Lammering / Gabbert / Sinapius Lamb-Wave Based Structural Health Monitoring in Polymer Composites

1. Auflage 2018
ISBN: 978-3-319-49715-0
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 476 Seiten

Reihe: Research Topics in Aerospace

The book focuses especially on the application of SHM technology to thin walled structural systems made from carbon fiber reinforced plastics. Here, guided elastic waves (Lamb-waves) show an excellent sensitivity to structural damages so that they are in the center of this book. It is divided into 4 sections dealing with analytical, numerical and experimental fundamentals, and subsequently with Lamb-wave propagation in fiber reinforced composites, SHM-systems and signal processing. The book is designed for engineering students as well as for researchers in the field of structural health monitoring and for users of this technology.

Autoren/Hrsg.

Lammering, Rolf

Gabbert, Ulrich

Sinapius, Michael

Schuster, Thomas

Wierach, Peter

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Part I Introduction;16
3.1;1 Motivation;17
3.1.1;1.1 Why Structural Health Monitoring?;17
3.1.2;1.2 What Should a SHM System Be Capable of?;19
3.1.3;1.3 What is the Foundation of the SHM Research Presented?;19
3.1.4;1.4 What Are the Challenges?;22
3.1.5;References;23
3.2;2 Objectives;24
4;Part II Foundations;27
4.1;3 Wave Propagation in Elastic Solids: An Analytical Approach;28
4.1.1;3.1 Introduction;28
4.1.2;3.2 Isotropic Solids;30
4.1.2.1;3.2.1 Lamé–Navier Equations;30
4.1.2.2;3.2.2 Waves in Infinite Solids;30
4.1.2.3;3.2.3 Waves in Thin-Walled Solids;31
4.1.2.3.1;3.2.3.1 Stress Boundary Conditions;35
4.1.2.3.2;3.2.3.2 Rayleigh–Lamb Wave Equation;36
4.1.2.3.3;3.2.3.3 Determination of the Displacement Field;37
4.1.2.3.4;3.2.3.4 Group Velocity;38
4.1.3;3.3 Anisotropic Solids;39
4.1.3.1;3.3.1 General Fundamentals;39
4.1.3.2;3.3.2 Wave Propagation Without Decoupling of Lamb Waves and Shear Horizontal Waves;41
4.1.3.2.1;Dispersion Relation;45
4.1.3.3;3.3.3 Wave Propagation with Decoupling of Lamb Waves and Shear Horizontal Waves;46
4.1.3.3.1;3.3.3.1 Dispersion Relation;49
4.1.4;3.4 Layered Anisotropic Solids;51
4.1.4.1;3.4.1 Transfer-Matrix Method;52
4.1.4.1.1;Separation of the Symmetric and Antisymmetric Wave Modes;55
4.1.4.2;3.4.2 Global-Matrix Method;58
4.1.4.2.1;Separation of the Symmetric and Antisymmetric Wave Modes;60
4.1.4.3;3.4.3 Stiffness-Matrix Method;60
4.1.4.3.1;Dispersion of a Quasi-Isotropic Specimen;63
4.1.4.3.2;3.4.3.1 Summary;64
4.1.5;Appendix 1: Characteristic Polynomial of the Christoffel Equation;65
4.1.6;Appendix 2: Summary of Stresses and Displacements of a Single Anisotropic Layer in a System of Equations;66
4.1.7;Appendix 3: Separated Dispersion Relations for the Symmetric and Antisymmetric Wave Modes;69
4.1.8;References;72
4.2;4 Fundamental Principles of the Finite Element Method;74
4.2.1;4.1 Governing Equations;74
4.2.2;4.2 Constitutive Equations;76
4.2.3;4.3 Weak Form of the Equations of Motion;77
4.2.4;4.4 Finite Element Equations;79
4.2.5;4.5 h-Version of the Finite Element Method;86
4.2.6;4.6 Time-Integration Methods;87
4.2.6.1;4.6.1 Explicit Time Integration: Central Difference Method;88
4.2.6.2;4.6.2 Implicit Time Integration: Newmark Method;90
4.2.6.3;4.6.3 Mass Lumping Techniques;93
4.2.6.3.1;4.6.3.1 Nodal Quadrature Technique;93
4.2.6.3.2;4.6.3.2 Row Sum Technique;94
4.2.6.3.3;4.6.3.3 Diagonal Scaling: HRZ Lumping Technique;95
4.2.7;4.7 Geometry Approximation;95
4.2.7.1;4.7.1 Subparametric Mapping;96
4.2.7.2;4.7.2 Isoparametric Mapping;97
4.2.7.3;4.7.3 Superparametric Mapping;98
4.2.7.3.1;4.7.3.1 Blending Function Method;98
4.2.8;References;100
4.3;5 Experimental Methods;102
4.3.1;5.1 Requirements for a Measurement System for High-Resolution Wave Field Recording of Lamb Waves;102
4.3.1.1;5.1.1 Measurement Principle;103
4.3.1.2;5.1.2 Flexibility;104
4.3.1.3;5.1.3 Speed;104
4.3.2;5.2 Ultrasonic Scanning Technique;104
4.3.3;5.3 Imaging Methods;106
4.3.4;5.4 3D Laser Vibrometry;108
4.3.4.1;5.4.1 Description of the Measurement Platform;108
4.3.4.2;5.4.2 Determining the Three-Dimensional Displacement;111
4.3.4.3;5.4.3 Sensitivity of In-Plane Displacement Measurements;114
4.3.5;5.5 Conclusion;121
4.3.6;References;122
5;Part III Efficient Numerical Methods for Wave Propagation Analysis;123
5.1;References;124
5.2;6 Higher Order Finite Element Methods;126
5.2.1;6.1 Higher Order Finite Element Methods: One-Dimensional Case;126
5.2.1.1;6.1.1 p-Version of the Finite Element Method;127
5.2.1.2;6.1.2 The Spectral Element Method;129
5.2.1.3;6.1.3 The Isogeometric Analysis;133
5.2.1.3.1;6.1.3.1 B-Spline Curve;133
5.2.1.3.2;6.1.3.2 Nonuniform Rational B-Spline Curve;134
5.2.2;6.2 Comparison of the Properties of Different Higher Order Finite Element Approaches;136
5.2.2.1;6.2.1 Hierarchic Basis Functions;136
5.2.2.2;6.2.2 Nodal Basis Functions;137
5.2.3;6.3 Multivariate Basis Functions;138
5.2.4;6.4 Benchmark Problems;138
5.2.4.1;6.4.1 p-FEM: Modal Analysis of a Three-Dimensional Piezoelectric Disc;139
5.2.4.1.1;6.4.1.1 Short-Circuited Electrodes;140
5.2.4.1.2;6.4.1.2 Open Electrodes;140
5.2.4.1.3;6.4.1.3 Eigenfrequencies and Mode Shapes of a Circular Disc;141
5.2.4.2;6.4.2 Spectral Element Method: Wave Propagation Analysis in a Two-Dimensional Porous Plate;144
5.2.4.3;6.4.3 Isogeometric Analysis: Wave Propagation Analysis in a Three-Dimensional Perforated Plate;151
5.2.5;6.5 Convergence Studies;153
5.2.5.1;6.5.1 Numerical Model;153
5.2.5.2;6.5.2 Signal Analysis;155
5.2.5.3;6.5.3 Polynomial Degree in x1;155
5.2.5.4;6.5.4 Polynomial Degree in x2;156
5.2.6;6.6 Industrial Applications;160
5.2.6.1;6.6.1 Stiffened Composite Plate;160
5.2.6.2;6.6.2 Rotor Blade of a Wind Turbine;163
5.2.7;References;165
5.3;7 Hybrid Simulation Methods: Combining Finite Element Methods and Analytical Solutions;169
5.3.1;7.1 The Semi-Analytical Finite Element Method;169
5.3.1.1;7.1.1 Motivation;170
5.3.1.2;7.1.2 Theoretical Principles;170
5.3.1.3;7.1.3 Plate with Infinite Dimensions;174
5.3.1.4;7.1.4 Dispersion Curves for Undamped Media;176
5.3.1.4.1;7.1.4.1 Phase and Group Velocities of Guided Waves;178
5.3.1.4.2;7.1.4.2 Verification;179
5.3.1.5;7.1.5 Interaction of Guided Waves with Perturbations;182
5.3.1.5.1;7.1.5.1 General approach;182
5.3.1.5.2;7.1.5.2 Verification;184
5.3.1.6;7.1.6 Force Response Analysis;187
5.3.1.6.1;7.1.6.1 General approach;187
5.3.1.6.2;7.1.6.2 Verification;188
5.3.1.7;7.1.7 Summary;190
5.3.2;7.2 Coupling of Analytical Solutions and the Spectral Element Method in the Frequency Domain;190
5.3.2.1;7.2.1 Motivation;190
5.3.2.2;7.2.2 Definition of the Problem;191
5.3.2.3;7.2.3 Analytical Solution to the Wave Propagation Problem in Isotropic Plates;193
5.3.2.3.1;7.2.3.1 Analytical Approach;193
5.3.2.3.2;7.2.3.2 Two-Dimensional Problem;194
5.3.2.4;7.2.4 Coupling Boundary Conditions;199
5.3.2.5;7.2.5 Numerical Results;200
5.3.3;References;203
5.4;8 Damping Boundary Conditions for a Reduced Solution Domain Size and Effective Numerical Analysis of HeterogeneousWaveguides;207
5.4.1;8.1 Objective;207
5.4.2;8.2 Non-reflecting Boundary Conditions;209
5.4.2.1;8.2.1 Basic Principles;210
5.4.2.1.1;8.2.1.1 Damping Factor;212
5.4.2.1.2;8.2.1.2 Direction of Dashpot Elements;213
5.4.2.1.3;8.2.1.3 Number of Dashpot Element Layers;214
5.4.2.2;8.2.2 Numerical Example;215
5.4.3;8.3 Parametric Studies of Wave Propagation in Cellular Materials;217
5.4.3.1;8.3.1 Sandwich Panel with a Foam Core;217
5.4.3.1.1;8.3.1.1 Numerical Model;217
5.4.3.1.2;8.3.1.2 Influence of the Excitation Frequency;219
5.4.3.1.3;8.3.1.3 Influence of Geometrical Dimensions;219
5.4.3.2;8.3.2 Sandwich Panel with a Honeycomb Core;220
5.4.3.2.1;8.3.2.1 Numerical Model;220
5.4.3.2.2;8.3.2.2 Influence of the Excitation Frequency;221
5.4.3.2.3;8.3.2.3 Influence of Geometrical Dimensions;221
5.4.4;References;223
5.5;9 The Finite Cell Method: A Higher Order Fictitious Domain Approach for Wave Propagation Analysis in Heterogeneous Structures;225
5.5.1;9.1 Motivation;225
5.5.2;9.2 Fictitious Domain Concept;228
5.5.3;9.3 Finite Cell Equations;230
5.5.4;9.4 Numerical Integration;232
5.5.4.1;9.4.1 Adaptive Quadrature Scheme;232
5.5.4.2;9.4.2 Improved Integration Algorithms;235
5.5.5;9.5 Geometry Description;237
5.5.5.1;9.5.1 Implicit Functions;237
5.5.5.2;9.5.2 Boundary Representation (B-Rep);238
5.5.5.3;9.5.3 CT-Scan;238
5.5.6;9.6 Numerical Results: Wave Propagation Analysis in a Two-Dimensional Porous Plate;239
5.5.7;9.7 Note on the Extension to Unstructured Discretizations;244
5.5.8;References;245
5.6;10 A Minimal Model for Fast Approximation of Lamb Wave Propagation in Complex Aircraft Parts;248
5.6.1;10.1 Lamb Wave Simulation and Its Applications;248
5.6.2;10.2 Minimal Model;250
5.6.2.1;10.2.1 Interaction of Lamb Waves with Discontinuities;251
5.6.2.2;10.2.2 Ray Tracing;253
5.6.2.3;10.2.3 Signal Synthesis;256
5.6.3;10.3 Experimental Results and Comparison;258
5.6.3.1;10.3.1 Aluminum Plate;259
5.6.3.2;10.3.2 Aluminum Plate with Cutout;262
5.6.4;10.4 Discussion;264
5.6.5;10.5 Conclusion;266
5.6.6;References;266
6;Part IV Continuous Mode Conversion;269
6.1;11 Continuous Mode Conversion in Experimental Observations;270
6.1.1;11.1 Mode Conversion in Polymer Composites;270
6.1.2;11.2 Occurrence and Characteristics of Continuous ModeConversion;272
6.1.2.1;11.2.1 CFRP Plates Made of Unidirectional Layers;272
6.1.2.2;11.2.2 CFRP Plates Made of Woven Layers;273
6.1.3;11.3 Physical Reasons of Continuous Mode Conversion in Woven Layers;274
6.1.3.1;11.3.1 Experimental Tensile Tests;274
6.1.3.2;11.3.2 Finite Element Modeling;276
6.1.3.3;11.3.3 Numerical Tensile Tests;277
6.1.3.4;11.3.4 Lamb Wave Simulation;278
6.1.3.5;11.3.5 Frequency Dependence of Coupling-Induced Mode Conversion;279
6.1.4;11.4 Conclusion;281
6.1.5;References;281
6.2;12 Material Modeling of Polymer Composites for Numerical Investigations of Continuous Mode Conversion;283
6.2.1;12.1 Analysis of the Wave Behavior in Simplified Models with Reference to the Continuous Mode Conversion;283
6.2.1.1;12.1.1 Aluminum Plates with Changes in Cross Section;285
6.2.1.1.1;12.1.1.1 Plate with Obstacles;285
6.2.1.1.2;12.1.1.2 Plate with Notches;287
6.2.1.1.3;12.1.1.3 Intermediate Results;289
6.2.1.2;12.1.2 Conventional Material Modeling of CFRP;289
6.2.1.2.1;12.1.2.1 General Rule of Mixture;290
6.2.1.2.2;12.1.2.2 Semiempirical Homogenization Method of Halpin and Tsai;291
6.2.1.3;12.1.3 Fiber–Matrix Models;291
6.2.1.4;12.1.4 Intermediate Results;294
6.2.2;12.2 Numerical Realization of the Continuous Mode ConversionEffect;295
6.2.2.1;12.2.1 Enhanced FE-Material Modeling of UD-Layers;295
6.2.2.2;12.2.2 Wave Propagation in UD-Layers Using the Enhanced FE-Material Modeling;297
6.2.3;12.3 Conclusion;299
6.2.4;References;301
7;Part V Signal Processing;302
7.1;13 Localization of Damaging Events and Damage in Anisotropic Plates by Migration Technique;303
7.1.1;13.1 Impact Localization;303
7.1.1.1;13.1.1 Migration Method for Isotropic Materials;303
7.1.1.2;13.1.2 Enhanced Migration Method for AnisotropicMaterials;305
7.1.1.2.1;13.1.2.1 Determination of the Wave Velocity;306
7.1.1.2.2;13.1.2.2 Determination by Experimental Data;306
7.1.1.2.3;13.1.2.3 Determination by Material Data;306
7.1.1.2.4;13.1.2.4 Parametrization of Wave Propagation;309
7.1.1.2.5;13.1.2.5 Formulation of the Enhanced Migration Method for Anisotropic Material;309
7.1.1.3;13.1.3 Solution Procedure;310
7.1.2;13.2 Damage Localization;311
7.1.3;13.3 Experimental Verification;312
7.1.3.1;13.3.1 Impact Localization;312
7.1.3.1.1;13.3.1.1 Experimental Setup;312
7.1.3.1.2;13.3.1.2 Shape of the Wave Front;313
7.1.3.1.3;13.3.1.3 Experimental Results and Data Analysis;314
7.1.3.1.4;13.3.1.4 Signal Analysis;314
7.1.3.1.5;13.3.1.5 Optimization;318
7.1.3.1.6;13.3.1.6 Results;318
7.1.3.1.7;13.3.1.7 Discussion of the Results;319
7.1.3.1.8;13.3.1.8 Influence of Time Resolution;321
7.1.3.1.9;13.3.1.9 Influence of the Wavelet Transform;321
7.1.3.1.10;13.3.1.10 Influence of the Reference Signal;322
7.1.3.1.11;13.3.1.11 Influence of the Number of Active Sensors;323
7.1.3.1.12;13.3.1.12 Quality of Results;324
7.1.3.2;13.3.2 Defect Localization;325
7.1.3.2.1;13.3.2.1 Experimental Setup;325
7.1.3.2.2;13.3.2.2 Determination of the Wave Propagation Pattern;327
7.1.3.2.3;13.3.2.3 Experimental Results and Evaluation;327
7.1.3.2.4;13.3.2.4 Results;328
7.1.3.2.5;13.3.2.5 Discussion of the Results;328
7.1.4;References;331
7.2;14 Time-of-Flight Calculation in Complex Structures;333
7.2.1;14.1 Requirements for Time-of-Flight Calculation;334
7.2.2;14.2 Algorithms for Time-of-Flight Calculation;336
7.2.2.1;14.2.1 Raytracing;336
7.2.2.2;14.2.2 Dijkstra Algorithm;337
7.2.2.3;14.2.3 Path Calculation in Segmented Areas;338
7.2.2.4;14.2.4 Bellman-Ford Algorithm;338
7.2.2.5;14.2.5 Floyd-Warshall Algorithm;339
7.2.2.6;14.2.6 Front Propagation Algorithms;339
7.2.3;14.3 Time-of-Flight Calculation for Lamb Waves in Complex Structures;340
7.2.3.1;14.3.1 Discretization of the Structure;341
7.2.3.2;14.3.2 Considerations for the Algorithm for the Time-of-Flight Calculation;345
7.2.3.2.1;14.3.2.1 Efficiency;345
7.2.3.2.2;14.3.2.2 Memory;345
7.2.3.2.3;14.3.2.3 Parallel Implementation;346
7.2.3.2.4;14.3.2.4 Classification of Nodes;346
7.2.3.2.5;14.3.2.5 Covered Nodes per Iteration;347
7.2.3.2.6;14.3.2.6 Number of Initial Sources;347
7.2.3.3;14.3.3 Algorithm for Time-of-Flight Calculation;347
7.2.4;14.4 Influences on the Time-of-Flight Calculation;349
7.2.4.1;14.4.1 Discretization;349
7.2.4.2;14.4.2 Non-isotropic Material Properties Inside the Elements;354
7.2.4.3;14.4.3 Non-convex Velocity Distributions Insidethe Elements;356
7.2.4.4;14.4.4 Subsequent Determination of Fastest Paths;357
7.2.5;References;358
7.3;15 The Determination of Dispersion Curves from Measurements by the Matrix Pencil Method;360
7.3.1;15.1 Introduction;360
7.3.2;15.2 Dispersion Relations via Mode Decomposition in the Wavenumber Domain;361
7.3.3;15.3 The Matrix Pencil Method;363
7.3.4;15.4 Experimental Setup;365
7.3.5;15.5 From Laser Vibrometer Data to Matrix Pencil Data;366
7.3.6;15.6 Numerical Results and Detection of BackwardPropagating Waves;368
7.3.7;15.7 Conclusions;372
7.3.8;References;373
7.4;16 Damage Identification by Dynamic Load Monitoring;374
7.4.1;16.1 Introduction;375
7.4.2;16.2 Dynamic Load Monitoring as a Minimization Problem;377
7.4.3;16.3 Numerical Solution of the Tikhonov Minimization Problem;386
7.4.4;16.4 Numerical Results;391
7.4.5;References;397
8;Part VI SHM: Systems;399
8.1;17 Mode Selective Actuator-Sensor-Systems;401
8.1.1;17.1 Introduction;401
8.1.2;17.2 Analytical Model for Mode SelectiveActuator-Sensor-Systems;406
8.1.2.1;17.2.1 Mode Tuning: 2D Problem;406
8.1.2.2;17.2.2 Acoustic Wave Field: 3D Problem;413
8.1.3;17.3 Experimental Verification of Mode Selective Actuator-Sensor-Systems;418
8.1.3.1;17.3.1 Manufacturing Technologies of Mode Selective Transducers;418
8.1.3.2;17.3.2 Experimental Setup;421
8.1.3.3;17.3.3 Experimental Results Regarding Mode Tuning;422
8.1.3.4;17.3.4 Experimental Results Regarding Acoustic Wave Field;425
8.1.4;Appendix;427
8.1.5;References;429
8.2;18 Virtual Sensors for SHM;431
8.2.1;18.1 Introduction;431
8.2.2;18.2 Leaky Guided Waves;432
8.2.3;18.3 Displacement Ratios;433
8.2.4;18.4 Adaption of Wave Radiation;436
8.2.5;18.5 Sensor Model;437
8.2.6;18.6 Experimental Validation;439
8.2.7;References;441
8.3;19 Lamb Wave Generation, Propagation, and Interactions in CFRP Plates;442
8.3.1;19.1 Experimental Setup;442
8.3.2;19.2 Characterization of Piezo-Actuators and Their Wave Fields;443
8.3.3;19.3 Velocity and Attenuation Measurement of Lamb Waves;447
8.3.3.1;19.3.1 Methods of Dispersion Curves Determination;447
8.3.3.2;19.3.2 Comparison of Lamb Wave Velocities in DifferentPlates;448
8.3.4;19.4 Attenuation of Lamb Waves;450
8.3.5;19.5 Interactions with Inhomogeneities;452
8.3.5.1;19.5.1 Non-Mode Converting Inhomogeneities;452
8.3.5.2;19.5.2 Mode Converting Inhomogeneities;452
8.3.5.2.1;19.5.2.1 Interactions with Asymmetric Wall Thickness Changes;452
8.3.5.2.2;19.5.2.2 Interactions with Stringers;454
8.3.5.2.3;19.5.2.3 Interactions with Stringer Defects;456
8.3.5.2.4;19.5.2.4 Continuous Mode Conversion;457
8.3.6;19.6 Conclusion;458
8.3.7;References;459
8.4;20 Structural Health Monitoring on the SARISTU Full Scale Door Surround Structure;461
8.4.1;20.1 Introduction;461
8.4.2;20.2 Integration of a SHM Network in the Structure;462
8.4.3;20.3 A Probability-Based Diagnostic Imaging Approach;464
8.4.4;20.4 Damage Assessment;465
8.4.5;20.5 Conclusion;469
8.4.6;References;470
9;Index;472