Mathematical methods in elasticity imaging / Habib Ammari, Abdul Wahab, Hyundae Lee, Elie Bretin, Josselin Garnier, Hyeonbae Kang.

Format:

Book

Author/Creator:

Ammari, Habib, author.

Bretin, Elie, author.

Garnier, Josselin, author.

Lee, Hyundae, author.

Wahab, Abdul, author.

Series:

Princeton series in applied mathematics.

Princeton Series in Applied Mathematics ; 52

Language:

English

Subjects (All):

Elasticity--Mathematics.

Elasticity.

Physical Description:

1 online resource (240 p.)

Place of Publication:

Princeton, NJ : Princeton University Press, [2015]

Language Note:

English

Summary:

This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.

Contents:

Frontmatter

Contents

Introduction

Chapter One. Layer Potential Techniques

Chapter Two. Elasticity Equations with High Contrast Parameters

Chapter Three. Small-Volume Expansions of the Displacement Fields

Chapter Four. Boundary Perturbations due to the Presence of Small Cracks

Chapter Five. Backpropagation and Multiple Signal Classification Imaging of Small Inclusions

Chapter Six. Topological Derivative Based Imaging of Small Inclusions in the Time-Harmonic Regime

Chapter Seven. Stability of Topological Derivative Based Imaging Functionals

Chapter Eight. Time-Reversal Imaging of Extended Source Terms

Chapter Nine. Optimal Control Imaging of Extended Inclusions

Chapter Ten. Imaging from Internal Data

Chapter Eleven. Vibration Testing

Appendix A. Introduction to Random Processes

Appendix B. Asymptotics of the Attenuation Operator

Appendix C. The Generalized Argument Principle and Rouché's Theorem

References

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400866625

1400866626

OCLC:

904686860