Table Of ContentIUTAM SYMPOSIUM ON RECENT DEVELOPMENTS IN
NON-LINEAR OSCILLATIONS OF MECHANICAL SYSTEMS
SOLID MECHANICS AND ITS APPLICATIONS
Volume 77
Series Editor: G.M.L. GLADWELL
Department of Civil Engineering
University of Waterloo
Waterloo, Ontario, Canada N2L 3GI
Aims and Scope of the Series
The fundamental questions arising in mechanics are: Why?, How?, and How much?
The aim of this series is to provide lucid accounts written bij authoritative researchers
giving vision and insight in answering these questions on the subject of mechanics as it
relates to solids.
The scope of the series covers the entire spectrum of solid mechanics. Thus it includes
the foundation of mechanics; variational formulations; computational mechanics;
statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and
structures; dynamical systems and chaos; the theories of elasticity, plasticity and
viscoelasticity; composite materials; rods, beams, shells and membranes; structural
control and stability; soils, rocks and geomechanics; fracture; tribology; experimental
mechanics; biomechanics and machine design.
The median level of presentation is the first year graduate student. Some texts are mono
graphs defining the current state of the field; others are accessible to final year under
graduates; but essentially the emphasis is on readability and clarity.
For a list of related mechanics titles, see final pages.
IUTAM Symposium on
Recent Developments in
Non-linear Oscillations
of Mechanical Systems
Proceedings of the lUTA M Symposium
held in Hanoi, Vietnam,
March 2-5, 1999
Edited by
Nguyen Van Dao
Vietnam National University, Hanoi
and
E.J. Kreuzer
Technical University,
Hamburg-Harburg, Germany
....
"
SPRINGER SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-5809-4 ISBN 978-94-011-4150-5 (eBook)
DOI 10.1007/978-94-011-4150-5
Printed on acid-free paper
AII Rights Reserved
© 2000 Springer Science+Business Media Dordrecht
Origina1ly published by Kluwer Academic Publishers in 2000
Softcover reprint ofthe hardcover lst edition 2000
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
CONTENTS
Preface IX
Awrejcewicz J. and Tomczak K.
Stability Improvement of the Impact Dynamical Systems-Analytical and
Numerical Methods.
Benedettini F.
Theoretical and Experimental Evidence of Symmetric Response Instability in the
Finite, Planar Dynamics of a Circular Arch. 11
Bevilacqua L., Battista R.B. and Ebecken N.F.F.
Dynamical Analysis of an Offshore Platform with Vibration Absorbers. 23
Bishop S.R.
Complex Dynamics of a "Simple" Mechanical System:
The Parametrically Excited Pendulum. 35
Chernousko F. L.
Control of Oscillations in Systems with Many Degrees of Freedom. 45
Czolczynski K., Kapitaniak T. and Brindley J.
Elimination of Instabilities in Rotors Supported in Gas Bearings. 55
Maisser P., Freudenberg H. and Pham Anh Tuan
Integrated Electromechanical Multi-Coordinate Drive with an Elastic
Deformable Slide. 65
Grebogi C., Baptista M.S., Hunt B.R., Ott E. and Yorke J.A.
Control of Shipboard Cranes. 75
Guo-Kang Er and Vai Pan Iu
A Consistent and Effective Method for Nonlinear Random Oscillations of
MDOF Systems. 85
Hu H.Y. and WU Z.Q.
Stability and Hopf Bifurcation of a Four-wheel-steering Vehicle Involving
Driver's Delay. 95
Kreuzer E. and Ellermann K.
Moored Crane Vessels in Regular Waves. 105
LeLuongTai
On the Stability of Systems of Differential Equations Unsolved for Derivatives. 115
Maisser P. and Jungnickel U.
Stability of Controlled Motion of a Gymnast in High-speed Mid Air Maneuvers. 121
v
vi
Mitropolsky Y. A.
Asymptotic Methods for investigating Non-linear Wave Processes. 131
Nguyen Van Dao
Some Problems on Non-linear Oscillations. 141
Nguyen Van Dinh and Tran Kim Chi
Stationary and Transient Processes in Oscillating Systems with Two Degrees of
Freedom Subjected to Parametric and Forced Excitations. 153
Nguyen Hai and Ostiguy G. L.
On the Application of Two Perturbation Methods to Non-linear Systems. 165
Nguyen Xuan Hung and Nguyen Xuan Hoang
New Method of Calculating the Vibration of Offshore Structure Subjected to
Wave Action. 175
Nguyen Van Khang, Hoang Ha, Vu Van Khiem and Do Xuan Tho
On the Transverse Vibrations of Beam-Bridges Under the Action of Some
Moving Bodies. 187
Nguyen Tien Khiem, Dao Nhu Mai, Nguyen Viet Khoa and Le Van Anh
Pile Soil System Identification by a Modal Testing Approach. 197
Nguyen Nhat Le, Dinh Van Phong and Do Sanh
On Numerical Methods for Constrained Mechanical Systems. 207
Nguyen DongAnh and Ninh Quang Hai
A Technique for Solving Nonlinear Systems Subject to Random Excitation. 217
Popp K. and Bruns J. U.
On the Identification of Nonlinear Systems. 227
Rega G., Lacarbonara W. and Nayfeh A.H.
Reduction Methods for Non-linear Vibrations of Spatially Continuous Systems
with Initial Curvature. 235
Samoilenko A.M.
Asymptotic Method for Investigation of m-frequency Oscillation Systems. 247
Schiehlen W. and Fritz A.
Nonlinear Oscillations of Vehicles in Convoy. 257
SchulzM.
Instability Phenomena of Foldable Structures with Unilateral Contact. 269
Spyrou K.J.
Similarities in the Yaw and Roll Dynamics of Ships in Extreme Astern Seas. 279
VII
Albrecht B., Steindl A., and Troger H.
Non-linear three-dimensional Oscillations of Fluid Conveying Viscoelastic
Tubes with an Additional Mass. 291
van de Vrande B. L. and van Campen D. H.
Nonlinear Dynamics of a Rigid Rotor on Compliant Journal Bearings. 30 I
Vestroni F. and Bernardini D.
Nonlinear Dynamic Behaviour of Shape Memory Alloy Oscillators. 311
WauerJ.
Nonlinear Waves in a Fluid-Filled Planar Duct with a flexible Wall. 321
Addresses of participants 333
List of Sponsors 341
PREFACE
This volume contains selected papers presented at the Symposium on "Recent
Developments in Non-linear Oscillations of Mechanical Systems", held in Hanoi,
Vietnam, from 2 -5 March 1999. This Symposium was initiated and sponsored by the
International Union of Theoretical and Applied Mechanics (lUIA M) and organised in
conjunction with Vietnam National University, Hanoi. Ihe purpose of the Symposium
was to bring together scientists active in different fields of oscillations with the aim to
review the recent progress in theory of oscillations and engineering applications and
to outline the prospects in its further achievements to then co-ordinate and direct
research in this field to further co-operation between scientists and various scientific
institutions.
An International Scientific Committee was appointed by the Bureau of IUIA M with
the following members:
Nguyen Van Dao (Vietnam, Co-Chairman)
E.J. Kreuzer (Germany, Co-Chairman)
D.H. van Campen (The Netherlands)
F.L. Chernousko (Russia)
A.H. Nayfeh (U.S.A)
Nguyen Xuan Hung (Vietnam)
W.O. Schiehlen (Germany)
J.M.T. Thompson (U.K)
Y. Veda (Japan).
This Committee selected the participants to be invited and the papers to be presented
at the Symposium. As a result of this procedure, 52 active scientists from 16 countries
responded to the invitation, and 42 papers were presented in lecture and poster
discussion sessions.
The scientific presentations were devoted to the following topics:
1. Non-linear Oscillations of beams, plates, vehicles and other dynamic systems;
2. Analysis and Control of Non-linear Systems;
3. Non-linear waves;
4. Dynamics of Offshore structures;
5. System Identification;
6. Mathematical and Numerical methods for investigating non-linear systems.
The papers of this volume are arranged in alphabetical order with respect to the family
name of the first author.
The presentations and discussions, including the round table discussion, during the
Symposium will certainly stimulate further theoretical and applied investigations in
non-linear oscillations. The publication of the proceedings will promote this
development.
The success of the Symposium would not have been possible without the excellent
work of the Local Organising Committee. Members of that Committee were Do Sanh
ix
x
(Chairman), Phan Nguyen Di, Nguyen Van Khang, Tran Quang Khoi, Nguyen Gao
Menh, Dinh Van Phong, Nguyen Thi Trung and Vu Ngoc Tu. The secretarial work for
both the Conference and this volume has been admirably undertaken by Mrs. Nguyen
Thi Hong Hanh.
We are sincerely grateful to Prof. Werner Schiehlen, President of IUTAM for his
encouragement to the success of this IUTAM Symposium and to Vietnam National
University, Hanoi, the host of this significant scientific event.
The editors wish to thank the participants of this IUT AM Symposium, especially the
authors of the papers, and all organisers for their enthusiastic and valuable
contributions to the Symposium.
Sincere thanks are also due to Prof. Graham Gladwell, and Kluwer Academic
Publishers for their help and co-operation.
We gratefully acknowledge financial support from IUTAM and the Vietnam Council
for Natural Science.
Nguyen Van Dao E.J. Kreuzer
STABILITY IMPROVEMENT OF THE IMPACT DYNAMICAL
SYSTEMS -ANALYTICAL AND NUMERICAL METHODS
1. AW REJCEWICZ and K. TOMCZAK
Division of Automatics and Biomechanics
Technical University ofL6dz
1/15 Stefanowskiego St., 90-924 L6dz, POLAND
1. Introduction
Vibro-impact vibration problems with one-degree-of-freedom systems
have a long history in mechanics. The problems like stationary
subharmonic motions and their stability, the influence of damping and
friction on vibro-impact dynamics, elastic and plastic type impacts, time
histories and phase portraits of the vibro-impact systems have been
considered [1-7].
In this work we propose an analytical approach to determine suitable
delay loop coefficients to realise the required vibro-impact periodic
dynamics for a non-resonance case. The obtained analytical formulas
allow for a proper choice of the delay loop coefficients in order to achieve
the required vibro-impact periodic motion quicker then in the case
without a loop. When the vibro-impact periodic motion is achieved the
delay loop is automatically switched off
2. The analysed system
A feedback control with the delay loop is used in order to improve a
stability of a vibro-impact periodic motion. It possesses the following
properties:
simple construction (a feedback loop with delay elements);
N. Dao et al. (eds.), IUTAM Symposium on Recent Developments in Non-linear
Oscillations of Mechanical Systems © Springer Science+Business Media Dordrecht 2000
