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Mathematical Methods in Elasticity Imaging$
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Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

Print publication date: 2015

Print ISBN-13: 9780691165318

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691165318.001.0001

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PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 17 May 2022

Vibration Testing

Vibration Testing

(p.168) Chapter Eleven Vibration Testing
Mathematical Methods in Elasticity Imaging

Habib Ammari

Elie Bretin

Josselin Garnier

Hyeonbae Kang

Hyundae Lee

Abdul Wahab

Princeton University Press

This chapter deals with vibration testing, which aims to identify inclusions, cracks, or shape changes in a structure by measuring its modal characteristics. The measured eigenparameters are related to the defect or damage location, orientation, and size. The chapter derives asymptotic formulas for eigenvalue perturbations due to small inclusions, cracks, and shape deformations. The main ingredients in deriving the results are the integral equations and the theory of meromorphic operator-valued functions. Using integral representations of solutions to the harmonic oscillatory linear elastic equation, this problem is reduced to the study of characteristic values of integral operators in the complex planes. The chapter focuses on three kinds of elastic inclusions: holes, hard inclusions, and soft inclusions.

Keywords:   vibration testing, crack, small inclusion, shape deformation, operator-valued function, elastic inclusion, hole, hard inclusions, soft inclusion, elastic equation

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