Iutam Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty: Proceedings of the IUTAM Symposium held in Nanjing, China, September 18-22, 2006

420 Pages·2007·20.958 MB·English

by  A. K. Bajaj, P. Davies, R. Ippili, T. Puri (auth.), Chairman H. Y. Hu, Co-Chairman Edwin Kreuzer (eds.)

IUTAM Symposium on Dynamics and Control
of Nonlinear Systems with Uncertainty
IUTAM BOOKSERIES
Volume2
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The IUTAMBookseries publishes the proceedings of IUTAMsymposia un-
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Foralistofrelatedmechanicstitles,seefinalpages.
IUTAM Symposium on
Dynamics and Control
of Nonlinear Systems
with Uncertainty
Proceedings of the IUTAM Symposium
held in Nanjing, China,
September 18-22, 2006
Edited by
H. Y. Hu
Nanjing University of Aeronautics and Astronautics,
Nanjing, China
and
E. Kreuzer
Hamburg University of Technology,
Hamburg, Germany
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CONTENTS

Preface ················································································································ ix
Opening Address ······························································································· xvii
Welcome Address ····························································································· xxi
Contributed Papers
PART 1 System Modeling with Uncertainty
A. K. Bajaj, P. Davies, R. Ippili and T. Puri
Nonlinear Multi-Body Dynamics of Seat-Occupant Systems Using
Experimentally Identified Viscoelastic Models of Polyurethne
Foam········································································································· 1
M. Hernandez-Garcia, S. F. Masri, R. Ghanem and F. Arrate
Data-Based Stochastic Models of Uncertain Nonlinear Systems ··········· 11
C. Proppe and C. Wetzel
Overturning Probability of Railway Vehicles under Wind Gust
Loads ······································································································· 23
W. Schiehlen and R. Seifried
Impact Systems with Uncertainty···························································· 33

v
vi Contents
PART 2 System Dynamics with Uncertainty
S. K. Au and D. P. Thunnissen
Uncertainty Propagation in Complex Engineering Systems
by Advanced Monte Carlo Methods ······················································· 45
T. F. Filippova
Trajectory Tubes in Control and Estimation Problems
under Uncertainty ···················································································· 55
A. Gaull and E. Kreuzer
Cell Mapping Applied to Random Dynamical Systems ························· 65
X. L. Leng
Numerical Analysis of Bifurcation and Chaos Response
in a Cracked Rotor System under White Noise Disturbance ·················· 77
X. B. Liu
The Maximal Lyapunov Exponent for a Stochastic System ··················· 87
W. V. Wedig
Stability and Density Analysis of Stochastic Duffing Oscillators ·········· 97
J. X. Xu and H. L. Zou
Uncertainties in Deterministic Dynamical Systems
and the Coherence of Stochastic Dynamical Systems····························· 109
W. Xu, Q. He and S. Li
The Cell Mapping Method for Approximating the Invariant
Manifolds·································································································· 117
PART 3 Nonlinear Dynamics
L. Bevilacqua and M. M. Barros
Dynamical Fractal Dimension: Direct and Inverse Problems·················· 127
T. Bódai, A. J. Fenwick and M. Wiercigroch
Ray Stability for Range-Dependent Background Sound Speed
Profiles····································································································· 137
N. D. Anh, N. Q. Hai and W. Schiehlen
Application of Extended Averaged Equations to Nonlinear
Vibration Analysis··················································································· 147
Z. Q. Wu and Y. S. Chen
Singularity Analysis on Constrained Bifurcations ·································· 157
Contents vii
H. Yabuno, Y. Kunitho, T. Inoue and Y. Ishida
Nonlinear Analysis of Rotor Dynamics by Using the Method
of Multiple Scales···················································································· 167
S. Yang and Y. Shen
Nonlinear Dynamics of a Spur Gear Pair with Slight Wear Fault··········· 177
K. Yunt and C. Glocker
A Combined Continuation and Penalty Method for the Determination
of Optimal Hybrid Mechanical Trajectories ··········································· 187
PART 4 Dynamics of High-Dimensional Systems
J. Awrejcewicz, G. Kudra and G. Wasilewski
Numerical Prediction and Experimental Observation of Triple
Pendulum Dynamics················································································ 197
A. J. Dick, B. Balachandran, and C. D. Mote, Jr.
Nonlinear Vibration Modes and Energy Localization
in Micro-Resonator Arrays······································································· 207
L. Q. Chen and X. D. Yang
Parametric Resonance of an Axially Accelerating Viscoelastic
Beam with Non-Typical Boundary Conditions······································· 217
F. L. Chernousko
Dynamics of a Body Controlled by Internal Motions····························· 227
W. Lacarbonara, A. Paolone and F. Vestroni
Linear and Nonlinear Elastodynamics of Nonshallow Cables················ 237
S. Lenci and G. Rega
Nonlinear Normal Modes of Homoclinic Orbits and their Use
for Dimension Reduction in Chaos Control ············································ 247
A. Teufel, A. Steindl and H. Troger
Rotating Slip Stick Separation Waves····················································· 257
M. H. Yao and W. Zhang
Many Pulses Homoclinic Orbits and Chaotic Dynamics
for Nonlinear Nonplanar Motion of a Cantilever Beam·························· 267
PART 5 Control of Nonlinear Dynamic Systems
I. Ananievski
Synthesis of Bounded Control for Nonlinear Uncertain
Mechanical Systems················································································· 277
viii Contents
P. Barthels and J. Wauer
Controlled Vibration Suppression of Structural Telescopic
Systems···································································································· 287
P. B. Gonçalves and D. Orlando
Influence of a Pendulum Absorber on the Nonlinear Behavior
and Instabilities of a Tall Tower ····························································· 297
H. Y. Hu and M. L. Yu
Robust Flutter Control of an Airfoil Section through an Ultrasonic
Motor ······································································································· 307
K. Czołczyński, A. Stefański, P. Perlikowski and T. Kapitaniak
Periodization and Synchronization of Duffing Oscillators
Suspended on Elastic Beam····································································· 317
Q. Y. Wang, Q. S. Lu, X. Shi and H. X. Wang
Effects of Noise on Synchronization and Spatial Patterns
in Coupled Neuronal Systems ································································· 323
PART 6 Dynamics of Time-Delay Systems
Y. F. Jin and H. Y. Hu
Stability and Response of Stochastic Delayed Systems
with Delayed Feedback Control ······························································ 333
G. Stépán and T. Insperger
Robust Time-Periodic Control of Time-Delayed Systems ····················· 343
P. Wahi, G. Stépán and A. Chatterjee
Self-Interrupted Regenerative Turning ··················································· 353
Z. H. Wang and H. Y. Hu
Robust Stability of Time-Delay Systems with Uncertain
Parameters ······························································································· 363
J. Xu, M. S. Huang and Y. Y. Zhang
Dynamics due to Non-Resonant Double Hopf Bifurcationin
in Van Del Pol-Duffing System with Delayed Position Feedback·········· 373
W. Q. Zhu and Z. H. Liu
Stability and Response of Quasi Integrable Hamiltonian Systems
with Time-Delayed Feedback Control ···················································· 383
Author Index······································································································ 393
PREFACE

The last decade has witnessed an increasing interest towards the
dynamics and control of nonlinear engineering systems from the scientists
engaged in nonlinear dynamics and the control engineers. Both groups of
people have recognized the importance of interaction between nonlinear
dynamics and robust control during their efforts to improve the dynamic
performance of engineering systems with uncertainty, which comes from
either the random excitations, such as wind and earthquake, or the modelling
errors of real systems including their sensors, controllers and actuators. The
dynamics and control of nonlinear systems with uncertainty, therefore,
is a vital interdisciplinary topic related to both stochastic systems and
deterministic systems.
This volume contains the papers presented at the IUTAM Symposium
on Dynamics and Control of Nonlinear Systems with Uncertainty, which
was sponsored by the International Union of Theoretical and Applied
Mechanics (IUTAM) and held at Nanjing University of Aeronautics and
Astronautics, China, 18-22 September, 2006. The aim of the symposium was
to bringing together the scientists to discuss the advances in dynamics and
control of nonlinear systems, especially those with uncertainties in either
system modeling or excitation.
The scientific committee, appointed by the Bureau of IUTAM, includes
the following members:
F. L. Chernousko, Moscow, Russia
E. Kreuzer, Hamburg, Germany (Co-Chairman)
H. Y. Hu, Nanjing, China (Chairman)
A. H. Nayfeh, Blacksburg, USA
G. Rega, Rome, Italy
W. Schiehlen, Stuttgart, Germany (IUTAM representative)
K. Sobczyk, Warsaw, Poland
G. Stepan, Budapest, Hungary
H. Troger, Wien, Austria
ix
x Preface

The committee selected the participants to be invited and the
presentations to be given at the symposium. As a result, 53 active scientists
from 17 countries accepted invitation, and 40 of them made oral presen-
tations at the symposium. The presentations cover the following topics:
1. System Modeling with Uncertainty. Uncertainties arising in system
modelling may have a great influence on system dynamics and control. In
modelling of mechanical systems, the descriptions of backlash and friction,
as well as hysteresis, most likely introduce uncertainties and have drawn
increasing attention over the past years. For example, W. Schiehlen et al.
observed in both experiments and computations that for a sphere striking a
beam, the coefficient of restitution was uncertain due to multiple impacts
resulting in chaotic behaviour. Based on this observation, they proposed an
efficient numerical approach for modelling, and verified the numerical
models by experiments. S. F. Masri et al. investigated some significant
issues in modelling uncertain parameters of hysteretic nonlinear systems
subject to deterministic excitation. He found that the parameters, such as the
yielding parameter, in the model were uncertain, and discussed also the
uncertainties in the identified coefficients and statistic features. In studying
practical engineering systems, A. K. Bajaj et al. developed a modelling
technique to predict the static equilibrium position of an occupant seated in a
car seat of polyurethane foam, and then used the model to identify the
system parameters. C. Proppe et al. proposed a consistent stochastic model
for wind gust and computed the probabilistic characteristic wind curves by
using a reliability analysis of the train-environment system.
2. System Dynamics with Uncertainty. The studies on the dynamic
systems with uncertainties, including both stochastic systems and deter-
ministic systems, are mainly a combination of theoretical and numerical
analysis. For instance, E. Kreuzer et al. extended the concept of Cell
Mapping to the global dynamics of randomly perturbed dynamical systems.
J. X. Xu et al. investigated the noise effect at different scales on the
boundary of Wada basin, including the crisis coming from a strong
perturbation. W. Xu et al. discussed the approximation of the invariant
manifolds of nonlinear systems with uncertainty by means of the method of
digraph cell mapping. W. V. Wedig and X. B. Liu studied the estimation and
computation of the maximal Lyapunov exponent for stochastic bifurcation
systems, respectively. T. Filippova studied the control and state estimation
of dynamical systems with uncertainty, described by differential equations
with measure (or impulsive control) component. For engineering appli-
cations, S. K. Au et al. introduced an advanced Monte Carlo method, named
Subset Simulation, to solve the problem of uncertainty propagation in