Controlling the amount of acoustic absorption by using clusters of hard cylinders

2021 ◽  
Vol 263 (2) ◽  
pp. 4608-4614
Author(s):  
Vicente Cutanda Henriquez ◽  
José Sánchez-Dehesa
Keyword(s):  
Boundary Element Method ◽  
Numerical Experiments ◽  
Hexagonal Lattice ◽  
Filling Ratio ◽  
Homogenization Theory ◽  
Acoustic Absorption ◽  
Effective Parameters ◽  
Filling Fraction ◽  
Homogenization Approach ◽  
Comprehensive Study

The viscothermal absorption of a cluster of hard cylinders periodically arranged in air is directly related with the filling fraction of the underlying lattice. In this work, we present a comprehensive study of the viscous absorption of clusters with circular external shape. The study has been performed by using a homogenization theory in which the clusters have been represented by a single fluid-like cylinder with effective parameters. The validity of the homogenization approach has been supported with numerical experiments in which the viscosity of the actual cluster is calculated with an improved version of the boundary element method. The simulations have been performed by embedding the clusters in a multimode impedance tube. For example, for a circular cluster containing 817 hard cylinders distributed in a hexagonal lattice with filling ratio of 0.836, the absorptive factor calculated with the homogenization approach is 41.5%, which underestimates by about 1% the value obtained with the complete cluster.

scholarly journals Effective Parameters for 1D Photonic Crystals with Isotropic and Anisotropic Magnetic Inclusions: Coherent Wave Homogenization Theory

Materials ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1475 ◽  
Author(s):  
J. Flores Méndez ◽  
A. C. Piñón Reyes ◽  
M. Moreno Moreno ◽  
A. Morales-Sánchez ◽  
Gustavo M. Minquiz ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Displacement Vector ◽  
Effective Permittivity ◽  
Homogenization Theory ◽  
Effective Parameters ◽  
Good Correspondence ◽  
Filling Fraction ◽  
Coherent Wave ◽  
Electric And Magnetic Fields ◽  
Magnetic Inclusions

A homogenization theory that can go beyond the regime of long wavelengths is proposed, namely, a theory that is still valid for vectors of waves near the edge of the first zone of Brillouin. In this paper, we consider that the displacement vector and the magnetic induction fields have averages in the volume of the cell associated with the values of the electric and magnetic fields in the edges of the cell, so they satisfy Maxwell’s equations. Applying Fourier formalism, explicit expressions were obtained for the case of a photonic crystal with arbitrary periodicity. In the case of one-dimensional (1D) photonic crystals, the expressions for the tensor of the effective bianisotropic response (effective permittivity, permeability and crossed magneto-electric tensors) are remarkably simplified. Specifically, the effective permittivity and permeability tensors are calculated for the case of 1D photonic crystals with isotropic and anisotropic magnetic inclusions. Through a numerical calculation, the dependence of these effective tensors upon the filling fraction of the magnetic inclusion is shown and analyzed. Our results show good correspondence with the approach solution of Rytov’s effective medium. The derived formulas can be very useful for the design of anisotropic systems with specific optical properties that exhibit metamaterial behavior.

Full Band-Gap Silicon Phononic Crystals for Surface Acoustic Waves

2006 ◽  
Author(s):  
Saeed Mohammadi ◽  
Abdelkrim Khelif ◽  
Ryan Westafer ◽  
Eric Massey ◽  
William D. Hunt ◽  
...  
Keyword(s):  
Band Gap ◽  
Acoustic Waves ◽  
Phononic Crystal ◽  
Surface Acoustic Waves ◽  
Hexagonal Lattice ◽  
Phononic Crystals ◽  
Bulk Wave ◽  
Filling Fraction ◽  
Phononic Band Gap ◽  
Wide Range

Periodic elastic structures, called phononic crystals, show interesting frequency domain characteristics that can greatly influence the performance of acoustic and ultrasonic devices for several applications. Phononic crystals are acoustic counterparts of the extensively-investigated photonic crystals that are made by varying material properties periodically. Here we demonstrate the existence of phononic band-gaps for surface acoustic waves (SAWs) in a half-space of two dimensional phononic crystals consisting of hexagonal (honeycomb) arrangement of air cylinders in a crystalline Silicon background with low filling fraction. A theoretical calculation of band structure for bulk wave using finite element method is also achieved and shows that there is no complete phononic band gap in the case of the low filling fraction. Fabrication of the holes in Silicon is done by optical lithography and deep Silicon dry etching. In the experimental characterization, we have used slanted finger interdigitated transducers deposited on a thin layer of Zinc oxide (sputtered on top of the phononic crystal structure to excite elastic surface waves in Silicon) to cover a wide range of frequencies. We believe this to be the first reported demonstration of phononic band-gap for SAWs in a hexagonal lattice phononic crystal at such a high frequency.

Wetting of rough surfaces: a homogenization approach

2005 ◽  
Vol 461 (2053) ◽  
pp. 79-97 ◽  
Author(s):  
Giovanni Alberti ◽  
Antonio DeSimone
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Transition Layer ◽  
Variational Formulation ◽  
Variational Approach ◽  
Rough Surfaces ◽  
Vapour Phase ◽  
Homogenization Theory ◽  
Minimal Energy ◽  
Homogenization Approach

The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness–induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapour phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational approach: the classical laws of Wenzel and Cassie–Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case.

Analytical Homogenization for Dynamic Analysis of Composite Membranes with Circular Inclusions in Hexagonal Lattice Structures

2017 ◽  
Vol 17 (05) ◽  
pp. 1740015 ◽  
Author(s):  
I. V. Andrianov ◽  
J. Awrejcewicz ◽  
B. Markert ◽  
G. A. Starushenko
Keyword(s):  
Effective Properties ◽  
Hexagonal Lattice ◽  
Composite Membranes ◽  
Circular Inclusion ◽  
Free Vibrations ◽  
Effective Characteristics ◽  
Homogeneous Material ◽  
Local Problem ◽  
Homogenization Approach ◽  
Complicated Part

Free vibrations of a composite membrane with a hexagonal lattice circular inclusion are investigated. We aim at a study of the lower frequency spectrum, i.e. it is assumed that the minimum space period of the eigenform is essentially larger than the characteristic dimension of the cell periodicity of the analyzed structure. This implies a possibility of approximating the composite structure by the homogenized one with effective characteristics. The latter is yielded by the multi-scale homogenization approach. Introduction of slow and fast variables yields both counterpart quasistatic local problem regarding the periodically repeated cell and global (homogenized) dynamic problem for homogeneous material with effective properties. The most complicated part of this approach concerns in finding a solution to the local problem. It has been analytically found in the presented paper for relatively large inclusion sizes using lubrication approach. The performed numerical validation of the obtained results shows high accuracy of the implemented approach.

scholarly journals Plane Wave-Perturbative Method for Evaluating the Effective Speed of Sound in 1D Phononic Crystals

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
J. Flores Méndez ◽  
M. Salazar Villanueva ◽  
R. C. Ambrosio Lázaro ◽  
B. Calixto Sirene ◽  
M. L. Mota González ◽  
...  
Keyword(s):  
Elastic Moduli ◽  
Mass Density ◽  
Wave Length ◽  
Phononic Crystal ◽  
Plane Waves ◽  
Phononic Crystals ◽  
Effective Parameters ◽  
Filling Fraction ◽  
Perturbative Method ◽  
Sound Velocities

A method for calculating the effective sound velocities for a 1D phononic crystal is presented; it is valid when the lattice constant is much smaller than the acoustic wave length; therefore, the periodic medium could be regarded as a homogeneous one. The method is based on the expansion of the displacements field into plane waves, satisfying the Bloch theorem. The expansion allows us to obtain a wave equation for the amplitude of the macroscopic displacements field. From the form of this equation we identify the effective parameters, namely, the effective sound velocities for the transverse and longitudinal macroscopic displacements in the homogenized 1D phononic crystal. As a result, the explicit expressions for the effective sound velocities in terms of the parameters of isotropic inclusions in the unit cell are obtained: mass density and elastic moduli. These expressions are used for studying the dependence of the effective, transverse and longitudinal, sound velocities for a binary 1D phononic crystal upon the inclusion filling fraction. A particular case is presented for 1D phononic crystals composed of W-Al and Polyethylene-Si, extending for a case solid-fluid.

scholarly journals Erratum: Flores, J., et al. Effective Parameters for 1D Photonic Crystals with Isotropic and Anisotropic Magnetic Inclusions: Coherent Wave Homogenization Theory. Materials 2020, 13, 1475

Materials ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3053
Author(s):  
J. Flores Méndez ◽  
A. C. Piñón Reyes ◽  
M. Moreno Moreno ◽  
A. Morales-Sánchez ◽  
Gustavo M. Minquiz ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Homogenization Theory ◽  
Effective Parameters ◽  
Coherent Wave ◽  
Magnetic Inclusions

The authors wish to make the following corrections to this paper [1]: replace: (37) 1 ε z = f ε m = 1 − f ε d and (39) 1 μ z = f μ m = 1 − f μ d with the correct expressions: (37) 1 ε z = f ε m + 1 − f ε d and (39) 1 μ z = f μ m + 1 − f μ d [...]

The Calculation of the Band Structure in 3D Phononic Crystal with Hexagonal Lattice

2015 ◽  
Vol 70 (12) ◽  
pp. 979-983
Author(s):  
Mahrokh Aryadoust ◽  
H. Salehi
Keyword(s):  
Band Structure ◽  
Band Gap ◽  
Acoustic Waves ◽  
Phononic Crystal ◽  
Hexagonal Lattice ◽  
Three Dimensions ◽  
Elastic Band ◽  
Maximum Width ◽  
Filling Fraction ◽  
Irreducible Part

AbstractIn this article, the propagation of acoustic waves in the phononic crystals (PCs) of three dimensions with the hexagonal (HEX) lattice is studied theoretically. The PCs are constituted of nickel (Ni) spheres embedded in epoxy. The calculations of the band structure and the density of states are performed using the plane wave expansion (PWE) method in the irreducible part of the Brillouin zone (BZ). In this study, we analyse the dependence of the band structures inside (the complete band gap width) on c/a and filling fraction in the irreducible part of the first BZ. Also, we have analysed the band structure of the ALHA and MLHKM planes. The results show that the maximum width of absolute elastic band gap (AEBG) (0.045) in the irreducible part of the BZ of HEX lattice is formed for c/a=6 and filling fraction equal to 0.01. In addition, the maximum of the first and second AEBG widths are 0.0884 and 0.0474, respectively, in the MLHKM plane, and the maximum of the first and second AEBG widths are 0.0851 and 0.0431, respectively, in the ALHA plane.

Focusing Properties of Axisymmetric Acoustic Metamaterials Made of Toroidal Scatterers

2012 ◽  
Author(s):  
V. Romero-García ◽  
R. Picó ◽  
A. Cebrecos ◽  
L. M. Garcia-Raffi ◽  
J. V. Sánchez-Pérez ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Axial Rotation ◽  
Acoustic Metamaterials ◽  
Effective Parameters ◽  
Radiation Properties ◽  
Homogenization Approach ◽  
2D System ◽  
Sonic Crystal ◽  
Axisymmetric Structure ◽  
Axisymmetric Structures

We present the theoretical analysis of a periodic structure based on a transformational design of an axisymmetric system from a two-dimensional (2D) Sonic Crystal (SC). Applying an axial rotation of a 2D SC, we obtain a three dimensional (3D) axisymmetric structure made up of toroidal scatterers. Based on the propagating properties of the 2D system, we interpret the scattering produced by the 3D axisymmetric structure, and one can also use the homogenization approach in the long wavelength regime to design a refractive media with controlled effective parameters. We use both the multiple scattering theory, for the analysis of the 2D systems, and the finite elements methods, for the case of 3D axisymmetric structures. This system, due to the axial symmetry, could be useful to manage the radiation properties of sources presenting that symmetry. Moreover it may be useful by transforming in scale to different sizes, and as a consequence, to be applied at different ranges of frequencies.

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