Guided Waves in Structures for SHM E-Book

Wieslaw Ostachowicz

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 352

Veröffentlichungsjahr: 2011

Beschreibung

Understanding and analysing the complex phenomena related to elastic wave propagation has been the subject of intense research for many years and has enabled application in numerous fields of technology, including structural health monitoring (SHM). In the course of the rapid advancement of diagnostic methods utilising elastic wave propagation, it has become clear that existing methods of elastic wave modeling and analysis are not always very useful; developing numerical methods aimed at modeling and analysing these phenomena has become a necessity. Furthermore, any methods developed need to be verified experimentally, which has become achievable with the advancement of measurement methods utilising laser vibrometry.

Guided Waves in Structures for SHM reports on the simulation, analysis and experimental investigation related propagation of elastic waves in isotropic or laminated structures. The full spectrum of theoretical and practical issues associated with propagation of elastic waves is presented and discussed in this one study.

Key features:

• Covers both numerical and experimental aspects of modeling, analysis and measurement of elastic wave propagation in structural elements formed from isotropic or composite materials
• Comprehensively discusses the application of the Spectral Finite Element Method for modelling and analysing elastic wave propagation in diverse structural elements
• Presents results of experimental measurements employing advanced laser technologies, validating the quality and correctness of the developed numerical models
• Accompanying website (www.wiley.com/go/ostachowicz) contains demonstration versions of commercial software developed by the authors for modelling and analyzing elastic wave propagation using the Spectral Finite Element Method

Guided Waves in Structures for SHM provides a state of the art resource for researchers and graduate students in structural health monitoring, signal processing and structural dynamics. This book should also provide a useful reference for practising engineers within structural health monitoring and non-destructive testing.

Leseprobe

Contents

Cover

Title Page

Copyright

Preface

1: Introduction to the Theory of Elastic Waves

1.1 Elastic waves

1.2 Basic Definitions

1.3 Bulk Waves in Three-Dimensional Media

1.4 Plane Waves

1.5 Wave Propagation in One-Dimensional Bodies of Circular Cross-Section

2: Spectral Finite Element Method

2.1 Shape Functions in the Spectral Finite Element Method

2.2 Approximating Displacement, Strain and Stress Fields

2.3 Equations of Motion of a Body Discretised Using Spectral Finite Elements

2.4 Computing Characteristic Matrices of Spectral Finite Elements

2.5 Solving Equations of Motion of a Body Discretised Using Spectral Finite Elements

3: Three-Dimensional Laser Vibrometry

3.1 Review of Elastic Wave Generation Methods

3.2 Review of Elastic Wave Registration Methods

3.3 Laser Vibrometry

3.4 Analysis of Methods of Elastic Wave Generation and Registration

3.5 Exemplary Results of Research on Elastic Wave Propagation Using 3D Laser Scanning Vibrometry

4: One-Dimensional Structural Elements

4.1 Theories of Rods

4.2 Displacement Fields of Structural Rod Elements

4.3 Theories of Beams

4.4 Displacement Fields of Structural Beam Elements

4.5 Dispersion Curves

4.6 Certain Numerical Considerations

4.7 Examples of Numerical Calculations

5: Two-Dimensional Structural Elements

5.1 Theories of Membranes, Plates and Shells

5.2 Displacement Fields of Structural Membrane Elements

5.3 Displacement Fields of Structural Plate Elements

5.4 Displacement Fields of Structural Shell Elements

5.5 Certain Numerical Considerations

5.6 Examples of Numerical Calculations

6: Three-Dimensional Structural Elements

6.1 Solid Spectral Elements

6.2 Displacement Fields of Solid Structural Elements

6.3 Certain Numerical Considerations

6.4 Modelling Electromechanical Coupling

6.5 Examples of Numerical Calculations

6.6 Modelling the Bonding Layer

7: Detection, Localisation and Identification of Damage by Elastic Wave Propagation

7.1 Elastic Waves in Structural Health Monitoring

7.2 Methods of Damage Detection, Localisation and Identification

7.3 Examples of Damage Localisation Methods

Appendix: EWavePro Software

A.1 Introduction

A.2 Theoretical Background and Scope of Applicability (Computation Module)

A.3 Functional Structure and Software Environment (Pre- and Post-Processors)

A.4 Elastic Wave Propagation in a Wing Skin of an Unmanned Plane (UAV)

A.5 Elastic Wave Propagation in a Composite Panel

Index

This edition first published 2012 © 2012 John Wiley & Sons Ltd.

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Library of Congress Cataloging-in-Publication Data:

Guided waves in structures for SHM : the time-domain spectral element method / [edited by] Wieslaw Ostachowicz . . . [et al.]. p. cm. Includes bibliographical references and index. ISBN 978-0-470-97983-9 (hardback) 1. Elastic analysis (Engineering) 2. Elastic wave propagation-Mathematical models. 3. Composite materials-Analysis. 4. Finite element method. I. Ostachowicz, W. M. (Wieslaw M.) TA653.G85 2012 531'.1133–dc23 2011043928

A catalogue record for this book is available from the British Library.

Print ISBN: 978-0-470-97983-9; oBook 9781119965855; ePDF 9781119965862; ePub 9781119966746; Mobi 9781119966753

Preface

This book is aimed at professionals whose scientific interests are directly associated with propagation of elastic waves in structural elements. This book may be useful not only for students of technical universities but also for researchers and engineers who solve practical problems involving propagation of elastic waves in structural elements made of isotropic materials or laminated composites.

Waves propagating in elastic media have been known for many centuries and have been the subject of scientific research of many scholars. Elastic waves result from stresses acting within the media and are associated with volume (compression and tension) and shape (shear) deformations. Better recognition and understanding of the complex phenomena behind the propagation of elastic waves in structural elements have promoted various novel and practical applications in many fields of technology. One such field is diagnostics of structural elements, where the use of elastic waves increases rapidly each year. Local methods employing elastic waves have been employed successfully for many years, but attempts to apply elastic waves in a global sense for diagnosing structural elements are still at an early stage of development. The measure of success in these attempts comes from various achievements made in parallel in several different fields. The first of them is the development of numerical simulation methods and tools aimed at modelling and analysing the phenomena associated with propagation of elastic waves in structural elements. The second, independent, one is the development of appropriate experimental methods and techniques allowing verification and validation results of numerical simulations. Recently these goals have become achievable in practice thanks to employing the most advanced measuring techniques based on three-dimensional (3D) laser scanning vibrometry.

This book is intended to report on the challenges associated with numerical simulation methods, analyses and experimental investigations related to the propagation of elastic waves in structural elements made of isotropic materials or composite laminates. For the first time the full spectrum of theoretical and practical issues associated with the propagation of elastic waves are presented and discussed in one study.

The first part of the book, devoted to various modelling and analysis issues associated with propagation of elastic waves, is focused on the Spectral Finite Element Method, which in the authors’ opinion is the most suitable modelling technique out of a variety of numerical methods used nowadays to solve wave propagation-related problems. This part of the book gives a broad overview of the existing state of the art and knowledge concerning modelling of elastic wave propagation in structural elements, while emphasising the problems associated with developing efficient numerical methods and tools and verifying them. Original solutions developed by the authors, suitable for constructing appropriate numerical models for simulating propagation of elastic waves in 1D, 2D and 3D structural elements made of isotropic and laminated composites are presented and discussed. Based on the developed spectral finite elements, a range of numerical tests has been carried out in order to verify the accuracy of the models, beginning from wave propagation in simple rods, beams, membranes and plates, and ending with shells or 3D structures.

The second part of the book, devoted to experimental measurements, presents the application of 3D laser scanning vibrometry for measuring, investigating and visualising the propagation of elastic waves in real-life structural elements. This part of the book naturally complements the theoretical and numerical investigations of the earlier part. Numerous scenarios and results of experimental measurements carried out on 1D, 2D and 3D structures are presented and discussed.

The last part of the book is concerned with various practical applications associated with wave propagation phenomena in structural elements. Problems of damage detection and location are discussed and investigated here. These problems are a part of a wide multidisciplinary research subject known as Structural Health Monitoring. Several damage detection methods developed or/and implemented by the authors and their practical applications in the context of Structural Health Monitoring are described in great detail, based on the results of either numerical or experimental investigations. The results of experimental studies included in this book make use of excitation and registration of elastic waves within structural elements using piezoelectric transducers. Additionally, and in parallel, independent registration of propagating elastic waves employs advanced 3D laser scanning vibrometry. These two techniques have been applied and investigated in order to qualitatively and quantitatively characterise the wave propagation phenomena.

The authors would like to underline the unique character of this book resulting from its complex and multidisciplinary character. Various acclaimed books dedicated to wave propagation phenomena in elastic media are usually theoretical in nature, while the question of appropriate verification of the developed numerical methods is addressed in a very limited manner. The authors of the studies mentioned often use analytical models of the wave propagation phenomena and/or apply different numerical methods based on either the finite element method or spectral methods in the frequency domain. The intention of the authors of this book is to present for the first time in one place new models of spectral finite elements defined in the time domain developed to facilitate analysis of propagation of elastic waves in structural elements. Originality of the material presented in this book comes from the attempt to connect together the results of both numerical and experimental investigations, as well as to indicate their practical implications. Until now, the original numerical models discussed in the book as well as the results of experimental studies using 3D laser scanning vibrometry have had no equivalents in published books dedicated to this field. Therefore the level of scientific research of this book, in the opinion of the authors, closely follows the latest trends in this area. It is worth noting that this book is accompanied by a demonstration version of software employing methods of analysing elastic wave propagation in structural elements using spectral finite elements. It should be emphasised that this software has been developed by the authors of this book.

Guided Waves in Structures for SHM: The Time-Domain Spectral Element Method is accompanied by a website (www.wiley.com/go/ostachowicz). The website contains and describes the EWavePro (Elastic WavePropagation) software, which can be used for analysing phenomena of propagation of longitudinal, shear and flexural waves in two and three–dimensional thin–walled structures composed of isotropic materials or composite laminates. The abbreviation EWavePro is used here to distinguish the software developed by the authors. The software is developed in order to facilitate better understanding of elastic wave propagation phenomena and to be used as a tool in designing structural health monitoring systems based on changes in the elastic wave propagation patterns.

The authors want to thank their colleagues from the Department of Mechanics of Intelligent Structures: Dr P. Malinowski, Dr M. Radzienski and Dr T. Wandowski for assistance with writing Chapters 3 and 7, as well as Dr L. Murawski for involvement in writing the Appendix. Their efforts contributed to the development of the mentioned parts of this book cannot be overstated.

1

Introduction to the Theory of Elastic Waves

1.1 Elastic waves

Elastic waves are mechanical waves propagating in an elastic medium as an effect of forces associated with volume deformation (compression and extension) and shape deformation (shear) of medium elements. External bodies causing these deformations are called wave sources. Elastic wave propagation involves exciting the movement of medium particles increasingly distant from the wave source. The main factor differentiating elastic waves from any other ordered motion of medium particles is that for small disturbances (linear approximation) elastic wave propagation does not result in matter transport.

Depending on restrictions imposed on the elastic medium, wave propagation may vary in character. Bulk waves propagate in infinite media. Within the class of bulk waves one can distinguish longitudinal waves (compressional waves) and shear waves. A three-dimensional medium bounded by one surface allows for propagation of surface waves (Rayleigh waves and Love waves). Propagation of bulk waves and surface waves is used for describing seismic wave phenomena. Bounding the elastic medium with two equidistant surfaces causes compressional waves and shear waves to interact, which results in the generation of Lamb waves. One can say that a free boundary restricting an elastic body guides and drives waves; therefore the term guided waves is also used. Lamb waves and guided waves are used in broadly considered diagnostics and nondestructive testing. There are also waves that propagate on media boundary (interface waves) with names derived from their discoverers: in the interface between two solids Stoneley waves propagate, while in the one between a solid and a liquid Scholte waves propagate.

Figure 1.1 Distribution of displacements for the horizontal shear wave

1.1.1 Longitudinal Waves (Compressional/Pressure/ Primary/P Waves)

Longitudinal waves are characterised by particle motion alternately of compression and stretching character. The direction of medium point motion is parallel to the direction of wave propagation (i.e. longitudinal).

1.1.2 Shear Waves (Transverse/Secondary/S Waves)

Shear waves are characterised by transverse particle movements in alternating direction. The direction of medium particle motion is perpendicular to the propagation direction (transverse). The transverse particle movement can occur horizontally (horizontal shear wave, SH; see Figure 1.1) or vertically (vertical shear wave, SV; see Figure 1.2).

Figure 1.2 Distribution of displacements for the vertical shear wave

1.1.3 Rayleigh Waves

Rayleigh waves (Figure 1.3) are characterised by particle motion composed of elliptical movements in the xy vertical plane and of motion parallel to the direction of propagation (along the x axis). Wave amplitude decreases with depth y, starting from the wave crest. Rayleigh waves propagate along surfaces of elastic bodies of thickness many times exceeding the wave height. Sea waves are a natural example of Rayleigh waves.