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A collection of 20 papers recently published in the Chinese journals, Vibration and Shock , Journal of Vibration Engineering , and Journal of Nonlinear Dynamics . The Chinese authors describe their research in nonlinear vibration, bifurcation, chaos control, and engineering applications. Topics include analysis of magnetic nonlinear coupled oscillations in the air gap of a generator rotor system, flutter and chaotic motions of a cantilevered pipe conveying fluid, and the solution of nonlinear impulsive integrodifferential equations in Banach spaces. Distributed by Ashgate. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Since the 1990s, significant advances have been made in the research on nonlinear dynamics in China. Many papers were published in Chinese in the Journal of Vibration Engineering, Journal of Nonlinear Dynamics, and Vibration and Shock. This work offers translations of selected articles.
Preface xiii
List of Contributors
xv
Review and Prospect 1(20)
Nonlinear Vibration, Bifurcation, Chaos and their Application in Engineering
3(18)
Y.S. Chen
W.H. Huang
Introduction
3(1)
The Bifurcation Theory of Periodic Solutions of Single-DOF Systems
4(3)
A method for studying bifurcation
4(2)
A classification of bifurcations of periodic solutions of single-DOF systems
6(1)
Singularity Theory of a Kind of High Co-dimensional Bifurcation
7(1)
Background of engineering
7(1)
The universal unfolding of amplitude bifurcation equation
7(1)
Transition sets and bifurcation diagrams
8(1)
Reduction, Simplification and Singularity Theory of M-DOF Nonlinear Systems
8(4)
Hopf bifurcation theory and central manifold theory
8(1)
Normal form theory
9(1)
Interaction between Hopf bifurcations
10(1)
Interactions of nonlinear modes
11(1)
Some New Results on Nonlinear Rotor Dynamics
12(1)
The stability margin of nonlinear rotor dynamical systems
12(1)
Rotor rub mechanism and rub suppression
12(1)
Mechanism of rotor nonlinear dynamics with support elements looseness
13(1)
Nonlinear dynamical behavior of cracked rotors
13(1)
New phenomena
13(1)
Numerical Methods of Nonlinear Dynamics
13(2)
Improvements on numerical methods
13(1)
Studies on some important theoretical problems of nonlinear dynamical systems
14(1)
Conclusion and Prospects
15(6)
References
15(6)
Phenomenon Study 21(40)
Nonlinear Vibration and Bifurcation of Tank Induced by Dry Friction
23(8)
X.J. Liu
D.J. Wang
Y.S. Chen
Introduction
23(1)
Fundamental Equations
24(2)
Numerical Solution of Equations
26(3)
Vibration Analysis of the Dragon Washbasin
29(1)
Concluding Remarks
30(1)
References
30(1)
Bifurcation Point Analysis of Airfoil Flutter with Structural Nonlinearity
31(8)
J.K. Liu
L.C. Zhao
T. Fang
Introduction
31(2)
Equations of Motion and Bifurcation Points
33(1)
Reduction of the System Dimension
33(2)
Analysis by the Method of Succeeding Function
35(1)
Analysis by the Method of Formal Series
36(1)
Conclusion
36(3)
References
37(2)
Flutter and Chaotic Motions of a Cantilevered Pipe Conveying Fluid
39(10)
J.D. Jin
G.S. Zou
Introduction
40(1)
Differential Equation of Motion
40(2)
Static Equilibria
42(1)
Numerical Analysis
43(1)
Local Bifurcations: Theoretical Analysis
44(1)
Conclusions
45(4)
References
46(3)
Bifurcation and Chaos of a Nonlinear Whirl Cracked Rotor
49(12)
J.B. Zheng
G. Meng
Introduction
49(1)
Mathematical Model
50(1)
Results and Discussion
51(8)
Summary and Conclusion
59(2)
References
59(1)
Appendix
60(1)
Theory Development 61(44)
A Method of Normal Mode Invariant Manifolds for Hopf Bifurcation Solutions of a Class of High Dimensional Systems
63(10)
W.P. Fu
J.X. Xu
T. Zhou
Introduction
63(1)
Normal Mode Invariant Manifolds
64(2)
The Method of Normal Mode Invariant Manifolds for the Analysis of Hopf Bifurcation
66(2)
The Generalized Nonlinear Normal Mode and Hopf Bifurcation in Mechanical-Electrical Coupled Systems
68(1)
Applications
68(2)
The flutter of 2-order discrete model for a simplified aeroelastic plate
69(1)
The self-excited oscillation in an electromagnetic vibrating machine
69(1)
Conclusions
70(3)
References
71(2)
Classification of Bifurcations for Nonlinear Dynamical Problems with Constraints
73(8)
Z.Q. Wu
Y.S. Chen
Introduction
73(2)
The Method and its Core Ideas
75(2)
Application Examples
77(2)
Eample 1
77(1)
Eample 2
78(1)
Eample 3
78(1)
Conclusion
79(2)
References
80(1)
Conditional Lyapunov Exponents in Hyperchaos Sporadic Driving Synchronization
81(6)
D.H. He
J.X. Xu
Y.H. Chen
Introduction
81(1)
A Method for Computation of the CLES
82(1)
Continuous Driving and Sporadic Driving
83(1)
Hyperchaos Rossler System Using Sporadic Driving
83(3)
Conclusion and Discussion
86(1)
References
86(1)
Solutions of Nonlinear Impulsive Integro differential Equations in Banach Spaces
87(10)
F.Q. Chen
Y.S. Chen
Introduction
87(1)
Preliminaries
88(2)
Main Theorems
90(7)
References
95(2)
Obstruction Sets and Nonlinear Dynamics
97(8)
Y. Tang
Introduction
97(1)
Concept of Obstruction Sets and Stability
98(2)
Computation to Local Obstruction Sets
100(2)
Nonlinear Dynamic Problems
102(3)
References
103(2)
Experimental Techniques 105(32)
Parameters Identification of Local Nonlinear Components by Optimal Tracking Technique
107(8)
Z.G. Wu
B.L. Wang
X.R. Ma
Introduction
108(1)
Concept of Optimal Control Solution to System Identification Problem
109(1)
Parameter Identification of Local Nonlinear Components
109(3)
Identification of restoring force by the technique of optimal tracking
109(1)
The precise integration method
110(1)
Parameter estimation
111(1)
Examples
112(1)
Conclusions
112(3)
References
113(2)
The Reconstruction Technology Based on Nonlinear Chaotic Time Series and Its Applications
115(14)
J.H. Ma
Y.S. Chen
G.D. Pang
Introduction
115(1)
The Decision of the Chaotic Characteristics of Time Series
116(1)
The Analysis and Study of the Related Characteristics of Fractal Dimension
116(2)
The Nonlinear Reconstruction Technology of Chaotic Time Series in Dynamical Systems
118(6)
The choice of the best delayed time interval τ0
119(1)
The linear auto-correlation function method
120(1)
The average mutual information method
120(1)
Reconstruction unfolding method
120(1)
The choice of the embedding dimension m
121(1)
Prediction error minimizing method
121(1)
Spurious adjoining point method
122(1)
The trajectory method and legendre coordinate method of the reconstruction of phase space
123(1)
Applications of the Reconstruction Technology of Measured Data of Dynamic Systems
124(1)
Calculation Results
124(2)
Conclusions
126(3)
References
126(3)
An Experimental Study on a Semi-active Vibration Absorber with an Adjustable Clearance
129(8)
H.Y. Hu
X.Y. Qian
Introduction
129(1)
Theoretical Background
130(1)
Control Law and Critical Frequency
131(2)
Design of Experimental Setup
133(1)
Consideration from mechanics
133(1)
Design of controller
134(1)
Electromagnetic clutch and driving circuit
134(1)
Step motor and driving circuit
134(1)
Results and Discussions
134(1)
Case study under variable excitation frequency
134(1)
Case study under variable excitation amplitude
135(1)
Concluding Remarks
135(2)
References
136(1)
Chaos Control 137(18)
Hopf Bifurcation Amplitude Control of Nonlinear Oscillation Systems
139(10)
X.D. Liu
W.H. Huang
Introduction
139(2)
Problem Formulation and Hopf Bifurcation Theorem
141(1)
Amplitude Controllability of Hopf Bifurcation
142(2)
Applications to Self Sustained Oscillation Control
144(3)
Conclusion
147(2)
References
147(2)
Synchronization and Detecting Hidden Frequencies in Time Series of Hyperchaotic System
149(6)
D.H. He
J.X. Xu
Y.H. Chen
Introduction
149(1)
The Detection Method Using the Discrete Wavelet Transformation
150(1)
Case Study on Hyperchaos Rossler System
151(3)
Conclusion
154(1)
References
154(1)
Engineering Applications 155(46)
Stability, Bifurcation and Chaos of a Gyro-Pendulum on a Rotating Basis
157(8)
Y.Z. Liu
G. Cheng
Introduction
157(1)
Relative Equilibrium
158(1)
Stability, Bifurcation and Global Behavior
159(2)
Chaotic Behavior
161(1)
Conclusions
162(3)
References
163(2)
The Study on Subharmonic Instability of Nonlinear Rotor/Seal Systems
165(10)
Q. Ding
Y.S. Chen
Introduction
165(1)
Equations of Motion
166(1)
Hopf Bifurcation of the Balanced System
167(1)
Periodically Perturbed Hopf Bifurcation in 1/2 Subharmonic Resonance of the Unbalanced System
168(4)
Reduction and averaging
168(1)
Stability and bifurcation of the averaged system
169(3)
Conclusions
172(3)
References
172(3)
Nonsmooth Bifurcation Analysis in A Rub-impacting Rotor System with Rigid Constraint
175(8)
Q.S. Liu
S.J. Zhang
S.M. Wang
Introduction
175(1)
Equations of Motion
176(3)
Numerical Simulations
179(2)
The effect of the rotation angular velocity ω
179(1)
The effect of the restitution coefficient k
180(1)
The effect of the static deflection
180(1)
Conclusion
181(2)
References
181(2)
Analysis on Magnetic Nonlinear Coupled Oscillations in the Air Gap of a Generator Rotor System
183(10)
Z.A. Yang
J.J. Qiu
W.L. Li
Introduction
183(1)
Air Gap Field with Saturated Magnetic Circuit
184(3)
Air gap flux guide
184(2)
Energy of air gap magnetic field
186(1)
Torsional Vibration Equations of Rotor Shafting System of a Generator
187(2)
The Parametric Resonance with Forced Vibration of Rotor Shafting System of a Generator
189(1)
Conclusion
190(3)
References
191(2)
Dynamical Characteristics of Nonlinear Rotor Systems with Slowly Changing Parameters
193(8)
B.C. Wen
B.X. Tang
H.Q. Yuan
Introduction
193(1)
Method of Piece-wise Calculation for Rotor Systems with Slowly Changing Parameters
193(2)
Rotor Systems with Slowly changing Supporting Stiffness
195(1)
Cracked Rotor Systems
196(3)
Conclusions
199(2)
References
199(2)
Index 201
Wenhu Huang, Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin, China.
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