Frequency-dependent acoustics of composites with interfaces

Marco Avellaneda, L. Berlyand, J. F. Clouet

Research output: Contribution to journalArticle

Abstract

We study the scattering of an incident wave by a composite medium with periodic microstructure in a slab geometry. We compute the expansion on the wave field in powers of the parameter ε = dλ, where d is the characteristic scale of the microstructure and λ is the wavelength. For ε = 0 this corresponds to homogenization theory. Here, we focus on the correction terms for ε>0 and compute the frequency-dependent impedance and the energy reflection coefficient as functions of ε, the material properties, and the volume fraction. This is used to describe the shape and amplitude of a transmitted or reflected pulse signal.

Original languageEnglish (US)
Pages (from-to)2143-2181
Number of pages39
JournalSIAM Journal on Applied Mathematics
Volume60
Issue number6
DOIs
StatePublished - May 2000

Fingerprint

Microstructure
Acoustics
Composite
Composite Media
Homogenization Theory
Dependent
Reflection Coefficient
Composite materials
Volume Fraction
Material Properties
Impedance
Volume fraction
Materials properties
Scattering
Wavelength
Geometry
Term
Energy

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Frequency-dependent acoustics of composites with interfaces. / Avellaneda, Marco; Berlyand, L.; Clouet, J. F.

In: SIAM Journal on Applied Mathematics, Vol. 60, No. 6, 05.2000, p. 2143-2181.

Research output: Contribution to journalArticle

Avellaneda, Marco ; Berlyand, L. ; Clouet, J. F. / Frequency-dependent acoustics of composites with interfaces. In: SIAM Journal on Applied Mathematics. 2000 ; Vol. 60, No. 6. pp. 2143-2181.
@article{58b6ebc973f44eec81aafe9f1e88bdc1,
title = "Frequency-dependent acoustics of composites with interfaces",
abstract = "We study the scattering of an incident wave by a composite medium with periodic microstructure in a slab geometry. We compute the expansion on the wave field in powers of the parameter ε = dλ, where d is the characteristic scale of the microstructure and λ is the wavelength. For ε = 0 this corresponds to homogenization theory. Here, we focus on the correction terms for ε>0 and compute the frequency-dependent impedance and the energy reflection coefficient as functions of ε, the material properties, and the volume fraction. This is used to describe the shape and amplitude of a transmitted or reflected pulse signal.",
author = "Marco Avellaneda and L. Berlyand and Clouet, {J. F.}",
year = "2000",
month = "5",
doi = "10.1137/S0036139998342818",
language = "English (US)",
volume = "60",
pages = "2143--2181",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "6",

}

TY - JOUR

T1 - Frequency-dependent acoustics of composites with interfaces

AU - Avellaneda, Marco

AU - Berlyand, L.

AU - Clouet, J. F.

PY - 2000/5

Y1 - 2000/5

N2 - We study the scattering of an incident wave by a composite medium with periodic microstructure in a slab geometry. We compute the expansion on the wave field in powers of the parameter ε = dλ, where d is the characteristic scale of the microstructure and λ is the wavelength. For ε = 0 this corresponds to homogenization theory. Here, we focus on the correction terms for ε>0 and compute the frequency-dependent impedance and the energy reflection coefficient as functions of ε, the material properties, and the volume fraction. This is used to describe the shape and amplitude of a transmitted or reflected pulse signal.

AB - We study the scattering of an incident wave by a composite medium with periodic microstructure in a slab geometry. We compute the expansion on the wave field in powers of the parameter ε = dλ, where d is the characteristic scale of the microstructure and λ is the wavelength. For ε = 0 this corresponds to homogenization theory. Here, we focus on the correction terms for ε>0 and compute the frequency-dependent impedance and the energy reflection coefficient as functions of ε, the material properties, and the volume fraction. This is used to describe the shape and amplitude of a transmitted or reflected pulse signal.

UR - http://www.scopus.com/inward/record.url?scp=0034479398&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034479398&partnerID=8YFLogxK

U2 - 10.1137/S0036139998342818

DO - 10.1137/S0036139998342818

M3 - Article

AN - SCOPUS:0034479398

VL - 60

SP - 2143

EP - 2181

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 6

ER -