Rose J.L. Ultrasonic guided waves in solid media (Cambridge, 2014). - ОГЛАВЛЕНИЕ / CONTENTS

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ОбложкаRose J.L. Ultrasonic guided waves in solid media. - Cambridge: Cambridge iniversity prerss, 2014. - xxii, 512 p., [8] l. ill.: ill. - Bibliogr. at the end of the chapters. - Ind.: p.507-512. - ISBN 978-1-107-04895-9
 

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Оглавление / Contents
 
Nomenclature ................................................. xiii
Preface ....................................................... xix
Acknowledgments ............................................... xxi
1  Introduction ................................................. 1
   1.1  Background .............................................. 1
   1.2  A Comparison of Bulk versus Guided Waves ................ 3
   1.3  What Is an Ultrasonic Guided Wave? ...................... 5
   1.4  The Difference between Structural Health Monitoring
        (SHM) and Nondestructive Testing (NDT) .................. 7
   1.5  Text Preview ............................................ 7
   1.6  Concluding Remarks ..................................... 12
   1.7  References ............................................. 14
2  Dispersion Principles ....................................... 16
   2.1  Introduction ........................................... 16
   2.2  Waves in a Taut String ................................. 16
        2.2.1  Governing Wave Equation ......................... 16
        2.2.2  Solution by Separation of Variables ............. 17
        2.2.3  D'Alembert's Solution ........................... 19
        2.2.4  Initial Value Considerations .................... 20
   2.3  String on an Elastic Base .............................. 21
   2.4  A Dispersive Wave Propagation Sample Problem ........... 24
   2.5  String on a Viscous Foundation ......................... 25
   2.6  String on a Viscoelastic Foundation .................... 26
   2.7  Graphical Representations of a Dispersive System ....... 26
   2.8  Group Velocity Concepts ................................ 28
   2.9  Exercises .............................................. 32
   2.10 References ............................................. 35
3  Unbounded Isotropic and Anisotropic Media ................... 36
   3.1  Introduction ........................................... 36
   3.2  Isotropic Media ........................................ 36
   3.1  Equations of Motion .................................... 36
        3.2.2  Dilatational and Distortional Waves ............. 38
   3.3  The Christoffel Equation for Anisotropic Media ......... 39
        3.3.1  Sample Problem .................................. 42
   3.4  On Velocity, Wave, and Slowness Surf aces .............. 46
   3.5  Exercises .............................................. 50
   3.6  References ............................................. 52
4  Reflection and Refraction ................................... 53
   4.1  Introduction ........................................... 53
   4.2  Normal Beam Incidence Reflection Factor ................ 53
   4.3  SnelPs Law for Angle Beam Analysis ..................... 58
   4.4  Critical Angles and Mode Conversion .................... 60
   4.5  Slowness Profiles for Refraction and Critical Angle
        Analysis ............................................... 63
   4.6  Exercises .............................................. 64
   4.7  References ............................................. 66
5  Oblique Incidence ........................................... 67
   5.1  Background ............................................. 67
   5.2  Reflection and Refraction Factors ...................... 68
        5.2.1  Solid-Solid Boundary Conditions ................. 68
        5.2.2  Solid-Liquid Boundary Conditions ................ 71
        5.2.3  Liquid-Solid Boundary Conditions ................ 72
   5.3  Moving Forward ......................................... 74
   5.4  Exercises .............................................. 74
   5.5  References ............................................. 75
6  Waves in Plates ............................................. 76
   6.1  Introduction ........................................... 76
   6.2  The Free Plate Problem ................................. 78
        6.2.1  Solution by the Method of Potentials ............ 79
        6.2.2  The Partial Wave Technique ...................... 82
   6.3  Numerical Solution of the Rayleigh-Lamb Frequency
        Equations .............................................. 84
   6.4  Group Velocity ......................................... 87
   6.5  Wave Structure Analysis ................................ 88
   6.6  Compressional and Flexural Waves ....................... 91
   6.7  Miscellaneous Topics ................................... 92
        6.7.1  Lamb Waves with Dominant Longitudinal
               Displacements ................................... 93
        6.7.2  Zeros and Poles for a Fluid-Coupled Elastic
               Layer .......................................... 102
        6.7.3  Mode Cutoff Frequency .......................... 103
   6.8  Exercises ............................................. 104
   6.9  References ............................................ 106
7  Surface and Subsurface Waves ............................... 107
   7.1  Background ............................................ 107
   7.2  Surface Waves ......................................... 107
   7.3  Generation and Reception of Surface Waves ............. 114
   7.4  Subsurface Longitudinal Waves ......................... 116
   7.5  Exercises ............................................. 117
   7.6  References ............................................ 118
8  Finite Element Method for Guided Wave Mechanics ............ 120
   8.1  Introduction .......................................... 120
   8.2  Overview of the Finite Element Method ................. 120
        8.2.1  Using the Finite Element Method to Solve
               a Problem ...................................... 120
        8.2.2  Quadratic Elements ............................. 125
        8.2.3  Dynamic Problem ................................ 126
        8.2.4  Error Control .................................. 128
   8.3  FEM Applications for Guided Wave Analysis ............. 129
        8.3.1  2-D Surface Wave Generation in a Plate ......... 129
        8.3.2  Guided Wave Defect Detection in a Two-Inch
               Steel Tube ..................................... 130
   8.4  Summary ............................................... 132
   8.5  Exercises ............................................. 133
   8.6  References ............................................ 134
9  The Semi-Analytical Finite Element Method .................. 135
   9.1  Introduction .......................................... 135
   9.2  SAFE Formulation for Plate Structures ................. 136
   9.3  Orthogonality-Based Mode Sorting ...................... 140
   9.4  Group Velocity Dispersion Curves ...................... 141
   9.5  Guided Wave Energy .................................... 142
        9.5.1  Poynting Vector ................................ 142
        9.5.2  Energy Velocity ................................ 142
        9.5.3  Skew Effects in Anisotropic Plates ............. 142
   9.6  Solution Convergence of the SAFE Method ............... 143
   9.7  Free Guided Waves in an Eight-Layer Quasi-Isotropic
        Plate ................................................. 143
   9.8  SAFE Formulation for Cylindrical Structures ........... 145
   9.9  Summary ............................................... 153
   9.10 Exercises ............................................. 153
   9.11 References ............................................ 154
10 Guided Waves in Hollow Cylinders ........................... 155
   10.1 Introduction .......................................... 155
   10.2 Guided Waves Propagating in an Axial Direction ........ 155
        10.2.1 Analytic Calculation Approach .................. 155
        10.2.2 Excitation Conditions and Angular Profiles ..... 164
        10.2.3 Source Influence ............................... 166
   10.3 Exercises ............................................. 171
   10.4 References ............................................ 172
11 Circumferential Guided Waves ............................... 174
   11.1 Introduction .......................................... 174
   11.2 Development of the Governing Wave Equations for
        Circumferential Waves ................................. 175
        11.2.1 Circumferential Shear Horizontal Waves in
               a Single-Layer Annulus ......................... 176
        11.2.2 Circumferential Lamb Type Waves in a Single-
               Layer Annulus .................................. 180
   11.3 Extension to Multilayer Annuli ........................ 184
   11.4 Numerical Solution of the Governing Wave Equations
        for Circumferential Guided Waves ...................... 187
        11.4.1 Numerical Results for CSH-Waves ................ 188
        11.4.2 Numerical Results for CLT-Waves ................ 193
        11.4.3 Computational Limitations of the Analytical
               Formulation .................................... 199
   11.5 The Effects of Protective Coating on Circumferential
        Wave Propagation in Pipe .............................. 202
   11.6 Exercises ............................................. 205
   11.7 References ............................................ 206
12 Guided Waves in Layered Structures ......................... 209
   12.1 Introduction .......................................... 209
   12.2 Interface Waves ....................................... 210
        12.2.1 Waves at a Solid-Solid Interface: Stoneley
               Wave ........................................... 210
        12.2.2 Waves at a Solid-Liquid Interface: Scholte
               Wave ........................................... 213
   12.3 Waves in a Layer on a Half-Space ...................... 215
        12.3.1 Rayleigh-Lamb Type Waves ....................... 215
        12.3.2 Love Waves ..................................... 219
   12.4 Waves in Multiple Layers .............................. 221
        12.4.1 The Global Matrix Method ....................... 222
        12.4.2 The Transfer Matrix Method ..................... 227
        12.4.3 Examples ....................................... 230
   12.5 Fluid-Coupled Elastic Layers .......................... 233
        12.5.1 Ultrasonic Wave Reflection and Transmission .... 234
        12.5.2 Leaky Guided Wave Modes ........................ 242
        12.5.3 Nonspecular Reflection and Transmission ........ 243
   12.6 Exercises ............................................. 244
   12.7 References ............................................ 245
13 Source Influence on Guided Wave Excitation ................. 246
   13.1 Introduction .......................................... 246
   13.2 Integral Transform Method ............................. 247
        13.2.1 A Shear Loading Example ........................ 247
   13.3 Normal Mode Expansion Method .......................... 251
        13.3.1 Normal Mode Expansion in Harmonic Loading ...... 253
        13.3.2 Transient Loading Source Influence ............. 257
   13.4 Exercises ............................................. 267
   13.5 References ............................................ 268
14 Horizontal Shear ........................................... 269
   14.1 Introduction .......................................... 269
   14.2 Dispersion Curves ..................................... 269
   14.3 Phase Velocities and Cutoff Frequencies ............... 272
   14.4 Group Velocity ........................................ 273
   14.5 Summary ............................................... 274
   14.6 Exercises ............................................. 275
   14.7 References ............................................ 275
15 Guided Waves in Anisotropic Media .......................... 276
   15.1 Introduction .......................................... 276
   15.2 Phase Velocity Dispersion ............................. 277
   15.3 Guided Wave Directional Dependency .................... 281
   15.4 Guided Wave Skew Angle ................................ 286
   15.5 Guided Waves in Composites with Multiple Layers ....... 287
   15.6 Exercises ............................................. 292
   15.7 References ............................................ 293
16 Guided Wave Phased Arrays in Piping ........................ 294
   16.1 Introduction .......................................... 294
   16.2 Guided Wave Phased Array Focus Theory ................. 295
   16.3 Numerical Calculations ................................ 303
   16.4 Finite Element Simulation of Guided Wave Focusing ..... 307
   16.5 Active Focusing Experiment ............................ 310
   16.6 Guided Wave Synthetic Focus ........................... 316
   16.7 Synthetic Focusing Experiment ......................... 319
   16.8 Summary ............................................... 321
   16.9 Exercises ............................................. 321
   16.10 References ........................................... 322
17 Guided Waves in Viscoelastic Media ......................... 323
   17.1  Introduction ......................................... 323
   17.2  Viscoelastic Models .................................. 324
         17.2.1 Material Viscoelastic Models .................. 324
         17.2.2 Kelvin-Voight Model ........................... 324
         17.2.3 Maxwell Model ................................. 325
         17.2.4 Further Aspects of the Hysteretic and
                Kelvin-Voight Models .......................... 326
   17.3  Measuring Viscoelastic Parameters .................... 327
   17.4  Viscoelastic Isotropic Plate ......................... 328
   17.5  Viscoelastic Orthotropic Plate ....................... 329
         17.5.1 Problem Formulation and Solution .............. 329
         17.5.2 Numerical Results ............................. 330
         17.5.3 Summary ....................................... 333
   17.6  Lamb Waves in a Viscoelastic Layer ................... 333
   17.7  Viscoelastic Composite Plate ......................... 334
   17.8  Pipes with Viscoelastic Coatings ..................... 340
   17.9  Exercises ............................................ 342
   17.10 References ........................................... 343
18  Ultrasonic Vibrations ..................................... 345
   18.1 Introduction .......................................... 345
   18.2 Practical Insights into the Ultrasonic Vibrations
        Problem ............................................... 350
   18.3 Concluding Remarks .................................... 357
   18.4 Exercises ............................................. 357
   18.5 References ............................................ 358
19 Guided Wave Array Transducers .............................. 359
   19.1 Introduction .......................................... 359
   19.2 Analytical Development ................................ 360
        19.2.1 Linear Comb Array Solution ..................... 361
        19.2.2 Annular Array Solution ......................... 366
   19.3 Phased Transducer Arrays for Mode Selection ........... 370
        19.3.1 Phased Array Analytical Development ............ 370
        19.3.2 Phased Array Analysis .......................... 371
   19.4 Concluding Remarks .................................... 376
   19.5 Exercises ............................................. 376
   19.6 References ............................................ 377
20 Introduction to Guided Wave Nonlinear Methods .............. 378
   20.1 Introduction .......................................... 378
   20.2 Bulk Waves in Weakly Nonlinear Elastic Media .......... 379
   20.3 Measurement of the Second Harmonic .................... 380
   20.4 Second Harmonic Generation Related to Microstructure .. 383
   20.5 Weakly Nonlinear Wave Equation ........................ 384
   20.6 Higher Harmonic Generation in Plates .................. 388
        20.6.1 Synchronism .................................... 388
        20.6.2 Power Flux ..................................... 391
        20.6.3 Group Velocity Matching ........................ 393
        20.6.4 Sample Laboratory Experiments .................. 393
   20.7 Applications of Higher Harmonic Generation by Guided
        Waves ................................................. 399
   20.8 Exercises ............................................. 399
   20.9 References ............................................ 400
21 Guided Wave Imaging Methods ................................ 402
   21.1 Introduction .......................................... 402
   21.2 Guided Wave through Transmission Dual Probe Imaging ... 402
   21.3 Defect Locus Map ...................................... 407
   21.4 Guided Wave Tomographic Imaging ....................... 408
   21.5 Guided Wave Phased Array in Plates .................... 412
   21.6 Long-Range Ultrasonic Guided Wave Pipe Inspection
        Images ................................................ 417
   21.7 Exercises ............................................. 418
   21.8 References ............................................ 419
Appendix A - Ultrasonic Nondestructive Testing Principles,
   Analysis, and Display Technology ........................... 421
   A.l  Some Physical Principles .............................. 421
   A.2  Wave Interference ..................................... 425
   A.3  Computational Model for a Single Point Source ......... 425
   A.4  Directivity Function for a Cylindrical Element ........ 430
   A.5  Ultrasonic Field Presentations ........................ 432
   A.6  Near-Field Calculations ............................... 433
   A.7  Angle-of-Divergence Calculations ...................... 434
   A.8  Ultrasonic Beam Control ............................... 435
   A.9  A Note on Ultrasonic Field Solution Techniques ........ 435
   A.10 Time and Frequency Domain Analysis .................... 436
   A.11 Pulsed Ultrasonic Field Effects ....................... 436
   A.12 Introduction to Display Technology .................... 440
   A.13 Amplitude Reduction of an Ultrasonic Waveform ......... 441
   A.14 Resolution and Penetration Principles ................. 441
        A.14.1 Axial Resolution ............................... 441
   A.14.2 Lateral Resolution .................................. 442
   A.15 Phased Arrays and Beam Focusing ....................... 443
   A.16 Exercises ............................................. 443
   A.17 References ............................................ 444
Appendix В - Basic Formulas and Concepts in the Theory of
   Elasticity ................................................. 445
   B.l  Introduction .......................................... 445
   B.2  Nomenclature .......................................... 445
   B.3  Stress, Strain, and Constitutive Equations ............ 448
   B.4  Elastic Constant Relationships ........................ 448
   B.5  Vector and Tensor Transformation ...................... 449
   B.6  Principal Stresses and Strains ........................ 449
   B.7  The Strain Displacement Equations ..................... 450
   B.8  Derivation of the Governing Wave Equation ............. 452
   B.9  Anisotropic Elastic Constants ......................... 452
   B.10 Exercises ............................................. 455
   B.11 References ............................................ 455
Appendix С - Physically Based Signal Processing Concepts
   for Guided Waves ........................................... 456
   C.I  General Concepts ...................................... 456
   C.2  The Fast Fourier Transform (FFT) ...................... 457
        C.2.1  Example FFT Use: Analytic Envelope ............. 460
        C.2.2  Example FFT Use: Feature Source for Pattern
               Recognition .................................... 462
        C.2.3  Discrete Fourier Transform Properties .......... 462
   C.3  The Short Time Fourier Transform (STFFT) .............. 463
        C.3.1  Example: STFFT to Dispersion Curves ............ 466
   C.4  The 2-D Fourier Transform (2DFFT) ..................... 467
   C.5  The Wavelet Transform (WT) ............................ 472
   C.6  Exercises ............................................. 477
   C.7  References ............................................ 477
Appendix D - Guided Wave Mode and Frequency Selection Tips .... 478
   D.l  Introduction .......................................... 478
   D.2  Mode and Frequency Selection Considerations ........... 480
        D.2.1  A Surface-Breaking Defect ...................... 481
        D.2.2  Mild Corrosion and Wall Thinning ............... 482
        D.2.3  Transverse Crack Detection in the Head of
               a Rail ......................................... 485
        D.2.4  Repair Patch Bonded to an Aluminum Layer ....... 487
        D.2.5  Water-Loaded Structures ........................ 487
        D.2.6  Frequency and Other Tuning Possibilities ....... 489
        D.2.7  Ice Detection with Ultrasonic Guided Waves ..... 491
        D.2.8  Deicing ........................................ 492
        D.2.9  Real-Time Phased Array Focusing in Pipe ........ 493
        D.2.10 Aircraft, Lap Splice, Tear Strap, and Skin-
               to-Core Delamination Inspection Potential ...... 495
        D.2.11 Coating Delamination and Axial Crack
               Detection ...................................... 498
        D.2.12 Multilayer Structures .......................... 502
        D.2.13 Concluding Remarks ............................. 502
   D.3  Exercises ............................................. 503
   D.4  References ............................................ 505
Index ......................................................... 507
Plate section follows page .................................... 266


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