fluid structure interactions docx

I FLUID-STRUCTURE INTERACTIONS SLENDER STRUCTURES AND AXIAL FLOW VOLUME 1 FLUID-STRUCTURE INTERACTIONS SLENDER STRUCTURES AND AXIAL FLOW VOLUME 1 MICHAEL P. PAIDOUSSIS Department of Mechanical Engineering, McGill University, Montreal, Que'bec, Canada W ACADEMIC PRESS SAN DIEGO LONDON NEW YORK BOSTON SYDNEY TOKYO TORONTO This book is printed on acid-free paper. Copyright 0 1998 by ACADEMIC PRESS All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Academic Press 525 B Street, Suite 1900, San Diego, California 92101-4495, USA http:llwww.apnet.com Academic Press Limited 24-28 Oval Road, London NW 1 7DX, UK http:llwww.hbuk.co.uWap/ ISBN 0-12-544360-9 A catalogue record for this book is available from the British Library Library of Congress Catalog Card Number: 98-86469 Typeset by Laser Words, Madras, India Printed in Great Britain by WBC Book Manufacturers, Bridgend, Mid-Glamorgan 98 99 00 01 02 03 WB 9 8 7 6 5 4 3 2 1 Preface Artwork Acknowledgnierits 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 2.1 Discrete and distributed parameter systems 2.1.1 The equations of motion 2.1.2 Brief review of discrete systems 2.1.3 The Galerkin method via a simple example 2.1.4 Galerkin’s method for a nonconservative system 2.1.5 Self-adjoint and positive definite continuous systems 2.1.6 Diagonalization, and forced vibrations of continuous systems 2.2 The fluid mechanics of fluid-structure interactions 2.2.1 General character and equations of fluid flow 2.2.2 Loading on coaxial shells filled with quiescent fluid 2.2.3 Loading on coaxial shells filled with quiescent viscous fluid 2.3 Linear and nonlinear dynamics 3 Pipes Conveying Fluid: Linear Dynamics I 3.1 Introduction 3.2 The fundamentals 3.2.1 Pipes with supported ends 3.2.2 Cantilevered pipes 3.2.3 On the various bifurcations 3.3 The equations of motion 3.3.1 Preamble 3.3.2 Newtonian derivation 3.3.3 Hamiltonian derivation 3.3.4 A comment on frictional forces 3.3.5 Nondimensional equation of motion 3.3.6 Methods of solution xi xiv 6 6 8 9 12 16 17 18 23 23 36 46 51 59 59 60 60 63 67 69 69 71 76 82 83 84 V vi CONTENTS 3.4 Pipes with supported ends 3.4.1 Main theoretical results 3.4.2 Pressurization, tensioning and gravity effects 3.4.3 Pipes on an elastic foundation 3.4.4 Experiments 3.5 Cantilevered pipes 3.5.1 Main thcoretical rcsults 3.5.2 The effect of gravity 3.5.3 The effect of dissipation 3.5.4 The S-shaped discontinuities 3.5.5 On destabilization by damping 3.5.6 Experiments 3.5.7 The effect of an elastic foundation 3.5.8 Effects of tension and refined fluid mechanics modelling Systems with added springs, supports, masses and other modifications 3.6.1 Pipes supported at 6 = 1/L < 1 3.6.2 Cantilevered pipes with additional spring supports 3.6.3 Pipes with additional point masses 3.6.4 Pipes with additional dashpots 3.6.7 Concluding remarks 3.6 3.6.5 Fluid follower forces 3.6.6 Pipes with attached plates 3.7 Long pipes and wave propagation 3.7.1 Wave propagation 3.7.2 Infinitely long pipe on elastic foundation 3.8 Articulated pipes 3.8.1 The basic dynamics 3.8.2 N-Degree-of-freedom pipes 3.8.3 Modified systems 3.8.4 Spatial systems 3.7.3 Periodically supported pipes 4 Pipes Conveying Fluid: Linear Dynamics I1 4.1 Introduction 4.2 Nonuniform pipes 4.2.1 The equation of motion 4.2.2 Analysis and results 4.2.3 Experiments 4.2.4 Other work on submerged pipes 4.3 Aspirating pipes and ocean mining 4.3.1 Background 4.3.2 Analysis of the ocean mining system 4.3.3 Recent developments 4.4 Short pipes and refined flow modelling 4.4.1 Equations of motion 4.4.2 Method of analysis 88 88 98 102 103 111 111 115 118 123 130 133 149 150 153 153 157 164 167 168 170 172 173 173 174 178 183 184 186 190 194 196 196 196 196 203 208 211 213 213 214 217 220 221 224 CONTENTS vii 4.4.3 The inviscid fluid-dynamic force 4.4.4 The fluid-dynamic force by the integral Fourier-transform method 4.4.5 Refined and plug-flow fluid-dynamic forces and specification of the outflow model 4.4.6 Stability of clamped-clamped pipes 4.4.7 Stability of cantilevered pipes 4.4.8 Comparison with experiment 4.4.10 Long pipes and refined flow theory 4.4.11 Pipes conveying compressible fluid 4.5 Pipes with harmonically perturbed flow 4.5.1 Simple parametric resonances 4.5.2 Combination resonances 4.5.3 Experiments 4.5.4 Parametric resonances by analytical methods 4.5.5 Articulated and modified systems 4.5.6 Two-phase and stochastically perturbed flows 4.6 Forced vibration 4.6.1 The dynamics of forced vibration 4.6.2 Analytical methods for forced vibration 4.7 Applications 4.7.1 The Coriolis mass-flow meter 4.7.2 Hydroelastic ichthyoid propulsion 4.7.3 Vibration attenuation 4.7.4 Stability of deep-water risers 4.7.5 High-precision piping vibration codes 4.7.7 Miscellaneous applications 4.8 Concluding remarks 5.1 Introductory comments 5.2 The nonlinear equations of motion Hamilton's principle and energy expressions 5.2.3 The equation of motion of a cantilevered pipe 5.2.5 Boundary conditions 5.2.6 Dissipative terms 5.2.7 Dimensionless equations 5.2.8 Comparison with other equations for cantilevers 5.2.10 Concluding remarks 5.3 Equations for articulated systems 5.4 Methods of solution and analysis 4.4.9 Concluding remarks on short pipes and refined-flow models 4.7.6 Vibration conveyance and vibration-induced flow 5 Pipes Conveying Fluid: Nonlinear and Chaotic Dynamics 5.2.1 Preliminaries 5.2.2 5.2.4 The equation of motion for a pipe fixed at both ends 5.2.9 Comparison with other equations for pipes with fixed ends 225 228 229 232 236 238 240 241 241 242 243 250 253 258 258 261 261 261 265 267 268 269 270 271 273 274 275 276 277 277 278 279 281 283 285 287 287 288 290 294 295 296 299 [...]... and, in the broadest sense of the word, students of systems involving fluid- structure interactions For, in many cases, the aforementioned problems were ‘solved’ without truly understanding either the cause of the original problem or the reasons why the cure worked, or both Some of the time-worn battery of ‘cures’, e.g making the structure stiffer via stiffeners or additional supports, usually work,... of slender systems interacting with axial flow are pipes and other flexible conduits containing flowing fluid, heat-exchanger tubes in axial flow regions of the secondary fluid and containing internal flow of the primary fluid, nuclear reactor fuel elements, monitoring and control tubes, thin-shell structures used as heat shields in aircraft engines and thermal shields in nuclear reactors, jet pumps,... interest even the cognoscenti The structure of Section 2.2, dealing with fluid mechanics, is rather different Some generalities on the various flow regimes of interest (e.g potential flow, turbulent flow) are given first, both physical and in terms of the governing equations This is then followed by two examples, in which the fluid forces exerted on an oscillating structure are calculated, for: (a)... structure are calculated, for: (a) two-dimensional vibration of coaxial shells coupled by inviscid fluid in the annulus; (b) two-dimensional vibration of a cylinder in a coaxial tube filled with viscous fluid Finally, in Section 2.3, a brief discussion is presented on the dynamical behaviour of fluid- structure- interaction systems, in particular the differences when this is obtained via nonlinear as... instability and involves local flow oscillations An example is the alternate vortex shedding from a cylindrical structure In this case it is important to consider the possible existence of a control mechanism governing and perhaps enhancing the strength of the excitation: e.g a fluid- resonance or a fluidelastic feedback The classical example is that of lock-in, when the vortex-shedding frequency is captured... also is an introductory chapter, where some of the basics of the dynamics of structures, fluids and coupled systems are briefly reviewed with the aid of a number of examples The treatment is highly selective and it is meant to be a refresher rather than a substitute for a more formal and complete development of either solid or fluid mechanics, or of systems dynamics Section 2.1 deals with the basics of... contains the flow or is immersed in it, or both Dyrzamics is used here in its genetic sense, including aspects of srabiliry, thus covering both self-excited and free or forced motions associated with fluid- structure interactions in such configurations Indeed, flow-induced instabilities - instabilities in the linear sense, namely, divergence and flutter - are a major concern of this book However, what is rather... Rockwell consider flow-induced excitation of both body and fluid oscillators, which leads to a 3 x 2 tabular matrix within which any given situation can be accommodated; in this book, however, we are mainly concerned with flow-induced 4 SLENDER STRUCTURES AND AXIAL FLOW structural motions, and hence only half of this matrix is of direct interest The structure, or ‘body oscillator’, is any component with... Netherlands Figure 4.38(a) from Lighthill (1969) by permission of Annual Review of Fluid Mechanics ~~ See bibliography for the complete reference xiv 1 Introduction 1.1 GENERAL OVERVIEW This book deals with the dynamics of slender, mainly cylindrical or quasi-cylindrical, bodies in contact with axial flow - such that the structure either contains the flow or is immersed in it, or both Dyrzamics is used... (x,y , z) J.2 The expressions for curvature and twist 5.3 Derivation of the fluid- acceleration vector 5.4 The equations of motion for the pipe K Matrices for the Analysis of an Extensible Curved Pipe Conveying Fluid References Index 522 522 523 523 524 529 , , 53 1 558 Preface A . I FLUID- STRUCTURE INTERACTIONS SLENDER STRUCTURES AND AXIAL FLOW VOLUME 1 FLUID- STRUCTURE INTERACTIONS SLENDER STRUCTURES AND AXIAL. continuous systems 2.2 The fluid mechanics of fluid- structure interactions 2.2.1 General character and equations of fluid flow 2.2.2 Loading on