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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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Vibration Testing

Vibration Testing

Chapter:
(p.168) Chapter Eleven Vibration Testing
Source:
Mathematical Methods in Elasticity Imaging
Author(s):

Habib Ammari

Elie Bretin

Josselin Garnier

Hyeonbae Kang

Hyundae Lee

Abdul Wahab

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691165318.003.0012

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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