### 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 language | English (US) |
---|---|

Pages (from-to) | 2143-2181 |

Number of pages | 39 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 60 |

Issue number | 6 |

DOIs | |

State | Published - May 2000 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*60*(6), 2143-2181. https://doi.org/10.1137/S0036139998342818

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

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 60, no. 6, pp. 2143-2181. https://doi.org/10.1137/S0036139998342818

}

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

VL - 60

SP - 2143

EP - 2181

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 6

ER -