.1085 ◽

2011 ◽

Vol 675-677 ◽

pp. 1085-1088

Author(s):

Zong Jian Yao ◽

Gui Lan Yu ◽

Jian Bao Li

Keyword(s):

Band Gap ◽

Thin Plate ◽

Mass Density ◽

Phononic Crystal ◽

Flexural Vibration ◽

Expansion Method ◽

Band Gaps ◽

Physical Parameters ◽

Vibration Band ◽

Filling Fraction

The band structures of flexural waves in a ternary locally resonant phononic crystal thin plate are studied using the improved plane wave expansion method. And the thin concrete plate composed of a square array of steel cylinders hemmed around by rubber is considered here. Absolute band gaps of flexural vibration with low frequency are shown. The calculation results show that the band gap width is strongly dependent on the filling fraction, the radius ratio, the mass density and the Young’s modulus contrasts between the core and the coating. So by changing these physical parameters, the required band gap could be obtained.

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Analytical formulation of three-dimensional dynamic homogenization for periodic elastic systems

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2011.0698 ◽

2012 ◽

Vol 468 (2142) ◽

pp. 1629-1651 ◽

Cited By ~ 60

Author(s):

A. N. Norris ◽

A. L. Shuvalov ◽

A. A. Kutsenko

Keyword(s):

Effective Medium Theory ◽

Equations Of Motion ◽

Three Dimensional ◽

Expansion Method ◽

Bloch Wave ◽

Dimensional System ◽

Medium Theory ◽

Material Parameters ◽

Elastic Systems ◽

Arbitrary Frequency

Homogenization of the equations of motion for a three-dimensional periodic elastic system is considered. Expressions are obtained for the fully dynamic effective material parameters governing the spatially averaged fields by using the plane wave expansion method. The effective equations are of Willis form with coupling between momentum and stress and tensorial inertia. The formulation demonstrates that the Willis equations of elastodynamics are closed under homogenization. The effective material parameters are obtained for arbitrary frequency and wavenumber combinations, including but not restricted to Bloch wave branches for wave propagation in the periodic medium. Numerical examples for a one-dimensional system illustrate the frequency dependence of the parameters on Bloch wave branches and provide a comparison with an alternative dynamic effective medium theory, which also reduces to Willis form but with different effective moduli.

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Observation of aerodynamic instability in the flow of a particle stream in a dilute gas

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833702 ◽

2019 ◽

Vol 622 ◽

pp. A151 ◽

Cited By ~ 1

Author(s):

Holly L. Capelo ◽

Jan Moláček ◽

Michiel Lambrechts ◽

John Lawson ◽

Anders Johansen ◽

...

Keyword(s):

Local Density ◽

Mass Density ◽

Density Ratio ◽

Three Dimensional ◽

Particle Number Density ◽

Solid Particles ◽

Dust Particles ◽

Drag Forces ◽

Velocity Statistics ◽

The Mean

Forming macroscopic solid bodies in circumstellar discs requires local dust concentration levels significantly higher than the mean. Interactions of the dust particles with the gas must serve to augment local particle densities, and facilitate growth past barriers in the metre size range. Amongst a number of mechanisms that can amplify the local density of solids, aerodynamic streaming instability (SI) is one of the most promising. This work tests the physical assumptions of models that lead to SI in protoplanetary discs (PPDs). We conduct laboratory experiments in which we track the three-dimensional motion of spherical solid particles fluidised in a low-pressure, laminar, incompressible, gas stream. The particle sizes span the Stokes–Epstein drag regime transition and the overall dust-to-gas mass density ratio,ϵ, is close to unity. A recently published study establishes the similarity of the laboratory flow to a simplified PPD model flow. We study velocity statistics and perform time-series analysis of the advected flow to obtain experimental results suggesting an instability due to particle-gas interaction: (i) there exist variations in particle concentration in the direction of the mean relative motion between the gas and the particles, that is the direction of the mean drag forces; (ii) the particles have a tendency to “catch up” to one another when they are in proximity; (iii) particle clumping occurs on very small scales, which implies local enhancements above the backgroundϵby factors of several tens; (iv) the presence of these density enhancements occurs for a meanϵapproaching or greater than 1; (v) we find evidence for collective particle drag reduction when the local particle number density becomes high and when the background gas pressure is high so that the drag is in the continuum regime. The experiments presented here are precedent-setting for observing SI under controlled conditions and may lead to a deeper understanding of how it operates in nature.

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