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.

Optimization of Phononic Crystals for the Simultaneous Attenuation of Out-of-Plane and In-Plane Waves

2011 ◽  
Author(s):  
Osama R. Bilal ◽  
Mahmoud I. Hussein
Keyword(s):  
Genetic Algorithm ◽  
Phononic Crystal ◽  
Plane Waves ◽  
Phononic Crystals ◽  
Gap Size ◽  
Two Dimensional ◽  
Dispersion Characteristics ◽  
Out Of Plane ◽  
Optimization Methodology ◽  
Application Specific

The topological distribution of the material phases inside the unit cell composing a phononic crystal has a significant effect on its dispersion characteristics. This topology can be engineered to produce application-specific requirements. In this paper, a specialized genetic-algorithm-based topology optimization methodology for the design of two-dimensional phononic crystals is presented. Specifically the target is the opening and maximization of band gap size for (i) out-of-plane waves, (ii) in-plane waves and (iii) both out-of-plane and in-plane waves simultaneously. The methodology as well as the resulting designs are presented.

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.

Flexural Vibration Band Gaps in a Ternary Phononic Crystal Thin Plate

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.

Flexural Vibration in a Ternary Locally Resonant Phononic Crystal Thin Plate with Defects

2010 ◽  
Vol 150-151 ◽  
pp. 1282-1285
Author(s):  
Zong Jian Yao ◽  
Gui Lan Yu ◽  
Yue Sheng Wang ◽  
Jian Bao Li
Keyword(s):  
Point Defect ◽  
Thin Plate ◽  
Mass Density ◽  
Phononic Crystal ◽  
Flexural Vibration ◽  
Defect Mode ◽  
Expansion Method ◽  
Flexural Waves ◽  
Filling Fraction ◽  
Linear Defects

The improved supercell plane wave expansion method is applied to theoretically study the propagation of flexural waves in a ternary locally resonant phononic crystal thin plate with a point defect and linear defects. The thin concrete plate composed of a square array of steel cylinders hemmed around by rubber is considered here. Absolute band gaps in low frequency are obtained. For the point defect, the defect mode is localized around the defect, and the magnitude of the resonant defect mode is strongly dependent on the defect filling fraction, mass density and Young’s modulus of the defect cylinder. For the straight linear defects, several resonant linear defect bands appear inside the absolute band gap. And the displacement distributions show that the flexural waves could well propagate along the linear defects.

SYMMETRY AND COUPLING EFFICIENCY OF THE DEFECT MODES IN TWO-DIMENSIONAL PHONONIC CRYSTALS

2007 ◽  
Vol 21 (22) ◽  
pp. 1479-1488 ◽  
Author(s):  
Y. J. CAO ◽  
Y. Z. LI
Keyword(s):  
Phononic Crystal ◽  
Plane Waves ◽  
Coupling Efficiency ◽  
Phononic Crystals ◽  
Two Dimensional ◽  
Defect Modes ◽  
Transmission Coefficients ◽  
Resonant Modes ◽  
Incident Plane ◽  
Match Theory

We study theoretically the symmetric property and coupling efficiency of the defect modes in a two-dimensional phononic crystal by calculating band structures, field distributions and transmission coefficients of the defect modes. The results show that the point defect could act as a microcavity surrounded by the phononic crystal, and the confining ability of the phononic crystal to the resonant modes strongly depends on the thickness of the phononic crystal. By investigating the transmission spectra, we also find that the defect modes cannot be absolutely excited by the normally incident plane waves. The transmission coefficients are calculated by using the eigen-mode match theory method under the supercell technique, which is applied to the phononic crystals with the defects for the first time.

Single-Negative Properties Based on the Bandgaps of One-Dimensional Phononic Crystal

2011 ◽  
Vol 105-107 ◽  
pp. 279-282 ◽  
Author(s):  
Wei Kai Xu ◽  
Wei Wang
Keyword(s):  
Potential Application ◽  
Negative Refraction ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Viscous Damping ◽  
Effective Parameters ◽  
One Dimensional ◽  
Equivalent Layer ◽  
Layer Concept

Phononic Crystals (PCs) have important potential application in engineering by the properties of bandgaps. In the paper, the bandgap characteristic of one-dimensional PCs is attributed to the results of Single-Negative (SN) properties, e.g. negative modulus or negative density. The effective parameters of the 1D PCs were predicted by the equivalent layer concept with considering viscous damping, and the results showed that during the frequency regions of the bandgaps, the negative parameters appeared. This will be a reference for the design of acoustic negative refraction metamaterials.

Buckling Behavior of Tire Breaker Structure

1983 ◽  
Vol 11 (1) ◽  
pp. 3-19
Author(s):  
T. Akasaka ◽  
S. Yamazaki ◽  
K. Asano
Keyword(s):  
Elastic Foundation ◽  
Elastic Moduli ◽  
Wave Length ◽  
Bending Moment ◽  
Experimental Results ◽  
Automobile Tire ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Steel Cord ◽  
Interlaminar Shear

Abstract The buckled wave length and the critical in-plane bending moment of laminated long composite strips of cord-reinforced rubber sheets on an elastic foundation is analyzed by Galerkin's method, with consideration of interlaminar shear deformation. An approximate formula for the wave length is given in terms of cord angle, elastic moduli of the constituent rubber and steel cord, and several structural dimensions. The calculated wave length for a 165SR13 automobile tire with steel breakers (belts) was very close to experimental results. An additional study was then conducted on the post-buckling behavior of a laminated biased composite beam on an elastic foundation. This beam is subjected to axial compression. The calculated relationship between the buckled wave rise and the compressive membrane force also agreed well with experimental results.

Thermal Design of Highly-Efficient Thermoelectric Materials With Atomic-Scale Three-Dimensional Phononic Crystals

2007 ◽  
Author(s):  
Jean-Numa Gillet ◽  
Yann Chalopin ◽  
Sebastian Volz
Keyword(s):  
Thermal Conductivity ◽  
Bulk Material ◽  
Phononic Crystal ◽  
Three Dimensional ◽  
Mean Free Path ◽  
Dispersion Curves ◽  
Phononic Crystals ◽  
Thermal Design ◽  
Atomic Scale ◽  
Thermal Insulating

Owing to their thermal insulating properties, superlattices have been extensively studied. A breakthrough in the performance of thermoelectric devices was achieved by using superlattice materials. The problem of those nanostructured materials is that they mainly affect heat transfer in only one direction. In this paper, the concept of canceling heat conduction in the three spatial directions by using atomic-scale three-dimensional (3D) phononic crystals is explored. A period of our atomic-scale 3D phononic crystal is made up of a large number of diamond-like cells of silicon atoms, which form a square supercell. At the center of each supercell, we substitute a smaller number of Si diamond-like cells by other diamond-like cells, which are composed of germanium atoms. This elementary heterostructure is periodically repeated to form a Si/Ge 3D nanostructure. To obtain different atomic configurations of the phononic crystal, the number of Ge diamond-like cells at the center of each supercell can be varied by substitution of Si diamond-like cells. The dispersion curves of those atomic configurations can be computed by lattice dynamics. With a general equation, the thermal conductivity of our atomic-scale 3D phononic crystal can be derived from the dispersion curves. The thermal conductivity can be reduced by at least one order of magnitude in an atomic-scale 3D phononic crystal compared to a bulk material. This reduction is due to the decrease of the phonon group velocities without taking into account that of the phonon average mean free path.

Acoustic wave frequency filtering in constant total length phononic crystals of Al/Pb multilayer

2021 ◽  
Author(s):  
Chittaranjan Nayak ◽  
Mehdi Solaimani ◽  
Alireza Aghajamali ◽  
Arafa H. Aly
Keyword(s):  
Acoustic Wave ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Geometrical Parameters ◽  
One Dimensional ◽  
Internal Geometry ◽  
Total Length ◽  
Acoustic Filters ◽  
System Length ◽  
Phononic Band Gaps

In this study, we have scrutinized the frequency gap generation by changing the geometrical parameters of a one-dimensional phononic crystal. For this purpose, we have calculated the transmission coefficient of an incident acoustic wave by using the transfer matrix method. We have retained and fixed the total length of the system and changed the system internal geometry not to increase the system length too much. Another reason was to adjust the phononic band gaps and get the desired transmission properties by finding the optimum internal geometry without increasing or decreasing the total length of phononic crystals. In addition, we also propose few structures with the opportunity of applications in acoustical devices such as sonic reflectors. Our results can also be of high interest to design acoustic filters in the case that transmission of certain frequencies is necessary.

PIEZOELECTRIC MATERIAL AND ONE-DIMENSIONAL PHONONIC CRYSTAL

2019 ◽  
Vol 26 (02) ◽  
pp. 1850144 ◽  
Author(s):  
ARAFA H. ALY ◽  
AHMED NAGATY ◽  
Z. KHALIFA
Keyword(s):  
Electric Field ◽  
Piezoelectric Material ◽  
Material Properties ◽  
Phononic Crystal ◽  
Defect Layer ◽  
Phononic Crystals ◽  
Localized Modes ◽  
One Dimensional ◽  
Energy Applications ◽  
Relative Change

We have theoretically obtained the transmittance properties of one-dimensional phononic crystals incorporating a piezoelectric material as a defect layer. We have used the transfer matrix method in our analysis with/without defect materials. By increasing the thickness of the defect layer, we obtained a sharp peak created within the bandgap, that indicates to the significance of defect layer thickness on the band structure. The localized modes and a particular intensity estimated within the bandgap depend on the piezoelectric material properties. By applying different quantities of an external electric field, the position of the peak shifts to different frequencies. The electric field induces a relative change in the piezoelectric thickness. Our structure may be very useful in some applications such as sensors, acoustic switches, and energy applications.

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