scholarly journals Band gap manipulation of viscoelastic functionally graded phononic crystal

2020 ◽  
Vol 9 (1) ◽  
pp. 515-523
Author(s):  
Zuguang Bian ◽  
Shuai Yang ◽  
Xiaoliang Zhou ◽  
David Hui
Keyword(s):  
Incident Angle ◽  
Phononic Crystal ◽  
Functionally Graded ◽  
Band Gaps ◽  
Heat Sources ◽  
Initial State ◽  
Final State ◽  
Sh Waves ◽  
Numerical Examples ◽  
The Matrix

AbstractIn this study, band gaps of SH-waves (horizontally polarized shear waves) propagating in a thermal-sensitive viscoelastic matrix are investigated. Metallic films acting as heat sources are periodically embedded into the matrix, which establishes a periodically inhomogeneous thermal field. The homogenous matrix is therefore transformed into functionally gradient phononic crystals (PCs). A three-parameter solid model is employed to describe the viscoelasticity of the present matrix. By virtue of a transfer matrix method incorporated within a laminated model, the dispersion equation of SH-waves is finally obtained, from which the band gaps are determined. The transmission spectra of a finite-periodic PC are also solved to validate the band gaps. In numerical examples, the influences of incident angles of SH-waves and viscoelasticity of matrix on band gaps are discussed first. Then the research focuses on the means to tune the band gaps by manipulating the inputted powers of heat sources. Numerical examples demonstrate that such a strategy is effective and convenient in tuning the positions and widths of band gaps. A viscous parameter, i.e., the ratio of initial-state to final-state storage moduli, significantly affects the band locations and bandwidths, while the locations of low-order band gaps hardly move with the incident angle of SH-waves. Band gaps of several orders are expected to locate in lower-frequency domain, and the total bandwidth becomes larger as the inputted heat flux increases. This paper lays theoretical foundation to manufacture viscoelastic functionally graded PCs which can be used in frequency-selective devices.

Transverse Shubnikov–de Haas effect and the manifestation of quantum diffraction

2020 ◽  
Vol 34 (05) ◽  
pp. 2050016
Author(s):  
Yu. A. Berezhnoy ◽  
A. S. Molev
Keyword(s):  
Matrix Element ◽  
Electron Transition ◽  
Amplitude Distribution ◽  
Fraunhofer Diffraction ◽  
Initial State ◽  
Final State ◽  
Quantum Diffraction ◽  
The Matrix ◽  
Transverse Conductivity ◽  
Haas Effect

A quantum diffraction interpretation of the transverse Shubnikov–de Haas effect is presented. Within the framework of the conventional theory of this effect, we show that the matrix element for the electron transition from an initial state to a final state used in calculating the transverse electrical conductivity can be represented as a diffraction-type amplitude distribution. The squared modulus of this matrix element under certain conditions exhibits the Fraunhofer diffraction pattern. It is shown that the oscillating part of the transverse conductivity has the same form as the amplitude for Fraunhofer diffraction by an annular aperture.

Free Energy Calculations of Precipitate Nucleation

2007 ◽  
Vol 539-543 ◽  
pp. 2395-2400 ◽  
Author(s):  
Shigeto R. Nishitani ◽  
Atsuto Seko ◽  
Koretaka Yuge ◽  
Isao Tanaka
Keyword(s):  
Free Energy ◽  
Energy Barrier ◽  
Harmonic Approximation ◽  
Free Energy Calculations ◽  
Free Energy Barrier ◽  
Initial State ◽  
Final State ◽  
The Matrix ◽  
Predicted Values ◽  
Vibrational Free Energy

Our recently proposed calculating method reliably predicts the nucleation free energy barrier of the homogeneous and coherent precipitations. Helmholtz free energy change is clearly defined and calculated by the purely enthalpic and entropic contributions between the initial state of the isolated solute atoms scattering around the matrix and the final state of the cluster of size n traveling around the matrix. The enthalpic term is calculated by the reliable first principles method and the entropic term is estimated by the ideal solution model. The vibrational free energy is also included by the quasi-harmonic approximation. The model calculation was performed on bcc Cu precipitations in the Fe-Cu system. The predicted values of the critical number of 12 atoms and the critical free energy barrier of 0.6eV show good agreement with the experimentally estimated ones for the annealing temperature of 773K and the initial concentration of 1.4at%Cu.

Bandgap Structures of SH-Wave in a One-Dimensional Phononic Crystal with Viscoelastic Interfaces

2017 ◽  
Vol 09 (07) ◽  
pp. 1750102 ◽  
Author(s):  
Yuhang Li ◽  
Xiaoliang Zhou ◽  
Zuguang Bian ◽  
Yufeng Xing ◽  
Jizhou Song
Keyword(s):  
Periodic Structure ◽  
Phononic Crystal ◽  
Adhesive Layer ◽  
Phononic Crystals ◽  
Sh Wave ◽  
Initial State ◽  
Final State ◽  
One Dimensional ◽  
Adhesive Layers ◽  
And Control

Phononic crystal is an artificial periodic structure with the ability to regulate and control the wave propagation of particular frequencies and has been widely used in many applications. The adhesive layer bonding different constituents in the periodic structure of phononic crystals is usually a viscoelastic material, which has frequency-dependent material properties. In this paper, an analytical model based on the transfer matrix method is developed to study the bandgap structures of SH-wave (a shear wave with the propagation direction normal to the motion plane) in a one-dimensional phononic crystal consisting of two different elastic constituents bonded by the viscoelastic adhesive layer. The results show that the viscosity of the adhesive layer has a significant influence on the bandgap structure at the region of high frequency. The effects of various material parameters of the viscoelastic adhesive layer such as the relaxation time, the final-state modulus and the initial-state modulus are systematically studied. These results are very helpful in the practical design of phononic crystals involving the viscoelastic adhesive layers.

scholarly journals Transmission and band gaps of elastic SH waves in functionally graded periodic laminates

2012 ◽  
Vol 49 (2) ◽  
pp. 344-354 ◽  
Author(s):  
M.V. Golub ◽  
S.I. Fomenko ◽  
T.Q. Bui ◽  
Ch. Zhang ◽  
Y.-S. Wang
Keyword(s):  
Functionally Graded ◽  
Band Gaps ◽  
Sh Waves

Propagation of SH Waves through an Interface between a Phononic Crystal and a Uniform Solid

2011 ◽  
Vol 675-677 ◽  
pp. 1061-1064
Author(s):  
Long Sheng Ci ◽  
Gui Lan Yu
Keyword(s):  
Energy Distribution ◽  
Phononic Crystal ◽  
Band Gaps ◽  
Refraction Coefficient ◽  
Sh Waves ◽  
One Dimensional ◽  
Reflection And Refraction ◽  
Lower Frequencies

The reflection and refraction of harmonic SH waves at the interface between a homogeneous solid and a one-dimensional phononic crystal is studied. The effects of wave frequencies on the refraction coefficients are investigated. The results show that for lower frequencies, most part of the energy is reflected into the homogeneous solid and that the frequency has little effects on the energy distribution at the interface. While for higher frequencies, SH waves cannot propagate in some directions because of the existence of the directional band gaps, which results in the discontinuity in the refraction coefficient curve. For waves passing through the interface, the higher the frequency is, the smaller the refraction coefficient is.

Flexural Wave Band Gaps in Phononic Crystal Thick Plates with Defects

2019 ◽  
Author(s):  
Edson Jansen Pedrosa de Miranda Junior ◽  
Jose Maria Campos dos Santos
Keyword(s):  
Phononic Crystal ◽  
Band Gaps ◽  
Flexural Wave ◽  
Wave Band ◽  
Thick Plates

scholarly journals Tunable characteristics of low-frequency bandgaps in two-dimensional multivibrator phononic crystal plates under prestrain

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hai-Fei Zhu ◽  
Xiao-Wei Sun ◽  
Ting Song ◽  
Xiao-Dong Wen ◽  
Xi-Xuan Liu ◽  
...  
Keyword(s):  
Phononic Crystal ◽  
Real Life ◽  
Low Frequency ◽  
Acoustic Vibration ◽  
Crystal Plate ◽  
Frequency Noise ◽  
Two Dimensional ◽  
The Matrix ◽  
Noise Frequency ◽  
Realtime Control

AbstractIn view of the influence of variability of low-frequency noise frequency on noise prevention in real life, we present a novel two-dimensional tunable phononic crystal plate which is consisted of lead columns deposited in a silicone rubber plate with periodic holes and calculate its bandgap characteristics by finite element method. The low-frequency bandgap mechanism of the designed model is discussed simultaneously. Accordingly, the influence of geometric parameters of the phononic crystal plate on the bandgap characteristics is analyzed and the bandgap adjustability under prestretch strain is further studied. Results show that the new designed phononic crystal plate has lower bandgap starting frequency and wider bandwidth than the traditional single-sided structure, which is due to the coupling between the resonance mode of the scatterer and the long traveling wave in the matrix with the introduction of periodic holes. Applying prestretch strain to the matrix can realize active realtime control of low-frequency bandgap under slight deformation and broaden the low-frequency bandgap, which can be explained as the multiple bands tend to be flattened due to the localization degree of unit cell vibration increases with the rise of prestrain. The presented structure improves the realtime adjustability of sound isolation and vibration reduction frequency for phononic crystal in complex acoustic vibration environments.

scholarly journals Dual subtractions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Renato Maria Prisco ◽  
Francesco Tramontano
Keyword(s):  
Field Theory ◽  
Quantum Field ◽  
Matrix Elements ◽  
Leading Order ◽  
Initial State ◽  
Final State ◽  
Dual Representation ◽  
Subtraction Scheme ◽  
Theoretical Predictions ◽  
Perturbative Quantum

Abstract We propose a novel local subtraction scheme for the computation of Next-to-Leading Order contributions to theoretical predictions for scattering processes in perturbative Quantum Field Theory. With respect to well known schemes proposed since many years that build upon the analysis of the real radiation matrix elements, our construction starts from the loop diagrams and exploits their dual representation. Our scheme implements exact phase space factorization, handles final state as well as initial state singularities and is suitable for both massless and massive particles.

Sign in / Sign up

Export Citation Format

Share Document