Leading and Second Order Homogenization of an Elastic Scattering Problem for Highly Oscillating Anisotropic Medium

We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic equation that describes the wave propagation of the effective or...

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Bibliographic Details
Published inJournal of elasticity Vol. 137; no. 2; pp. 177 - 217
Main Authors Lin, Yi-Hsuan, Meng, Shixu
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2019
Subjects
Automotive Engineering
Classical Mechanics
Physics
Physics and Astronomy
35B27
Periodic media
Two-scale homogenization
74J20
74B05
Second-order homogenization
Elastic scattering
Wave dispersion
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Summary:We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic equation that describes the wave propagation of the effective or overall wave field. We further pursue a higher-order homogenization with the help of complimentary boundary correctors and provide a detailed analysis on the rate of higher-order convergence. Finally we provide preliminary numerical examples to demonstrate the higher-order homogenization.
ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-019-09725-z