Mechanics of elastic waves and ultrasonic nondestructive evaluation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
CRC Press, Taylor & Francis Group
[2019]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xvii, 377 pages Illustrationen |
| ISBN: | 9781138035942 |
Internformat
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| 245 | 1 | 0 | |a Mechanics of elastic waves and ultrasonic nondestructive evaluation |c Dr. Tribikram Kundu |
| 264 | 1 | |a Boca Raton |b CRC Press, Taylor & Francis Group |c [2019] | |
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| 650 | 4 | |a Elastic waves | |
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Datensatz im Suchindex
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| adam_text | Contents Preface...............................................................................................................xv Author.............................................................................................................xvii 1 Mechanics of Elastic Waves - Linear Analysis.............................................1 1.1 Fundamentals of the Continuum Mechanics and the Theory of Elasticity.................................................................................................1 1.1.1 Deformation and Strain Tensor.................................................. 1 1.1.1.1 Interpretation of and for Small Displacement Gradient......................................................................... 2 1.1.2 Traction and Stress Tensor...........................................................5 1.1.3 Traction-Stress Relation.............................................................. 7 1.1.4 Equilibrium Equations................................................................ 8 1.1.4.1 Force Equilibrium......................................................... 8 1.1.4.2 Moment Equilibrium..................................................... 9 1.1.5 Stress Transformation...............................................................10 1.1.5.1 Kronecker Delta Symbol (б,,) and Permutation Symbol (eijk).................................................................. 11 1.1.6 Definition of Tensor.................................................................. 12 1.1.7 Principal Stresses and Principal Planes....................................12
1.1.8 Transformation of Displacement and Other Vectors..................16 1.1.9 Strain Transformation...............................................................16 1.1.10 Definition of Elastic Material and Stress-Strain Relation....... 17 1.1.11 Number of Independent Material Constants............................ 20 1.1.12 Material Planes of Symmetry....................................................21 1.1.12.1 One Plane of Symmetry.............................................. 21 1.1.12.2 Two and Three Planes of Symmetry............................ 22 1.1.12.3 Three Planes of Symmetry and One Axis of Symmetry....................................................................22 1.1.12.4 Three Planes of Symmetry and Two or Three Axes of Symmetry................................................................ 23 1.1.13 Stress-Strain Relation for Isotropic Materials - Green s Approach.................................................................................. 25 1.1.13.1 Hooke s Law in Terms of Young s Modulus and Poisson s Ratio.............................................................. 27 1.1.14 Navier s Equation of Equilibrium.............................................28 vii
CONTENTS 1.1.15 Fundamental Equations of Elasticity in Other Coordinate Systems............................................................................................30 1.2 Time Dependent Problems or Dynamic Problems...............................31 1.2.1 Some Simple Dynamic Problems..................................................31 1.2.2 Stokes-Helmholtz Decomposition................................................37 1.2.3 Two-Dimensional In-Plane Problems.......................................... 38 1.2.4 P- and S-Waves.............................................................................. 40 1.2.5 Harmonic Waves.............................................................................40 1.2.6 Interaction between Plane Waves and Stress-Free Plane Boundary........................................................................................42 1.2.6.1 P-wave Incident on a Stress-Free Plane Boundary .... 42 1.2.6.2 Summary of Plane Р-Wave Reflection by a Stress-Free Surface....................................................... 44 1.2.6.3 Shear Wave Incident on a Stress-Free Plane Boundary...........................................................................46 1.2.7 Out-of-Plane or Antiplane Motion - SH Wave.............................48 1.2.7.1 Interaction of SH-Wave and Stress-Free Plane Boundary...........................................................................50 1.2.7.2 Interaction of SH-Wave and a Plane Interface............. 51 1.2.8 Interaction of P-and SV-Waves with Plane Interface...................52 1.2.8.1 Р-Wave Striking an
Interface.........................................52 1.2.8.2 SV-Wave Striking an Interface........................................ 56 1.2.9 Rayleigh Waves in a Homogeneous Half-Space.......................... 59 1.2.10 Love Wave...................................................................................... 63 1.2.11 Rayleigh Waves in a Layered Half-Space.................................... 64 1.2.12 Plate Waves.................................................................................... 66 1.2.12.1 Antiplane Waves in a Plate..............................................66 1.2.12.2 In-plane Waves in a Plate (Lamb Waves).......................69 1.2.13 Phase Velocity and Group Velocity..............................................73 1.2.14 Point Source Excitation................................................................... 76 1.2.15 Wave Propagation in Fluid........................................................... 79 1.2.15.1 Relation between Pressure and Velocity.......................80 1.2.15.2 Reflection and Transmission of Plane Waves at the Fluid-Fluid Interface....................................................... 80 1.2.15.3 Plane Wave Potential in a Fluid...................................... 82 1.2.15.4 Point Source in a Fluid..................................................... 84 vm
CONTENTS 1.2.16 Reflection and Transmission of Plane Waves at a Fluid-Solid Interface...................................................................86 1.2.17 Reflection and Transmission of Plane Waves by a Solid Plate Immersed in a Fluid............................................................. 91 1.2.18 Elastic Properties of Different Materials......................................94 1.3 Concluding Remarks................................................................................ 94 Exercise Problems............................................................................................100 References........................................................................................................Ill 2 Guided Elastic Waves - Analysis and Applications in Nondestructive Evaluation........................................................................................................113 2.1 Guided Waves and Wave-Guides..........................................................113 2.1.1 Lamb Waves and Leaky Lamb Waves........................................ 114 2.2 Basic Equations - Homogeneous Elastic Plates in a Vacuum............ 114 2.2.1 Dispersion Curves and Mode Shapes........................................ 117 2.2.1.1 Dispersion Curves......................................................... 117 2.2.1.2 Mode Shapes................................................................... 120 2.3 Homogeneous Elastic Plates Immersed in a Fluid.............................. 123 2.3.1 Symmetric
Motion.......................................................................126 2.3.2 Anti-Symmetric Motion............................................................... 131 2.4 Plane Р-Waves Striking a Solid Plate Immersed in a Fluid................ 135 2.4.1 Plate Inspection by Lamb Waves................................................138 2.4.1.1 Generation of Multiple Lamb Modes by Narrowband and Broadband Transducers...................138 2.4.1.2 Nondestructive Inspection of Large Plates................. 140 2.5 Guided Waves in Multilayered Plates....................................................148 2.5.1 n-Layered Plates in a Vacuum......................................................148 2.5.1.1 Numerical Instability......................................................151 2.5.1.2 Global Matrix Method....................................................152 2.5.2 «-Layered Plates in a Fluid......................................................... 154 2.5.2.1 Global Matrix Method....................................................157 2.5.3 «-Layered Plate Immersed in a Fluid, and Struck by a Plane P-Wave.........................................................................158 2.5.3.1 Global Matrix Method....................................................159 2.6 Guided Waves in Single and Multilayered Composite Plates............160 2.6.1 Single Layer Composite Plates Immersed in a Fluid................. 167 2.6.2 Multilayered Composite Plates Immersed in a Fluid............... 167 ix
CONTENTS 2.6.3 Multilayered Composite Plates in a Vacuum (Dispersion Equation)...................................................................................... 169 2.6.4 Composite Plate Analysis with Attenuation...............................170 2.7 Defect Detection in Multilayered Composite Plates Experimental Investigation.....................................................................172 2.7.1 Specimen Description................................................................. 173 2.7.2 Numerical and Experimental Results........................................ 174 2.8 Guided Wave Propagation in the Circumferential Direction of a Pipe................................................................................................... 181 2.8.1 Fundamental Equations............................................................... 182 2.8.2 Wave Form.................................................................................... 183 2.8.3 Governing Differential Equations..............................................184 2.8.4 Boundary Conditions................................................................... 185 2.8.5 Solution..........................................................................................185 2.8.6 Numerica! Results.........................................................................187 2.8.6.1 Comparison with Isotropic Flat Plate Results............. 187 2.8.6.2 Comparison with Anisotropic Flat PlateResults .... 187 2.8.6.3 Comparison of Results for Isotropic Pipes................... 191 2.8.Ó.4 Anisotropic Pipe of Smaller
Radius.............................191 2.9 Guided Wave Propagation in the Axial Direction of a Pipe............... 192 2.9.1 Formulation.................................................................................. 195 2.9.2 Use of Cylindrical Guided Waves for Damage Detection in Pipe wall..................................................................................200 2.10 Concluding Remarks..............................................................................205 Exercise Problems........................................................................................... 205 References.......................................................................................................208 3 Modeling Elastic Waves by Distributed Point Source Method (DPSM)... 215 3.1 Modeling a Finite Plane Source by a Distribution of Point Sources ... .215 3.2 Planar Piston Transducer in a Fluid..................................................... 217 3.2.1 Analytical Solution...................................................................... 217 3.2.2 Numerical Solution.......................................................................218 3.2.3 Semi-Analytical DPSM Solution................................................. 219 3.2.4 Computed Results........................................................................ 223 3.2.5 Required Spacing Between Neighboring Point Sources...........232 3.3 Focused Transducer in a Homogeneous Fluid....................................234 3.3.1 Computed Results for a Focused Transducer............................ 235 3.4
Ultrasonic Field in a Non-Homogeneous Fluid in Presence of an Interface..........................................................................................235 3.4.1 Field Computation in Fluid 1..................................................... 236 x
CONTENTS 3.4.2 Field Computation in Fluid 2.....................................................238 3.4.3 Satisfaction of Continuity Conditions and Evaluation of Unknowns....................................................................................239 3.5 Ultrasonic Field in Presence of a Scatterer............................................240 3.5.1 DPSM Modeling.......................................................................... 240 3.5.1.1 Very Small Cavity Modeled by a Single Point Source ... 242 3.5.1.2 Small Cavity Modeled with Multiple Point Sources...... 242 3.5.1.3 Complete Solution for Large Cavity........................... 242 3.5.2 Analytical Solution...................................................................... 243 3.5.3 Numerical Results for the Cavity Problem................................ 244 3.6 Ultrasonic Field in Multilayered Fluid Medium..................................249 3.7 Ultrasonic Field Computation in Presence of a Fluid-Solid Interface................................................................................................... 251 3.7.1 Fluid-Solid Interface...................................................................251 3.7.2 A Fluid Wedge Over a Solid Half-Space - DPSM Formulation..................................................................................253 3.7.3 Solid-Solid Interface.................................................................... 259 3.8 DPSM Modeling for Transient Problems............................................. 259 3.8.1 Fluid-Solid Interface Excited by a Bounded Beam ֊ DPSM
Formulation..................................................................................260 3.8.1.1 Transient Analysis........................................................262 3.8.1.2 Computed Results........................................................ 262 3.9 DPSM Modeling for Anisotropic Media............................................... 268 3.9.1 DPSM Modeling of a Solid Plate Immersed in a Fluid.............270 3.9.2 The Windowing Technique.........................................................272 3.9.3 Elastodynamic Green s Function............................................... 274 3.9.3.1 General Anisotropic Materials.....................................274 3.9.3.2 Residue Method............................................................. 276 3.9.3.3 Reduction of Integration Domain for Transversely Isotropic Materials.........................................................277 3.9.4 Numerical Examples...................................................................278 3.9.4.1 Isotropic Plate................................................................278 3.9.4.2 Transversely Isotropic Plate......................................... 280 3.10 Concluding Remarks.............................................................................. 281 References....................................................................................................... 282 4 Nonlinear Ultrasonic Techniques for Nondestructive Evaluation........... 287 4.1 Introduction............................................................................................ 287 xi
CONTENTS 4.2 One-Dimensional Analysis of Wave Propagation in a Nonlinear Material....................................................................................................289 4.2.1 Stress-Strain Relations of Linear and Nonlinear Materials.... 289 4.2.2 Nonlinear Material Excited by a Wave of Single Frequency........289 4.2.3 Nonlinear Material Excited by Waves of Two Different Frequencies.................................................................................. 293 4.2.4 Detailed Analysis of One-Dimensional Wave Propagation in a Nonlinear Rod.......................................................................294 4.2.5 Higher Harmonic Generation for Other Types of Wave...........297 4.2.5.1 Transverse Wave Propagation in a Nonlinear Bulk Material...........................................................................297 4.2.5.2 Guided Wave Propagation in a Nonlinear Wave-guide.....................................................................297 4.3 Use of Nonlinear Bulk Waves for Nondestructive Evaluation...........299 4.3.1 Nonlinear Acoustic Parameter Measurement.......................... 299 4.3.2 Experimental Results...................................................................300 4.4 Use of Nonlinear Lamb Waves for Nondestructive Evaluation........302 4.4.1 Phase Matching for Nonlinear Lamb Wave Experiments .... 302 4.4.2 Experimental Results...................................................................303 4.5 Nonlinear Resonance Technique........................................................... 305 4.6 Pump Wave and Probe Wave
Based Technique.................................. 307 4.7 Sideband Peak Count (SPC) Technique................................................. 309 4.7.1 Experimental Evidence of SPC Measuring Material Nonlinearity.................................................................................. 310 4.8 Concluding Remarks...............................................................................313 References........................................................................................................314 5 Acoustic Source Localization.........................................................................317 5.1 Introduction.............................................................................................. 317 5.2 Source Localization in Isotropic Plates..................................................318 5.2.1 Triangulation Technique for Isotropic Plates with Known Wave Speed...................................................................................318 5.2.2 Triangulation Technique for Isotropic Plates with Unknown Wave Speed................................................................. 320 5.2.3 Optimization Based Technique for Isotropic Plates with Unknown Wave Speed................................................................. 321 5.2.4 Beamforming Technique for Isotropic Plates............................ 323 5.2.5 Strain Rossette Technique for Isotropic Plates with Unknown Wave Speed................................................................. 324 xn
CONTENTS 5.2.6 Source Localization by Modal Acoustic Emission................ 325 5.3 Source Localization in Anisotropic Plates......................................... 325 5.3.1 Beamforming Technique for Anisotropic Structure................325 5.3.2 Optimization Based Technique for Source Localization in Anisotropic Plates.................................................................... 326 5.3.3 Source Localization in Anisotropic Plates without Knowing Their Material Properties.........................................330 5.3.3.1 Determination of t¡¡....................................................333 5.3.3.2 Improving and Checking the Accuracy of Prediction... 334 5.3.3.3 Experimental Verification...........................................334 5.3.4 Source Localization and Its Strength Estimation without Knowing the Plate Material Properties by Poynting Vector Technique.................................................................................336 5.4 Source Localization in Complex Structures....................................... 337 5.4.1 Source Localization in Complex Structures by Time Reversal and Artificial Neural Network Techniques..............338 5.4.2 Source Localization by Densely Distributed Sensors..............339 5.5 Source Localization in Three-Dimensional Structures..................... 340 5.6 Automatic Determination of Time of Arrival.................................. 340 5.7 Uncertainty in Acoustic Source Prediction......................................340 5.8 Source Localization in Anisotropic Plates by Analyzing Propagating Wave
Fronts................................................................. 340 5.8.1 Wave Propagation Direction Vector Measurement by Sensor Clusters.................................................................... 341 5.8.2 Numerical Simulation of Wave Propagation in an Anisotropic Plate...................................................................... 343 5.8.3 Wave Front Based Source Localization Technique................. 344 5.8.3.1 Rhombus Wave Front................................................ 344 5.8.3.2 Elliptical Wave Front.................................................. 349 5.8.3.3 Numerical Validation for Rhombus Wave Front....... 353 5.8.3.4 Wave Front Modeled by Non-Elliptical Parametric Curve..........................................................................354 5.8.3.5 Numerical Validation for Non-Elliptical Wave Fronts... .358 5.9 Concluding Remarks.........................................................................363 References................................................................................................ 364 Index............................................................................................................... 371 xiii
This book presents necessary background knowledge on mechanics to understand and analyze elastic wave propagation in solids and fluids. This knowledge is necessary for elastic wave propagation modeling and for interpreting experimental data generated during ultrasonic nondestructive testing and evaluation (NDT E). The book covers both linear and nonlinear analyses of ultrasonic NDT E techniques. The materials presented here also include some exercise problems and solution manual. Therefore, this book can serve as a textbook or reference book for a graduate level course on elastic waves and/or ultrasonic nondestructive evaluation. It will be also useful for instructors who are interested in designing short courses on elastic wave propagation in solids or NDT E. The materials covered in the first two chapters provide the fundamental knowledge on linear mechanics of deformable solids while Chapter 4 covers nonlinear mechanics. Thus, both linear and nonlinear ultrasonic techniques are covered here. Nonlinear ultrasonic techniques are becoming more popular in recent years for detecting very small defects and damages. However, this topic is hardly covered in currently available textbooks. Researchers mostly rely on published research papers and research monographs to learn about nonlinear ultrasonic techniques. Chapter 3 describes elastic wave propagation modeling techniques using DPSM. Chapter 5 is dedicated to an important and very active research field - acoustic source localization - that is essential for structural health monitoring and for localizing crack and other type of
damage initiation regions. Features • Introduces Linear and Nonlinear ultrasonic techniques in a single book. • Commences with basic definitions of displacement, displacement gradient, traction and stress. • Provides step by step derivations of fundamental equations of mechanics as well as linear and nonlinear wave propagation analysis. • Discusses basic theory in addition to providing detailed NDE applications. • Provides extensive example and exercise problems along with an extensive solutions manual. 9781138035942
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| indexdate | 2024-07-10T08:34:35Z |
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| isbn | 9781138035942 |
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| publisher | CRC Press, Taylor & Francis Group |
| record_format | marc |
| spelling | Kundu, Tribikram Verfasser aut Mechanics of elastic waves and ultrasonic nondestructive evaluation Dr. Tribikram Kundu Boca Raton CRC Press, Taylor & Francis Group [2019] xvii, 377 pages Illustrationen txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Ultrasonic testing Elastic waves Elastische Welle (DE-588)4151684-9 gnd rswk-swf Zerstörungsfreie Werkstoffprüfung (DE-588)4067689-4 gnd rswk-swf Werkstoffprüfung (DE-588)4037934-6 gnd rswk-swf Zerstörungsfreie Werkstoffprüfung (DE-588)4067689-4 s DE-604 Elastische Welle (DE-588)4151684-9 s Werkstoffprüfung (DE-588)4037934-6 s Erscheint auch als Online-Ausgabe 978-1-315-22619-4 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031459007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031459007&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kundu, Tribikram Mechanics of elastic waves and ultrasonic nondestructive evaluation Ultrasonic testing Elastic waves Elastische Welle (DE-588)4151684-9 gnd Zerstörungsfreie Werkstoffprüfung (DE-588)4067689-4 gnd Werkstoffprüfung (DE-588)4037934-6 gnd |
| subject_GND | (DE-588)4151684-9 (DE-588)4067689-4 (DE-588)4037934-6 |
| title | Mechanics of elastic waves and ultrasonic nondestructive evaluation |
| title_auth | Mechanics of elastic waves and ultrasonic nondestructive evaluation |
| title_exact_search | Mechanics of elastic waves and ultrasonic nondestructive evaluation |
| title_full | Mechanics of elastic waves and ultrasonic nondestructive evaluation Dr. Tribikram Kundu |
| title_fullStr | Mechanics of elastic waves and ultrasonic nondestructive evaluation Dr. Tribikram Kundu |
| title_full_unstemmed | Mechanics of elastic waves and ultrasonic nondestructive evaluation Dr. Tribikram Kundu |
| title_short | Mechanics of elastic waves and ultrasonic nondestructive evaluation |
| title_sort | mechanics of elastic waves and ultrasonic nondestructive evaluation |
| topic | Ultrasonic testing Elastic waves Elastische Welle (DE-588)4151684-9 gnd Zerstörungsfreie Werkstoffprüfung (DE-588)4067689-4 gnd Werkstoffprüfung (DE-588)4037934-6 gnd |
| topic_facet | Ultrasonic testing Elastic waves Elastische Welle Zerstörungsfreie Werkstoffprüfung Werkstoffprüfung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031459007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031459007&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kundutribikram mechanicsofelasticwavesandultrasonicnondestructiveevaluation |