Page 8 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

Preface ................................................ xi
Artwork Acknowledgnierits .................................... xiv

1 Introduction
1.1 General overview ....................................
1.2 Classification of flow-induced vibrations .....................
1.3 Scope and contents of volume 1 ...........................
1.4 Contents of volume 2 ..................................

2 Concepts. Definitions and Methods 6
2.1 Discrete and distributed parameter systems .................... 6
2.1.1 The equations of motion ........................... 8
2.1.2 Brief review of discrete systems ...................... 9
2.1.3 The Galerkin method via a simple example .............. 12
2.1.4 Galerkin’s method for a nonconservative system ........... 16
2.1.5 Self-adjoint and positive definite continuous systems ........ 17
2.1.6 Diagonalization, and forced vibrations of continuous
systems ...................................... 18
2.2 The fluid mechanics of fluid-structure interactions ............... 23
2.2.1 General character and equations of fluid flow ............. 23
2.2.2 Loading on coaxial shells filled with quiescent fluid ......... 36
2.2.3 Loading on coaxial shells filled with quiescent
viscous fluid ................................... 46
2.3 Linear and nonlinear dynamics ............................ 51
3 Pipes Conveying Fluid: Linear Dynamics I 59
3.1 Introduction ........................................ 59
3.2 The fundamentals .................................... 60
3.2.1 Pipes with supported ends .......................... 60
3.2.2 Cantilevered pipes ............................... 63
3.2.3 On the various bifurcations ......................... 67
3.3 The equations of motion ................................ 69
3.3.1 Preamble ..................................... 69
3.3.2 Newtonian derivation ............................. 71
3.3.3 Hamiltonian derivation ............................ 76
3.3.4 A comment on frictional forces ...................... 82
3.3.5 Nondimensional equation of motion ................... 83
3.3.6 Methods of solution .............................. 84

V