scholarly journals High-frequency homogenization in periodic media with imperfect interfaces

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200402
Author(s):  
Raphaël C. Assier ◽  
Marie Touboul ◽  
Bruno Lombard ◽  
Cédric Bellis
Keyword(s):  
Wave Field ◽  
Brillouin Zone ◽  
Uniform Approximation ◽  
High Frequency ◽  
Periodic Media ◽  
Dispersion Diagram ◽  
Periodic Cell ◽  
Imperfect Interfaces ◽  
Propagation Of Elastic Waves ◽  
Mass Type

In this work, the concept of high-frequency homogenization is extended to the case of one-dimensional periodic media with imperfect interfaces of the spring-mass type. In other words, when considering the propagation of elastic waves in such media, displacement and stress discontinuities are allowed across the borders of the periodic cell. As is customary in high-frequency homogenization, the homogenization is carried out about the periodic and antiperiodic solutions corresponding to the edges of the Brillouin zone. Asymptotic approximations are provided for both the higher branches of the dispersion diagram (second-order) and the resulting wave field (leading-order). The special case of two branches of the dispersion diagram intersecting with a non-zero slope at an edge of the Brillouin zone (occurrence of a so-called Dirac point) is also considered in detail, resulting in an approximation of the dispersion diagram (first-order) and the wave field (zeroth-order) near these points. Finally, a uniform approximation valid for both Dirac and non-Dirac points is provided. Numerical comparisons are made with the exact solutions obtained by the Bloch–Floquet approach for the particular examples of monolayered and bilayered materials. In these two cases, convergence measurements are carried out to validate the approach, and we show that the uniform approximation remains a very good approximation even far from the edges of the Brillouin zone.

scholarly journals Research of the process of vegetable oil extracting under the influence of a high frequency wave field

2020 ◽  
Vol 941 ◽  
pp. 012052
Author(s):  
V Yu Ovsyannikov ◽  
A A Berestovoy ◽  
N N Lobacheva ◽  
V V Toroptsev ◽  
S A Trunov
Keyword(s):  
Wave Field ◽  
Vegetable Oil ◽  
High Frequency ◽  
Frequency Wave ◽  
High Frequency Wave

High-Frequency Response of an Elastic Spherical Shell

1969 ◽  
Vol 36 (4) ◽  
pp. 859-864 ◽  
Author(s):  
David Feit ◽  
M. C. Junger
Keyword(s):  
Spherical Shell ◽  
Flat Plate ◽  
Wave Field ◽  
Classical Solution ◽  
High Frequency ◽  
Natural Frequencies ◽  
Near Field ◽  
Flexural Wave ◽  
High Frequency Response ◽  
Field Response

The classical solution of the point-excited spherical shell, in the form of a normal-mode series, converges poorly for large frequencies. By applying the Watson-Sommerfeld transformation to this series, the response is expressed as a sum of only two terms. These terms can be interpreted, respectively, as the near-field response and propagating flexural wave field of an infinite flat plate, the latter term being multiplied by a factor whose maxima coincide with the natural frequencies of the shell.

New model for acoustic waves propagating through a vortical flow

2017 ◽  
Vol 823 ◽  
pp. 658-674 ◽  
Author(s):  
Jim Thomas
Keyword(s):  
Asymptotic Analysis ◽  
Wave Field ◽  
Time Scale ◽  
Acoustic Waves ◽  
High Frequency ◽  
Spatial Scales ◽  
Amplitude Equation ◽  
Vortical Flow ◽  
Reduced Model ◽  
Scale Separation

A new amplitude equation is derived for high-frequency acoustic waves propagating through an incompressible vortical flow using multi-time-scale asymptotic analysis. The reduced model is derived without an explicit spatial-scale separation ansatz between the wave and vortical fields. As a consequence, the model is seen to capture very well the features of the wave field in the regime where the spatial scales of the wave and vortical fields are comparable, a regime for which an optimal reduced model does not seem to be available.

scholarly journals High-frequency homogenization for periodic media

2010 ◽  
Vol 466 (2120) ◽  
pp. 2341-2362 ◽  
Author(s):  
R. V. Craster ◽  
J. Kaplunov ◽  
A. V. Pichugin
Keyword(s):  
High Frequency ◽  
Wave Equations ◽  
Standing Waves ◽  
Low Frequency ◽  
Homogenization Theory ◽  
Periodic Media ◽  
Mode Spectrum ◽  
Bloch Mode ◽  
Long Wavelength Asymptotics ◽  
Model Equations

An asymptotic procedure based upon a two-scale approach is developed for wave propagation in a doubly periodic inhomogeneous medium with a characteristic length scale of microstructure far less than that of the macrostructure. In periodic media, there are frequencies for which standing waves, periodic with the period or double period of the cell, on the microscale emerge. These frequencies do not belong to the low-frequency range of validity covered by the classical homogenization theory, which motivates our use of the term ‘high-frequency homogenization’ when perturbing about these standing waves. The resulting long-wave equations are deduced only explicitly dependent upon the macroscale, with the microscale represented by integral quantities. These equations accurately reproduce the behaviour of the Bloch mode spectrum near the edges of the Brillouin zone, hence yielding an explicit way for homogenizing periodic media in the vicinity of ‘cell resonances’. The similarity of such model equations to high-frequency long wavelength asymptotics, for homogeneous acoustic and elastic waveguides, valid in the vicinities of thickness resonances is emphasized. Several illustrative examples are considered and show the efficacy of the developed techniques.

Detection of Contact-Type Damages by Utilizing Nonlinear Piezoelectric Impedance Modulation of Self-Excited Structures

2013 ◽  
Author(s):  
Arata Masuda ◽  
Yuya Ogawa ◽  
Akira Sone
Keyword(s):  
Damage Detection ◽  
Wave Field ◽  
High Frequency ◽  
Detection Method ◽  
Piezoelectric Sensor ◽  
Frequency Wave ◽  
Contact Type ◽  
Impedance Modulation ◽  
Excited Oscillation ◽  
Piezoelectric Impedance

This paper presents an improvement of a nonlinear piezoelectric impedance modulation (NPIM)-based damage detection method, a damage-sensitive, baseline-free structural health monitoring technique proposed by the authors, by introducing self-excited oscillation. The NPIM-based damage detection utilizes the modulation of high-frequency wave field of structures caused by the contact acoustic nonlinearity at the damaged part. In this study, the high-frequency wave field is induced as a self-excited oscillation of the structure by positively feed-backing the strain signal measured by a surface-bonded piezoelectric sensor, followed by a phase-shift in 90 degrees and a nonlinear element consisting of a saturation element and a negative linear gain. The induced self-excitation can have multiple stable limit cycles at certain eigenmode frequencies, and one can switch among them by inputting an auxiliary excitation signal into the feedback loop. The current flowing through the piezoelectric sensor is measured to detect its modulation due to the stiffness fluctuation due to the existence of the contact-type damage. Experiments using a specimen with a simulated damage are conducted to examine the performance of the self-excitation circuit and its applicability to the NPIM-based damage detection method.

scholarly journals High-frequency homogenization for travelling waves in periodic media

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160066 ◽  
Author(s):  
Davit Harutyunyan ◽  
Graeme W. Milton ◽  
Richard V. Craster
Keyword(s):  
Wave Equation ◽  
High Frequency ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Coupling Constants ◽  
Convergence Theory ◽  
Periodicity Cell ◽  
Periodic Media ◽  
Carrier Wave ◽  
Convergence Type

We consider high-frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schrödinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wavevector k and frequency ω 1 plus a modulated Bloch carrier wave having crystal wavevector m and frequency ω 2 . We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless ω 1 = ω 2 and ( k − m ) ⊙ Λ ∈ 2 π Z d , where Λ =(λ 1 λ 2 …λ d ) is the periodicity cell of the medium and for any two vectors a = ( a 1 , a 2 , … , a d ) , b = ( b 1 , b 2 , … , b d ) ∈ R d , the product a ⊙ b is defined to be the vector ( a 1 b 1 , a 2 b 2 ,…, a d b d ). This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigour as that of Allaire and co-workers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.

Sign in / Sign up

Export Citation Format

Share Document