Flow-Induced Vibration

254 Pages·2001·26.082 MB·English

by  Robert D. Blevins

Flow-Induced Vibration
•'''i :.
Second Edition
Robert D. Blevins
'I
i
·'
KRIEGER PUBLISHING COMPA NY
MALABAR, FLORIDA
2001
Second Edition 1990
Reprint Edition 1994 w/updating and new preface
Reprint Edition 200 I
Contents
Printed and Published by
KRIEGER PUBLISHING COMPANY
KRIEGER DRIVE
MALABAR, FLORIDA 32950 Preface vii
Nomenclature ix
Copyright© 1990 by Van Nostrand Reinhold Company, Inc.
Transferred to Author 2000
Reprinted by Arrangement.
1
Dimensional Analysis 5
1.1 Nondimensional parameters 5
All rights reserved. No part of this book may be reproduced in any form or by any
1.2 Application 9
means, electronic or mechanical, including information storage and retrieval systems ·2 Ideal Fluid Models 12
without permission in writing from the publisher.
2.1 Fundamentals of potential flow 12
No liability is assumed with respect to the use oft he information contain.ed herein.
2.2 Added mass ' 20
Printed in the United States ofA merica.
2.3 Fluid coupling 26
2.4 Vortex motion 31
FROM A DECLARATION OF PRINCIPLES JOINTLY ADOPTED BY A ). ·Vortex-induced Vibration 43
COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COM 3.1 Vortex wake of a stationary circular cylinder 43
MITTEE OF PUBLISHERS: 3.2 Strouhal number ~ 47
This publication is designed to provide accurate and authoritative information 3.3 Effect of cylinder motion on wake 54
in regard to the subject matter covered. It is sold with the understanding that the
3.4 Analysis of vortex-induced vibration 58
publisher is not engaged in rendering legal, accounting, or other
professional service. If legal advice or other expert assistance is required, the 3.5 Models for vortex-induced vibration 60
services of a competent professional person should be sought. 3.6 Reduction of vortex-induced vibration 77
J.7 The problem with bridge decks 82
3.8 Example: Marine cables and pipelines 85
Library of Congress Cataloging-In-Publication Data Galloping and Flutter ·104
4.1 Introduction to galloping 104
Blevins, Robert D.
4.2 Galloping instability 105
Flow-induced vibration I Robert D. Blevins. - 2nd ed.
4.3 Galloping response 113
p.cm.
4.4 Vortex shedding, turbulence, and galloping 125
Originally published: New York: Van Nostrand Reinhold.
4.5 Flutter 130
c1990.
4.6 Prevention of galloping and flutter 139
Includes bibliographical references and indexes.
4. 7 Example: Flutter analysis of 1927 Ryan NYP 142
ISBN 1-57524-183-8 (alk. paper)
4.8 Example: Galloping of a cable 144
I. Vibration. 2. Fluid dynamics. I. Title.
Instability of Tube and Cylinder Arrays 153
[TA355.B52 1993]
5 .1 Description of fluid elastic instability 153
620. 3-dc20 92-40221
CIP 5.2 Theory of fluid elastic instability 161
5.3 Practical considerations for heat exchangers 171
5.4 Vibration of pairs of cylinders 174
10 9 8 7 6 5 4 3 5.5 Example: Tube instability in a heat exchanger 185
v
6 Vibrations Induced by Oscillating Flow 194
6.1 Inline forces and their maximum 194
6.2 Inline motion 199
6.3 Fluid force coefficients 209
6.4 Transverse force and response 216
Preface
6.5 Reduction of vibration induced by oscillating flow 221
6.6 Example: Ocean wave-induced vibration of a riser 221
6. 7 Ship motion in a seaway . 225
7 Vibration Induced by Turbulence and Sound 239
7 .1 Elements of the theory of random vibrations 239 The purpose of this book is to provide mechanical engineers,
7 .2 Sound-and turbulence-induced vibration of panels 245 aeronautical engineers, civil engineers, marine engineers, and students
7 .3 Turbulence-induced vibration of tubes and rods 260 with analytical tools for the analysis of the vibrations of structures
7.4 Vibration induced by winds 271 exposed to fluid flow. The book assumes some knowledge of structural
7 .5 Response of aircraft to gusts 291 ·vibrations and fluid mechanics. Since the book is basically introductory, a
7.6 Reduction of vibration induced by turbulence 296
review of vibrations of structures is provided in the appendices, and some
7. 7 Example: Wind-induced vibration of a building 296
·explanatory material on the theory of random vibrations is also
8 Damping of Structures 305
8.1 Elements of damping 305 pre~ented. The text is organized according to the fluid dynamic
mechanism for exciting vibration rather than by type of structure, since
8.2 Fluid damping 308
8.3 Structural damping 316 any given structure may be subject to several mechanisms for
8.4 Damping of bridges, towers, buildings, piping, and aircraft flow-induced vibration.
structures 325 This book represents the sum of twenty-five years of research at
8.5 Material damping and dampers 336 General Atomics, San Diego, California; the California Institute of
9 Sonnd Induced by Vortex Shedding 349 Technology, Pasadena, California; .David Taylor Model Basin,
9 .1 Sound from single cylinders 349 Carderock, Maryland; and Rohr IndustriFs, Chula Vista, California. The
9 .2 Sound from vibrating cylinders 359 second edition is revised and expanded from the first edition. The chapter
9.3 Sound from multiple tubes and heat exchangers 364
. on ideal fluid models is entirely new. All other chapters have been
9 .4 Sound from flow over cavities 375
' . updated and expanded. There is new material on aeronautical problems
10 Vibrations of a Pipe Containing a Fluid Flow 384
of flutter and sonic fatigue i1J addition to the heat-exchanger, offshore,
10.1 Instability of fluid-conveying pipes 384
10.2 External axial flow 399 and wind-engineering topics treated in the fir~t edition. Many exercises
I 0.3 Pipe whip 401 · . and examples have been added to make the book more suitable for use as
10.4 Acoustical Forcing and Leakage-induced Vibration 405 a text book.
In this Krieger reprint edition, all known errors have been corrected
~nd updates have been made to reflect current research. Since many
Appendix A: Modal Analysis 415 systems that are prone to flow-induced vibration are also governed by
Appendix B: Principal Coordinates 421 ')the ASME code, new information on vibration-related code rules has
Appendix C: Aerodynamic Sources of Sound 426 ,;; -:: been added.
Appendix D: Digital Spectral and Fourier Analysis 430
:.··.. . Appendix E contains procedures for flow~induced vibration analysis
Appendix E: ASME Code on Flow-Induced Vibration 436
given in Appendix N, Code Section 3, of the American Society of
Author Index 463 '1
·:<· .. ·Mechanical Engineers Boiler. and Pressure Vessel Code, 1992. Table
Subject Index 471
13-2 gives Code recommendations· for calculating vortex-induced
... vibration of cylinders, Figure 5-6(a) gives Code recommendations for
.,, .calculation of instability in ·tube arrays, and Sections 7 .3.2 and
73.3 present methods consistent with the Code for turbulence-induced
vibration.
vii
~vmpuu;;.i p.iv0H1.m:s LHctL unp1emen1 many or tne so1ut1ons in this book
are available from
Avian Software
P.O. Box 80374
San Diego, CA 92138
Nomenclature
The programs include discrete vortex motion, vortex-induced vibration,
flutter, heat-exchanger vibration analysis, and sonic fatigue of plates. As
of this writing, the price is $179 for individual copies or class license. The
programs are provided on disks suitable for IBM PC or compatible. A Cross-sectional area or amplitude of vibration (one-half
peak-to-peak displacement)
The author is indebted ·to many individuals for their help with the
Drag coefficient
second edition. Colleagues, especially H. Aref, M. K. Au-Yang, B.
Added mass coefficient
Bickers, M. Gharib, I. Holehouse, T. M. Mulcahy, M. P. Paidoussis, M.
Lift coefficient
W. Parkin, M. J. Pettigrew, J. Sandifer, T. Sarpkaya, and D.S. Weaver,
Moment coefficient
provided insight, inspiration, and data. Kathleen Cudahy withstood the
Inertia coefficient
paper blizzard that covered our house and supported the author with
. Vertical force coefficient
kindness during endless rewrites. Boecky Y alof edited every word in the
manuscript and the book is much better for her skill. Width or characteristic length used in forming aerodynamic
coefficients
This book is dedicated to people who will never know my name or
yours. They are the people who travel in the airplanes, work in the F Force per unit length or moment per unit length
G Gust factor
buildings, and are warmed by the power plants that this book endeavors
I Area bending moment of inertia
to analyze and protect. They motivate our work and they are our first
responsibility. · lo Mass polar moment of inertia
+
Kc Keulegan-Carpenter number
L Spanwise structural length
M Mass or added mass
Re Reynolds number
S Strauhal number
SP Pressure spectral density
SPL Sound pressure level,
u
Fluid velocity in free stream or at minimum area
v
Velocity of structure
y Volume
.X Position parallel to free stream
y
Position normal to free stream
c Speed of sound in fluid or chord of airfoil
Frequency (Hz)
Acceleration of gravity
Peak-to-rms ratio
Integer or imaginary constant
Spring constant per unit length
Correlation length
Mass per unit length
Pressure or probability
ix
'1. JJyuam1c pressure, pU.&./2
r Correlation function
t Time
v Transverse fluid velocity
w Fluid displacement parameter
x Displacement of coordinate parallel to free stream
Introduction
y Displacement of coordinate normal to free stream
z . Spanwise coordinate or complex number
a Angle of attack
8 Logrithmic decrement of damping
Or Reduced damping, 2m(2nC)/(pD2 The flow of fluids around structures, ranging from clarinet reeds to
)
C Damping factor skyscrapers, can cause destructive vibrations as well as useful motions.
(} Rotation angle Wind rustles leaves, rings wind chimes, uproots crops, and destroys
A. Eigenvalue or wavelf?ngth whole communities. The sea currents that fan leaves of kelp also bring
v Kinematic viscosity offshore platforms crashing into the ocean. The liquid sodium that cools
1/J · Stream function the core of a breeder reactor can break shielding and precipitate melting
</> Phase angle or potential function of the reactor core. Such flow-induced vibrations have become
-r Time lag increasingly important in recent years because designers are using
p Fluid density materials to their limits, causing structures to become progressively
ro Circul~ frequency (radians/sec) or vorticity ·lighter, more flexible, and more prone to vibration.
A new jargon has developed to describe these flow-induced vibrations.
Ice-coated transmission lines in Canada "gallop" in a steady wind;
Subscripts and Superscripts marine tow cables suspending hydrophones "strum" at predictable
frequencies; slender wings of aircraft ~flutter" above a critical speed;
a Acoustic heat-exchanger tube arrays experience "fluid elastic instability." Each
D .Drag of these vibrations arises from distinct fluid-dynamic phenomena that
L Lift can be classified by the nature of the flow and the structure, as shown in
Integer or imaginary constant ( -1)112 Figure A.
j Integer · This book explores the vibrations of structures induced by a subsonic
m Maximum value flow. Many of the structures considered are bluff. A bluff structure i~ one
rms Square root of mean of square in which the flow separates from a large section of the structure's surface.
x Parallel to free stream Most civil engineering structures, such as bridges or heat-exchanger
y Normal to·free stream tubes, are bluff structures. The primary purpose of these structures is not
(} Torsion to gain lift or minimize drag as it is with aircraft components, but rather
(") Differentiation with respect to time to bear loads, contain flow, or provide heat transfer surface. These
n
Average (mean) with respect to time structures are not aerodynamically optimized. Flow-induced vibrations
B Vector quantity (boldface) are usll:ally regarded as a secondary design consideration, at least until a
(-) Mode shape, a function of x, y, or z failure occurs.
The fluid flo~ and the structure are coupled through the force exerted
on the structure by the fluid, as shown in Figure B. The fluid force causes
the structure to deform. As the structure deforms, its orientation to the
flow changes, and the fluid force may change. In some cases, such as the
excitation of ship hull plates by turbulence of rushing water, the fluid
force is independent of small changes in the position <lf the structure. In
1
FLUID FORCE ON STRUCTURE
Magnitude
Coherence
/Time lag
wCl 1- FLUID DYNAMICS STRUCTURAL DYNAMICS
u:::: > (!J 2w (w!J Velocity, density, viscosity Natural frequency
z_C::I: Zc ~to-----t a::::::> External flow field Mass
<( er.>
xcr.i a: Turbulence Damping
IcW-c eOr.: I- Vortices /Vibration amplitude
wCu l 0> u
::::> e~r.> W0:W0:
zC l ::::> 1-:E FLUID/STRUCTURE BOUNDARY MOTION
x~---~ u0 s<(::<!E Oscillating separation
w <( :::c
I- c0 c Local surface velocity
C>0C w<( zc::=::iW> lnstantal)eous angle of attack
<( (!J Motio_n r~lative to a gap
..... cc~
----~~
a:u Fig. B Feedback between 'fluid and structure.
~2
3: 2~ other cases, such as ice-coated power lines in a steady wind, the fluid
3: .0.. .J ...J force is completely determined by the orientation and velocity of the
0 u.. <(
.u....J. > Cl structure relative to the fluid flow. Finally, just as the fluid exerts a force
>IC<w (l u 1Ccz<wr. >(-l e:e0z:r:: n.:> > folnui dth. eT shtreu csttururec,t utrhee fsotrrcuec tuorne tehxee rftsl uaind ~eaqnu asly bnucht roopnpizoes itveo rftoirccees oinn tthhee
C/) ->- ::::> wake and produce large-amplitude vibration.
t;; !:::
<(....J In the analysis of flow-induced vibration, models are generated for
.w.. ,<CJC ( both the structure and the fluid. Since most structures are near-linear in
Cll
=-c>r2.i deformation with increasing load, the structures are modeled as linear
-'
u.. oscillators. If only a single structural degree of freedom is excited, tire·
>- w
:1J- (c2! :J: ZClC::::!:J> structural motion is described by a single linear equation with fluid
<( forcing. If more than one degree of structural freedom is present, such as
0 eel-
ta<;:;(i .....- --- ........JJ <Clu~ translation and torsion, linear systems of equations are required. Fluid
<( o
2 (!J a:Z models are more difficult. Fluid mechanics is an inherently nonlinear,
cco
er.> multi-degree-of-freedom phenomenon. Fluid models are generally
cc
w formed from a combination of basic principles and experimental data.
I
I From the database of physical laws and experimental data, model
::::>
.u....J. solutions are generated for the response of structure to flow. The
solutions lead to a prediction that can be compared with new
experimental data. The error between the new data and the prediction
reflects the limitation of the models. Unfortunately, only a few general
solutions are available. Most results rely on experimental data. There are .
sets of parameters that have proven useful in a wide variety of problems.
These nondimensional parameters are discussed in Chapter 1.
In Chapter 2, ideal fluid models are considered. In Chapters 3 through
5, analysis is developed for the response of structures in a steady flow.
2
The effects of oscillatory flow, turbulence, and sound on a structure are
examined in Chapters 6 and 7. In Chapter 8, damping of struct~res
which is the primary mechanism for "limiting flow-induced vibration, i~
Chapter 1
explored analytically and experimentally. Flow-induced sound (aero
acoustics) is investigated in Chapter 9, while the effect of internal flow on
a pipe is presented in Chapter 10. The appendices present mathematical
Dimensional Analysis
fundamentals of structural dynamics, aeroacoustics, and spectral analysis.
Figure 1-1 shows a two-dimensional, spring-supported, damped building
model exposed to a steady flow. This model is prototypical of elastic
structures exposed to a fluid flow. The vibrations of this model can be
' described in terms of nondimensional parameters governing the fluid
,flow, the model, and the fluid-structure interaction. These parameters
·are useful· for scaling flow-induced vibration and estimating the
,:, 'importance of different fluid phenomena.
NONDIMENSIONAL PARAMETERS
l~l.1. Geometry
Geometry is the most important parameter in ~termining the fluid force
on a structure. The geometry of the building model can be specified by its
:.. fineness ratio:
I length .
D =width= fineness ratJ.o. (1-1)
",;\·.tsp~cification of geometry ordinarily includes the ratio of length in the
!third dimension to width (this is called aspect ratio) and the ratio of
r
. .1~urface roughness to width .
~,·r I
:'.,t~i '
:y•,tt.1~2. Reduced Velocity, Dimensionless Amplitude
~-:, }· ''
.
~> ~As the model vibrates in the flow, it traces out the path shown in Figure
\: .:1-2. For steady vibration, the length of the path for one cycle is U If,
'.. 1,where U is the free stream velocity and f is the frequency of vibration.
:;Y. (;The width of the path is 2Ay, where Ay is the amplitude of the vibration.
{''.These path dimensions can be related to the structural dimension:
.!!_ path length per cycle d d . (l- )
re uce ve1 o c1ty, 2
fD model width
Ay vibration amplitude
- = dimensionless amplitude. (1-3)
D model width
5
Keulegan-Carpenter number is used for oscillating flows, such as ocean
waves; see Chapter 6. It is identical in form to the reduced velocity but
with U defined as the amplitude of velocity of a flow that oscillates with
frequency f about a structure of diameter D. The Strouhal number is
S = fsD I U, where ls is the frequency of periodic vortex shedding from
a structure of diameter D in a steady flow of velocity U; see Chapter 3.
1.1.3. Mass Ratio
The ratio of the model mass to the mass of fluid it displaces is
proportional to
Fig. 1-1 Vibration of a two-dimensional, spring-supported, damped model. m mass per unit length of model .
----------.- -=mass ratio, (1-4)
pD2 fluid density x model w1dth2
The first of these· parameters is commonly called reduced velocity or where m ordinarily includes structural mass and the "added mass" of
nondimen_sional velocity. Its inverse is called nondimensional frequency. fluid entrained by the moving model (see Chapter 2). The mass ratio is a
The maximum model width (D) is ordinarily used in forming these measure of the relative importance of buoyancy and added mass effects
parameters, because this width tends to govern the width of the wake. If on the model. It is often used to measure the susceptibility of lightweight
reduced velocity is between 2 and 8, then the model often interacts structures to flow-induced vibration. As the ratio of fluid mass to
strongly with vortex shedding in its own wake. structural mass increases, so does ~he propensity for flow-induced
Two nondimensional parameters that are closely related to reduced vibration.
velocity are Keulegan-Carpenter number and Strouhal number. The
1.1.4. Reynolds Number
>-
Boundary layer growth and flow separation are determined by fluid
+.:
c: forces on a microscopic level. The boundary layer is impelled about the
Q)
E q model by the inertia of the flow. Viscous friction at the model surface
~ or-~~~-t..;......~-r~~-\-!-~~~~~r-~...,.~-=~-' retards the boundary layer. It can be shown that the ratio of inertial force
CtS to viscous force in the boundary layer is (Schlichting, 1_968)
a.
(/) UD inertial force Id
0 • '£ = Reyno s number, (1-5)
v VISCOUS orce
where v is the kinematic viscosity of the fluid and is equal to the absolute
Time, t viscosity divided by density. The Reynolds number, abbreviated Re,
scales the boundary layer thickness and transition from laminar to
Fig. 1-2 Free vibration of a viscously damped structure· co is the natural frequency of turbulent flow. Flow separates from the back of bluff bodies at Reynolds
vibration in radians per second. ' Y numbers, based on the width of the structure, greater than about 50.
1.1.5. Mach Number, Turbulence Intensity Increasing reduced damping ordinarily reduces the amplitude of
flow-induced vibrations.
Mach number is equal to
U fluid velocity
1.2. .APPLICATION
Mach number, (1-6)
c speed of sound
The nondimensional parameters that have been found most useful in
where c is the speed. of sound in the fluid. Mach number measures the describing the vibrations of an elastic structure in a subsonic (Mach
tendency of fluid to compress as it encounters a structure. Most of the number less than 0.3) steady flow are:
analysis in this book is limited to Mach numbers less than 0.3, at which
compressibility does not ordinarily influence the vibration.
1. Geometry (l/D).
Turbulence intensity, like Mach number, is a measurement relative to 2. Reduced velocity (U/fD).
the· free stream fluid velocity. The turbulence intensity, 3. Dimensionless amplitude (Ay/D).
u:ms 4. Mass ratio (ml pD2
= root mean square turbulence ).
(1-7) 5. Reynolds number (UD/v).
U free' stream fluid velocity
6. Damping factor ( C).
measures the turbulence in the flow. Usually the turbulence is generated 7. Turbulence intensity ( u 'I U).
upstream of the model. The model will respond to this random
excitation. Low-turbulence .wind tunnels typically have turbulence levels Some of these nondimensional parameters will appear in every
equal to 0.1 % of the free stream velocity. Turbulence induced by wind is flow-induced vibra~ion analysis. Other parameters may appear as well.
a factor of 100 greater (Section 7.4.1).
DAMPING FACTOR. ~ ~ _L
-o
1.1.6. Damping Factor, Reduced Damping 0.0037
u-=~====rf
--~0.0076
The energy dissipated by a structure as it vibrates is characterized by its --00.014
damping factor, ---vo.0212 Ay
0.2
--eo.044
r __ energy dissipated per cycle
damping fc;ictor. (1-8)
1=i 4n x total energy of structure
Ci s called the damping factor or damping ratio. It is. often expressed as a
fraction of, l, the critical damping factor. For linear, viscously damped
structures, .. 2nC is equal to the natural logarithm o! the ratio of the 0.1
amplitudes of any two successive cycles of a lightly damped structure in
free decay, as shown in Figure 1-2. If the energy input to a structure by
the fl0w. is less .than the energy expended in damping, then the
flow-induced vibrations will diminish. Many real structures have damping
factors on the order of 0.01 (i.e., 1 % of critical); see Chapter 8.
A very useful parameter, variously called mass damping, reduced 0
damping, or Scruton number (see Walshe, 1983), can be formed by the JL
product of mass ratio and the damping factor: fD
Fig. 1-3 Lateral response of a spring-supported, damped building model with a side
2mp(D2nC) = reduced damping. (1-9) '.ratio of 2. The natural frequency of the model is 6 Hz, D = 3.35 in, and m/(pD2) = 129.5.
2 (Novak, 1971.)
.l..L
The objective of the majority of the analysis presented in this book is REFERENCES
to predict the dimensionless amplitude of flow-induced vibration as a
function of the remaining parameters, Novak, M. (1971) "Galloping and Vortex Induced Oscillation of Structures," Proceedings
of the Conference on Wind Effects on Buildings and Structure, held in Tokyo, Japan.
Schlichting, H. (1968) Boundary Layer Theory, McGraw-Hill, New York.
(1-10) Walshe, D. E. _(198~) "Scruton Number," Jounal of Wind Engineering and Industrial
Aerodynamics, 12, 99.
For example, Figure 1-3 shows the dimensionless amplitude of
flow-induced vibration of a building · model as a function of reduced
velocity and damping factor. The vibrations occur at the natural
frequency of the model. The two peaks in vibration amplitude are caused
by different phenomena. Periodic vortex shedding occurs at a frequency
given by ls= SU ID, where Sis approximately 0.2. The natural frequency
is the characteristic frequency f and the reduced velocity at which the
vortex shedding frequency equals the structural natural frequency is
U/(fD) = l/S = 5. Thus, the first peak in the vibrations is caused by
vortex shedding. The second peak, beginning at a reduced velocity of
about 11, is associated with an instability called galloping, which is similar
to aircraft flutter. Note that both sets of vibration decrease with
increasing damping.
Exercise
1. Estimate each of the nondimensional parameters in this
chapter for wind over your library building. D is the width of the
building on the narrow side and L is the building height. Estimate
the maximum wind velocity as 150 ft/sec (45 m/sec), or alternately,
use the extreme wind data of Figs. 7-17 and 7-18 of Chapter 7. The
room-temperature properties of air are: p = 0.075 lb/ft3
(1.2 kg/m3), v = 0.00016 ff /sec (0.000015 m2/sec), c = 1100 ft/sec
(343 m/sec). Assume a typical building average density of 10 lb/ft3
(150 kg/m3 Calculate library mass per unit height. Estimate the
).
natural frequency of the fundamental mode as f = 10/N Hz, where
N is the number of stories, or use Eq. 7-85. Estimate the damping
factor as C= 0.0076 or use the data presented in Chapter 8, Section
8.4.3~ Estimate therms turbulence as u:.nis = 0.2U or use the data in
Section 7.4.1, Eq. 7-64. If you don't feel your building moves
significantly during the wind, then Ay = 0. Plot your library on
Figure 1-3. How many stories high must your library be for
U/(fD) = 5?