本書通過兩自由度非線性振子、并基于有限傅里葉級數(shù)的解析方法，首次給出了流體誘導(dǎo)繩索馳振的解析解。此有限傅里葉級數(shù)法提供了非線性系統(tǒng)從時(shí)域到頻域的非線性變換，從而應(yīng)用頻幅特征來確定非線性系統(tǒng)的動(dòng)力學(xué)行為。根據(jù)其解析解，展示馳振繩索的周期運(yùn)動(dòng)到混沌的解析分岔道路。本書提供了解決工程中流體誘導(dǎo)振動(dòng)的解決方法，幫助人們更好地理解例如飛機(jī)、橋梁、高層建筑、換熱器管道、高壓電纜線中的流體誘導(dǎo)振動(dòng)。
This book is about analytical galloping dynamics of nonlinear cables under fiow-induced dynamical loading. The galloping dynamics of cable under such fiuid dynamical loading is the fiow-induced structural vibration， which has been studied since the early nineteenth century. Flow-induced structural vibrations extensively exist in engineering， such as aircraft， bridge， power transmission lines， high structures and buildings. When a steady flow comes to an asymmetric slender elastic structure， the asymmetric flow vortex formed around such a structure will cause its structural vibration. To understand the mechanisms of such a phenomenon， different mathematical models and techniques have been developed. However， due to the nonlinearity of fluid forces relative to the orientation and velocity of the structure， in addition to experimental observation， one has developed linear modeling of structures with nonlinear fluid dynamical forces， and the perturbation method was employed to determine the inherent dynamical characteristics. In fact， the results are far behind experimental observed results. Without significant analytical results， one has a difficulty to determine the dynamic characteristics of fiow-induced structural vibrations. In this book， the galloping instability to chaos of nonlinea/r cables is considered as an example to show how to determine the analytical solutions of periodic motions in fluid-induced structural vibrations and further to find the frequency-amplitude characteristics which can be hired to control fiuid-induced structural vibrations.
1 Introduction
1．1 Analytical Methods
1．1．1 Traditional Methods
1．1．2 Generalized Harmonic Balance
1．2 Galloping Phenomena
1．2．1 A Brief History cf Galloping Modeling
1．2．2 Mathematical Modeling
1．2．3 Aerodynamic Force and Moment
1．3 Book Layout
References
2 Nonlinear Dynamical Systems
2．1 Continuous Systems
2．2 Equilibriums and Stability
2．3 Bifurcation and Stability Switching
2．3．1 Stability and Switching
2．3．2 Bifurcations
References
3 Analytical Methods
3．1 Periodic Motions
3．2 Quasiperiodic Motions
References
4 A Quadratic Nonlinear Oscillator
4．1 Analytical Period-m Motions
4．2 Analytical Bifurcation Trees
4．3 Numerical Illustrations
References
5 Two-Degree-of-Freedom Nonlinear Oscillators
5．1 Analytical Solution Formulation
5．2 Frequency-Amplitude Characteristics
5．3 Numerical Simulations
References
6 Linear Cable Galloping
6．1 Analytical Period-1 Motions
6．2 Frequency-Amplitude Characteristics
6．3 Numerical Simulations and Comparisons
References
7 Nonlinear Cable Galloping
7．1 Analytical Period-m Motions
7．2 Analytical Bifurcation Trees
7．3 Numerical Illustrations
References
Appendix A： Coefficients for Cable Galloping
Index
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