Page 9 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

vi CONTENTS

3.4 Pipes with supported ends ............................... 88
3.4.1 Main theoretical results ........................... 88
3.4.2 Pressurization, tensioning and gravity effects ............. 98
3.4.3 Pipes on an elastic foundation ....................... 102
3.4.4 Experiments ................................... 103
3.5 Cantilevered pipes .................................... 111
3.5.1 Main thcoretical rcsults ........................... 111
3.5.2 The effect of gravity ............................. 115
3.5.3 The effect of dissipation ........................... 118
3.5.4 The S-shaped discontinuities ........................ 123
3.5.5 On destabilization by damping ....................... 130
3.5.6 Experiments ................................... 133
3.5.7 The effect of an elastic foundation .................... 149
3.5.8 Effects of tension and refined fluid mechanics modelling ...... 150
3.6 Systems with added springs, supports, masses and other
modifications ....................................... 153
3.6.1 Pipes supported at 6 = 1/L < 1 ...................... 153
3.6.2 Cantilevered pipes with additional spring supports .......... 157
3.6.3 Pipes with additional point masses .................... 164
3.6.4 Pipes with additional dashpots ....................... 167
3.6.5 Fluid follower forces ............................. 168
3.6.6 Pipes with attached plates .......................... 170
3.6.7 Concluding remarks .............................. 172
3.7 Long pipes and wave propagation .......................... 173
3.7.1 Wave propagation ............................... 173
3.7.2 Infinitely long pipe on elastic foundation ................ 174
3.7.3 Periodically supported pipes ........................ 178
3.8 Articulated pipes ..................................... 183
3.8.1 The basic dynamics .............................. 184
3.8.2 N-Degree-of-freedom pipes ......................... 186
3.8.3 Modified systems ............................... 190
3.8.4 Spatial systems ................................. 194

4 Pipes Conveying Fluid: Linear Dynamics I1 196
4.1 Introduction ........................................ 196
4.2 Nonuniform pipes .................................... 196
4.2.1 The equation of motion ........................... 196
4.2.2 Analysis and results .............................. 203
4.2.3 Experiments ................................... 208
4.2.4 Other work on submerged pipes ...................... 211
4.3 Aspirating pipes and ocean mining ......................... 213
4.3.1 Background ................................... 213
4.3.2 Analysis of the ocean mining system .................. 214
4.3.3 Recent developments ............................. 217
4.4 Short pipes and refined flow modelling ....................... 220
4.4.1 Equations of motion .............................. 221
4.4.2 Method of analysis .............................. 224