Reconstruction of small interface changes of an inclusion from modal measurements II: The elastic case

被引：33

作者：

Ammari, Habib ^{[1
,2
]}

Beretta, Elena ^{[3
]}

Francini, Elisa ^{[4
]}

Kang, Hyeonbae ^{[5
]}

Lim, Mikyoung ^{[6
]}

机构：

[1] CNRS, Ctr Math Appl, UMR 7641, F-91128 Palaiseau, France

[2] Ecole Polytech, F-91128 Palaiseau, France

[3] Univ Roma La Sapienza, Dipartimento Matemat G Castelnuovo, I-00185 Rome, Italy

[4] Univ Firenze Ulisse Dini, Dipartimento Matemat, I-50134 Florence, Italy

[5] Inha Univ, Dept Math, Inchon 402751, South Korea

[6] Korea Adv Inst Sci & Technol, Dept Math Sci, Taejon 305701, South Korea

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2010年 / 94卷 / 03期

关键词：

Reconstruction; Elastic inclusion; Interface changes; Eigenvalue problem; Modal measurements;

D O I：

10.1016/j.matpur.2010.02.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In order to reconstruct small changes in the interface of an elastic inclusion from modal measurements, we rigorously derive an asymptotic formula which is in some sense dual to the leading-order term in the asymptotic expansion of the perturbations in the eigenvalues due to interface changes of the inclusion. Based on this (dual) formula we propose an algorithm to reconstruct the interface perturbation. We also consider an optimal way of representing the interface change and the reconstruction problem using incomplete data. A discussion on resolution is included. Proposed algorithms are implemented numerically to show their viability. (C) 2010 Elsevier Masson SAS. All rights reserved.

引用

页码：322 / 339

页数：18

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