Asymptotic analysis of Bloch-Floquet waves in a thin bi-material strip with a periodic array of finite-length cracks

Gennady Mishuris; A. B. Movchan; J. P. Bercial

doi:10.1080/17455030701288137

Asymptotic analysis of Bloch-Floquet waves in a thin bi-material strip with a periodic array of finite-length cracks

Gennady Mishuris, A. B. Movchan, J. P. Bercial

Department of Physics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We present an asymptotic algorithm to solve a problem of wave propagation in a thin bi-material strip with an array of cracks situated at the interface between two materials. For small frequencies we construct an asymptotic solution which takes into account the singular behavior near the crack tips and the smooth nature of the oscillation far away from them. We construct the boundary layer solutions near the crack tips. The boundary layers are harmonic solutions in scaled domains. Dispersion equations are derived and solved within the frame of the asymptotic model.

Original language	English
Pages (from-to)	511-533
Number of pages	23
Journal	Waves in Random and Complex Media
Volume	17
Issue number	4
DOIs	https://doi.org/10.1080/17455030701288137
Publication status	Published - 2007

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http://hdl.handle.net/2160/3324

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title = "Asymptotic analysis of Bloch-Floquet waves in a thin bi-material strip with a periodic array of finite-length cracks",

abstract = "We present an asymptotic algorithm to solve a problem of wave propagation in a thin bi-material strip with an array of cracks situated at the interface between two materials. For small frequencies we construct an asymptotic solution which takes into account the singular behavior near the crack tips and the smooth nature of the oscillation far away from them. We construct the boundary layer solutions near the crack tips. The boundary layers are harmonic solutions in scaled domains. Dispersion equations are derived and solved within the frame of the asymptotic model.",

author = "Gennady Mishuris and Movchan, {A. B.} and Bercial, {J. P.}",

note = "Mishuris, GS; Movchan, AB; Bercial, JP. Asymptotic analysis of Bloch-Floquet waves in a thin bi-material strip with a periodic array of finite-length cracks. Waves in Random and Complex Media. 2007, 17(4), 511-533",

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T1 - Asymptotic analysis of Bloch-Floquet waves in a thin bi-material strip with a periodic array of finite-length cracks

AU - Mishuris, Gennady

AU - Movchan, A. B.

AU - Bercial, J. P.

N1 - Mishuris, GS; Movchan, AB; Bercial, JP. Asymptotic analysis of Bloch-Floquet waves in a thin bi-material strip with a periodic array of finite-length cracks. Waves in Random and Complex Media. 2007, 17(4), 511-533

PY - 2007

Y1 - 2007

N2 - We present an asymptotic algorithm to solve a problem of wave propagation in a thin bi-material strip with an array of cracks situated at the interface between two materials. For small frequencies we construct an asymptotic solution which takes into account the singular behavior near the crack tips and the smooth nature of the oscillation far away from them. We construct the boundary layer solutions near the crack tips. The boundary layers are harmonic solutions in scaled domains. Dispersion equations are derived and solved within the frame of the asymptotic model.

AB - We present an asymptotic algorithm to solve a problem of wave propagation in a thin bi-material strip with an array of cracks situated at the interface between two materials. For small frequencies we construct an asymptotic solution which takes into account the singular behavior near the crack tips and the smooth nature of the oscillation far away from them. We construct the boundary layer solutions near the crack tips. The boundary layers are harmonic solutions in scaled domains. Dispersion equations are derived and solved within the frame of the asymptotic model.

U2 - 10.1080/17455030701288137

DO - 10.1080/17455030701288137

M3 - Article

SN - 1745-5049

VL - 17

SP - 511

EP - 533

JO - Waves in Random and Complex Media

JF - Waves in Random and Complex Media

IS - 4

ER -

Asymptotic analysis of Bloch-Floquet waves in a thin bi-material strip with a periodic array of finite-length cracks

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