Page 10 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

CONTENTS vii

4.4.3 The inviscid fluid-dynamic force ..................... 225
4.4.4 The fluid-dynamic force by the integral Fourier-transform
method ...................................... 228
4.4.5 Refined and plug-flow fluid-dynamic forces and specification
of the outflow model ............................. 229
4.4.6 Stability of clamped-clamped pipes ................... 232
4.4.7 Stability of cantilevered pipes ....................... 236
4.4.8 Comparison with experiment ........................ 238
4.4.9 Concluding remarks on short pipes and refined-flow
models ...................................... 240
4.4.10 Long pipes and refined flow theory .................... 241
4.4.11 Pipes conveying compressible fluid .................... 241
4.5 Pipes with harmonically perturbed flow ...................... 242
4.5.1 Simple parametric resonances ....................... 243
4.5.2 Combination resonances ........................... 250
4.5.3 Experiments ................................... 253
4.5.4 Parametric resonances by analytical methods ............. 258
4.5.5 Articulated and modified systems ..................... 258
4.5.6 Two-phase and stochastically perturbed flows ............. 261
4.6 Forced vibration ..................................... 261
4.6.1 The dynamics of forced vibration ..................... 261
4.6.2 Analytical methods for forced vibration ................. 265
4.7 Applications ........................................ 267
4.7.1 The Coriolis mass-flow meter ....................... 268
4.7.2 Hydroelastic ichthyoid propulsion ..................... 269
4.7.3 Vibration attenuation ............................. 270
4.7.4 Stability of deep-water risers ........................ 271
4.7.5 High-precision piping vibration codes .................. 273
4.7.6 Vibration conveyance and vibration-induced flow .......... 274
4.7.7 Miscellaneous applications ......................... 275
4.8 Concluding remarks ................................... 276

5 Pipes Conveying Fluid: Nonlinear and Chaotic Dynamics 277
5.1 Introductory comments ................................. 277
5.2 The nonlinear equations of motion ......................... 278
5.2.1 Preliminaries .................................. 279
5.2.2 Hamilton's principle and energy expressions .............. 281
5.2.3 The equation of motion of a cantilevered pipe ............ 283
5.2.4 The equation of motion for a pipe fixed at both ends ........ 285
5.2.5 Boundary conditions ............................. 287
5.2.6 Dissipative terms ................................ 287
5.2.7 Dimensionless equations ........................... 288
5.2.8 Comparison with other equations for cantilevers ........... 290
5.2.9 Comparison with other equations for pipes with fixed ends .... 294
5.2.10 Concluding remarks .............................. 295
5.3 Equations for articulated systems .......................... 296
5.4 Methods of solution and analysis .......................... 299