1 Introduction 1
1.1 General Overview 1
1.2 Concepts and Mechanisms 3
1.2.1 Self-excited oscillations and instabilities 4
1.2.2 Argand diagrams and bifurcations 8
1.2.3 Energy considerations 12
1.3 Notation 13
1.4 Contents of the Book 14
2 Prisms in Cross-Flow – Galloping 15
2.1 Introductory Comments 15
2.2 The Mechanism of Galloping 19
2.2.1 The linear threshold of galloping 20
2.2.2 Nonlinear aspects 24
2.3 Further Work on Translational Galloping 30
2.3.1 The effect of sectional shape 30
2.3.2 Novak’s “universal response curve” and continuous
structures 38
2.3.3 Unsteady effects and analytical models 43
2.3.4 Some comments on the flow field 45
2.3.5 Shear-layer reattachment 49
2.4 Low-Speed Galloping 50
2.5 Prisms and Cylinders with a Splitter Plate 55
2.6 Wake Breathing and Streamwise Oscillation 62
2.6.1 Wake breathing of the first type 62
2.6.2 Wake breathing of the second type 64
2.7 Torsional Galloping 66
2.7.1 General comments 66
2.7.2 Linear quasi-steady analysis 67
2.7.3 Nonlinear quasi-steady analysis 70
2.7.4 Disqualification of quasi-steady theory 72
2.7.5 Unsteady theory 75
2.8 Multi-Degree-of-Freedom Galloping 77
2.8.1 Quasi-steady models 77
2.8.2 Unsteady models 81
2.9 Turbulence and Shear Effects 81
2.10 Conjoint Galloping and Vortex Shedding 86
2.11 Elongated and Bridge-Deck Sections 90
2.12 Concluding Remarks 102
3 Vortex-Induced Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.1 Elementary Case 105
3.2 Two-Dimensional VIV Phenomenology 108
3.2.1 Bluff-body wake instability 110
3.2.2 Wake instability of a fixed cylinder 112
3.2.3 Wake of a cylinder forced to move 115
3.2.4 Cylinder free to move 120
3.3 Modelling Vortex-Induced Vibrations 124
3.3.1 A classification of models 124
3.3.2 Type A: Forced system models 127
3.3.3 Type B: Fluidelastic system models 129
3.3.4 Type C: Coupled system models 132
3.4 Advanced Aspects 139
3.4.1 The issue of added mass 139
3.4.2 From sectional to three-dimensional VIV 146
3.4.3 VIV of noncircular cross-sections 149
3.4.4 Summary and concluding remarks 153
4 Wake-Induced Instabilities of Pairs and Small Groups of Cylinders . . . 155
4.1 The Mechanisms 155
4.1.1 Modified quasi-steady theory 156
4.1.2 The damping-controlled mechanism 157
4.1.3 The wake-flutter mechanism 158
4.2 Wake-Induced Flutter of Transmission Lines 160
4.2.1 Analysis for a fixed windward conductor 162
4.2.2 Analysis for a moving windward conductor 183
4.2.3 Three-dimensional effects and application to real
transmission lines 192
4.3 Fluidelastic Instability of Offshore Risers 195
4.3.1 Experimental evidence for the existence of fluidelastic
instability in riser bundles 196
4.3.2 Analytical models 200
5 Fluidelastic Instabilities in Cylinder Arrays . . . . . . . . . . . . . . . . . . 215
5.1 Description, Background, Repercussions 215
5.2 The Mechanisms 220
5.2.1 The damping-controlled one-degree-of-freedom mechanism 220Contents vii
5.2.2 Static divergence instability 223
5.2.3 The stiffness-controlled wake-flutter mechanism 224
5.2.4 Dependence of the wake-flutter mechanism on mechanical damping 227
5.2.5 Wake-flutter stability boundaries for cylinder rows 229
5.2.6 Concluding remarks 230
5.3 Fluidelastic Instability Models 232
5.3.1 Jet-switch model 232
5.3.2 Quasi-static models 235
5.3.3 Unsteady models 239
5.3.4 Semi-analytical models 249
5.3.5 Quasi-steady models 254
5.3.6 Computational fluid-dynamic models 261
5.3.7 Nonlinear models 265
5.3.8 Nonuniform flow 270
5.4 Comparison of the Models 274
5.4.1 Experimental support for and against Connors’ equation 275
5.4.2 Comparison of theoretical models with experimental data 277
5.4.3 State of the art 287
6 Ovalling Instabilities of Shells in Cross-Flow . . . . . . . . . . . . . . . . . 291
6.1 A Historical Perspective 291
6.2 The Vortex-Shedding Hypothesis 293
6.3 Ovalling with No Periodic Vortex Shedding 296
6.3.1 Pa¨ ?doussis and Helleur’s 1979 experiments 296
6.3.2 In search of a new cause 302
6.4 Further Evidence Contradicting Vortex-Shedding Hypothesis 304
6.4.1 Further experiments with cantilevered shells 304
6.4.2 Experiments with clamped-clamped shells 307
6.5 Counterattack by the Vortex-Shedding Proponents and Rebuttal 311
6.5.1 The “peak of resonance” argument 311
6.5.2 Have splitter plates been ineffectual? 312
6.5.3 Denouement ´ 313
6.6 Simple Aeroelastic-Flutter Model 314
6.6.1 Equations of motion and boundary conditions 315
6.6.2 Solution of the equations 317
6.6.3 Theoretical results and comparison with experiment 319
6.7 A Three-Dimensional Flutter Model 322
6.7.1 The model and methods of solution 323
6.7.2 Theoretical results 327
6.7.3 Comparison with experiment 329
6.7.4 Improvements to the theory 331
6.8 An Energy-Transfer Analysis 334
6.9 Another Variant of the Aeroelastic-Flutter Model 338
6.9.1 The flutter model 338
6.9.2 Typical results 340
6.9.3 An empirical relationship for Uthr 342
6.10 Concluding Remarks 344viii Contents
7 Rain-and-Wind-Induced Vibrations . . . . . . . . . . . . . . . . . . . . . . . 345
7.1 Experimental Evidence 345
7.1.1 Field cases 345
7.1.2 Wind-tunnel experiments 346
7.2 Modelling Rainwater Rivulets 348
7.2.1 Development of rivulets 348
7.2.2 Tearing of rivulets 349
7.3 VIV, Galloping and Drag Crisis 351
7.4 Yamaguchi’s Model: A Cylinder-Rivulet-Coupled Instability 354
7.5 Concluding Remarks 355
Epilogue 357
Appendix A The Multiple Scales Method 359
Appendix B Measurement of Modal Damping for the Shells Used
in Ovalling Experiments 361
References 365
Index 397
TOC- paidoussis- Fluid-Structure Interactions: Cross-Flow-Induced Instabilities
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