Table Of ContentSERIES ON STABILITY, VIBRATION AND CONTROL OF SYSTEMS
Series B Volume 7
Dynamics with Friction
Modeling, Analysis and Experiment
Parti
Editors
Ardeshir Guran, Friedrich Pfeiffer & Karl Popp
WWoorrlldd SScciieennttiiffiicc
Dynamics with Friction
Modeling, Analysis and Experiment
Parti
SERIES ON STABILITY, VIBRATION AND CONTROL OF SYSTEMS
Series Editors: Ardeshir Guran & Daniel J. Inman
About the Series
Rapid developments in system dynamics and control, areas related to many other
topics in applied mathematics, call for comprehensive presentations of current
topics. This series contains textbooks, monographs, treatises, conference proceed
ings and a collection of thematically organized research or pedagogical articles
addressing dynamical systems and control.
The material is ideal for a general scientific and engineering readership, and is
also mathematically precise enough to be a useful reference for research specialists
in mechanics and control, nonlinear dynamics, and in applied mathematics and
physics.
Selected Forthcoming Volumes
Series A. Textbooks, Monographs and Treatises
Dynamics of Gyroscopic Systems: Flow Induced Vibration of Structures,
Gyroelasticity, Oscillation of Rotors and Mechanics of High Speed Axially
Moving Material Systems
Authors: A. Guran, A. Bajaj, G. D'Eleuterio, N. Perkins and Y. Ishida
Adaptive Control of Nonlinear Systems
Authors: R. Ghanadan, A. Guran and G. Blankenship
Series B. Conference Proceedings and Special Theme Issues
Wave Motion, Intelligent Structures and Nonlinear Mechanics
Editors: A. Guran and D. J. Inman
Acoustic Interactions with Submerged Elastic Structures
Part I: Acoustic Scattering and Resonances
Editors: A. Guran, J. Ripoche and F. Ziegler
Part II: Propagation, Ocean Acoustics and Scattering
Editors: A. Guran, G. Maugin and J. Engelbrecht
Part III: Acoustic Propagation and Scattering, Wavelets and
Time-Frequency Analysis
Editors: A. Guran, A. de Hoop and D. Guicking
Part IV: Non-destructive Testing, Acoustic Wave Propagation and Scattering
Editors: A. Guran, A. Bostrom, A. Gerard and G. Maze
Structronic Systems: Active Structures, Devices, and Systems
Editors: H.-S. Tzou, A. Guran, G. Anderson, D. J. Inman and M. C. Natori
Dynamics with Friction: Modeling, Analysis, and Experiment
Editors: A. Guran, F. Pfeiffer and K. Popp
Proceedings of the First European Conference on Structural Control
Editors: A. Baratta and J. Rodellar .
SERIES ON STABILITY, VIBRATION AND CONTROL OF SYSTEMS
Series B Volume 7
Series Editors: Ardeshir Guran & Daniel J Inman
Dynamics with Friction
Modeling, Analysis and Experiment
Parti
Editors
Ardeshir Guran
University of Southern California
Friedrich Pfeiffer
Technical University of Munich
Karl Popp
University of Hannover
World Scientific
Singapore • New Jersey • London • Hong Kong
Published by
World Scientific Publishing Co Pte Ltd
P O Box 128, Farrer Road, Singapore 912805
USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
DYNAMICS WITH FRICTION: MODELING, ANALYSIS AND EXPERIMENT
Copyright © 1996 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance
Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA.
ISBN 981-02-2953-4
Printed in Singapore by Uto-Print
STABILITY, VIBRATION
AND
CONTROL OF SYSTEMS
Editor-in-chief: Ardeshir Guran
Co-editor: Daniel J. Inman
Advisory Board
Henry Abarbanel Toshio Fukuda Jerrold Marsden Jon Juel Thomson
University of California Nagoya University California Inst. of Tech. Tech. Univ. of Denmark
San Diego Nagoya Pasadena Lyngby
USA JAPAN USA DENMARK
Gary Anderson Alain Gerard Hans Natke Horn-Sen Tzou
Army Research Office Laboratoire de Mecanique Universitat Hannover University of Kentucky
Research Triangle Park Bordeaux Hannover Lexington
USA FRANCE GERMANY USA
Jorge Angeles Hans Irschik Paul Newton Herbert Uberall
McGill University Johannes Kepler Universitat University of S. California Catholic Univ. of America
Montreal Linz Los Angeles Washington
CANADA AUSTRIA USA USA
Leon Bahar Heikki Isomaki Michihiro Natori Firdaus Udwadia
Drexel University Helsinki Univ. of Tech. Inst. of Space & Astro. University of S. California
Philadelphia Helsinki Kanagwa Los Angeles
USA FINLAND JAPAN USA
Anil Bajaj Jer-nan Juang Friedrich Pfeiffer Dick van Campen
Purdue University Lang ley Research Center Technische Universitat University of Technology
Lafayette Hampton Miinchen Eindhoven
USA USA GERMANY NETHERLANDS
Anders Bostrom John Junkins Raymond Plant Jorg Wauer
Chalmers Technical Univ. Texas A&M University Virginia Poly. Inst. Technische Universitat
Goteborg College Station Blacksburg Karlsruhe
SWEDEN USA USA GERMANY
RRRaaafffaaaeeelll CCCaaarrrbbbooo---FFFiiittteee YY'ooouuudddaaannn KKKiiimmm Karl Popp Joanne Wegner
C.S.I.C. Seoul National University Universitat Hannover University of Victoria
Madrid Seoul Hannover Victoria
SPAIN KOREA GERMANY CANADA
Fabio Casciati James Knowles Richard Rand James Yao
Universita di Pavia California Inst. of Tech. Cornell University Texas A&M University
Pavia Pasadena Ithaca College Station
ITALY USA USA USA
Juri Engelbrecht Edwin Kreuzer Jean Ripoche Lotfi Zadeh
Estonian Academy of Sci. Technische Universitat University of Le Havre University of California
Tallin Hamburg-Harburg Le Havre Berkeley
ESTONIA GERMANY FRANCE USA
Lucia Faravelli Oswald Leroy Kazimirez Sobczyk Franz Ziegler
Universita di Pavia Catholic University of Polish Academy of Sci. Technische Universitat
Pavia Louvain Warsaw Wien
ITALY BELGIUM POLAND AUSTRIA
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In memoriam
Leonardo da Vinci (1452-1519)
Charles Augustine de Coulomb (1736-1806)
John William Strutt (1842-1919)
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Preface
The pictures on the front cover of this book depict an example of stick-slip vibrations: the sound
of a violin. Playing a violin is a complex task, involving load transmission throughout the body,
intricate balance, eyes-head-neck-hand-fingers coordination and the execution of movements which
leads to stick-slip vibrations. The quest toward understanding how we perform such tasks with skill
and grace often in the presence of unpredicatable perturbations has a long history. However, despite
a history of magnificent music and musical acoustics, until recent times our state of knowledge of
friction induced oscillations occuring in such a basic mechanical system as well as in our everyday
life was rather primitive.
The study of friction oscillators is not a mature discipline. For instance, within this book, re
spected leaders in the field find that understanding even simple stereotype movements in presence
of friction is quite challenging. Similarly, researchers in deployable space structures find that it is
surprisingly difficult to get machines to move gracefully or to interact intelligently in a dissipative
environment. Yet a young violinist can perform a countless variety of tasks involving complex non
linear dynamics of oscillations with slip-slick friction quite effortlessly. Firction dynamics is a field
that consistently humbles the researchers. Because of the complexity of friction, different friction
laws are used to model different phenomena. For example, to model the self-excited oscillations in
a violin bow and string, it is sufficient to express the friction as a function of sliding velocity, where
the friction has a negative slope. To model stick-slip motions, the friction law used is a Coulomb
law, featuring a multivalued static friction. Static friction is multivalued because it can take on a
range of values to balance externally applied loads. Modern friction laws take into account variables
in addition to normal load and velocity, in hope that these additional state variables can model
the hysteretic effects of plastic deformation, creep and other mechanisms which may be unknown.
Such friction laws have been used for analytical treatment of friction damped systems which had
lead to mathematical models that are highly nonlinear, discontinuous and non-smooth. Discontin
uous and/or non-smooth processes introduce problems with phase-space reconstructions, rendering
analytical techniques such as perturbation methods and linearization in the vicinity of equilibrium
impossible. Numerical treatments of these systems using time integration are also hampered by
the non-smooth nature of the system models. Another impediment to the treatment of friction
damped systems is that friction is not understood well enough to express its behavior in terms of
its state variables. To this end, many researchers have made friction measurements using clever
tools such as load cells, optical interference, and inverse calculations. Results have shown friction to
be dependent on materials, geometry, scale, temperature, humidity, and the history of the motion
(a so-called memory effect). Furthermore, friction properties have been known to show a depen
dence on the system in which the frictional interface is placed; this causes the frictional properties
measured in test rigs to differ from those that exist in situ.
This book is designed to help synthesize our current knowledge regarding the role of friction
in engineering systems as well as in everyday life. In some ways the task of creating this book is
analogous to planning and executing a task in presence of friction. We first had to define our task
and its goals. We then had to work out a strategy that could help us meet these criteria. Our goals
were: i) to provide contributions of high quality that span the entire field of dissipative dynamics,
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