Routes to chaos in power systems are studied. Using a three-bus simple system, three routes that can lead power system to chaos are presented, illustrated and discussed. They are cascading period doubling bifurcation,...Routes to chaos in power systems are studied. Using a three-bus simple system, three routes that can lead power system to chaos are presented, illustrated and discussed. They are cascading period doubling bifurcation, torus bifurcation and route directly initiated by a large disturbance. Period doubling bifurcation is caused by a real Floquet multiplier going out of the unit circle from point (-1,0), while torus bifurcation is caused by a couple of conjugated Floquet multipliers going out of the unit circle with a non-zero imaginary part in the complex plane. Cascading period doubling bifurcation and torus bifurcation are two typical routes to chaos in dynamic systems, which have been investigated in the previous studies. The last route, i.e. directly initiated by a large disturbance, is reported and studied. This phenomenon reveals that chaos is caused by external disturbances in power systems.展开更多
Nonlinear dynamic behaviors of a rotor dynamical system with finite hydrodynamic bearing supports were investigated. In order to increase the numerical accuracy and decrease computing costs, the isoparametric finite e...Nonlinear dynamic behaviors of a rotor dynamical system with finite hydrodynamic bearing supports were investigated. In order to increase the numerical accuracy and decrease computing costs, the isoparametric finite element method based on variational constraint approach is introduced because analytical bearing forces are not available. This method calculates the oil film forces and their Jacobians simultaneously while it can ensure that they have compatible accuracy. Nonlinear motion of the bearing-rotor system is caused by strong nonlinearity of oil film forces with respect to the displacements and velocities of the center of the rotor. A method consisting of a predictor-corrector mechanism and Newton-Raphson method is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of the bearing-rotor system. Meanwhile the dynamic coefficients of bearing are obtained. The nonlinear unbalance periodic responses of the system are obtained by using Poincaré-Newton-Floquet method and a combination of predic- tor-corrector mechanism and Poincaré-Newton-Floquet method. The local stability and bifuration behaviors of periodic motions are analyzed by the Floquet theory. Chaotic motion of long term dynamic behaviors of the system is analyzed with power spectrum. The numerical results reveal such complex nonlinear behaviors as periodic, quasi-periodic, chaotic, jumped and coexistent solutions.展开更多
Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they a...Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.展开更多
综述了输液管系统的各类物理模型及其相应的数学模型,在流体满足基本假设条件下,对于管道内径远远小于管道长度的直管和曲管,详细叙述了梁模型管动力学数学模型的建模过程以及建模方法,针对在水动压力作用下以及管道短而且薄的情形,综...综述了输液管系统的各类物理模型及其相应的数学模型,在流体满足基本假设条件下,对于管道内径远远小于管道长度的直管和曲管,详细叙述了梁模型管动力学数学模型的建模过程以及建模方法,针对在水动压力作用下以及管道短而且薄的情形,综述了壳模型的输液管道的动力学方程。在此基础上,概述了近几年来输液管道的非线性振动、稳定性、分岔与混沌、特别是管道控制的研究现状,并对今后的发展趋势作了分析和预测。综观非线性动力学理论的发展历程可以发现选取研究对象和典型的数学模型是至关重要的。对于低维的非线性系统,常常选用Van der Pol、Duffing、Mathieu、Lorenz等典型系统来进行研究工作的。通过本文可以看出,对于研究高维非线性系统动力学,流诱发输液管的动力学问题是非常典型的模型之一,它有着容易理解的工程背景、包含了梁和壳的振动问题,并且它的数学模型相对简单,然而却能包含非常复杂的非线性动力学现象,同时容易解释数学方法得到的结果易对应到工程中的实际现象。本文希望通过对输液管动力学模型及其非线性动力学和控制研究现状的综述,建立高维非线性动力学的分析模型,以便发展高维非线性动力学的分岔与混沌理论,同时建立相应的控制理论基础。展开更多
基金Supported by the Foundation for the Author of National Excellent Doctoral Dissertation(No.200439)Key Project of Chinese Ministryof Education (No.105047)+2 种基金Program for New Century Excellent Talents in University,Fok Ying Tung Education Foundation(No.104019)Innovation Fund of Tianjin Municipal(No.06TXTJJC13700),Natural Science Foundation of China(No.50595413) theSpecial Fund of the National Fundamental Research (2004CB217904)of China.
文摘Routes to chaos in power systems are studied. Using a three-bus simple system, three routes that can lead power system to chaos are presented, illustrated and discussed. They are cascading period doubling bifurcation, torus bifurcation and route directly initiated by a large disturbance. Period doubling bifurcation is caused by a real Floquet multiplier going out of the unit circle from point (-1,0), while torus bifurcation is caused by a couple of conjugated Floquet multipliers going out of the unit circle with a non-zero imaginary part in the complex plane. Cascading period doubling bifurcation and torus bifurcation are two typical routes to chaos in dynamic systems, which have been investigated in the previous studies. The last route, i.e. directly initiated by a large disturbance, is reported and studied. This phenomenon reveals that chaos is caused by external disturbances in power systems.
基金Project supported by National Natural Science Foundation of China （Grant No. 50275116）, and National High-Technology Research and Development Program of China （ Nos. 2002AA414060, 2002AA503020）
文摘Nonlinear dynamic behaviors of a rotor dynamical system with finite hydrodynamic bearing supports were investigated. In order to increase the numerical accuracy and decrease computing costs, the isoparametric finite element method based on variational constraint approach is introduced because analytical bearing forces are not available. This method calculates the oil film forces and their Jacobians simultaneously while it can ensure that they have compatible accuracy. Nonlinear motion of the bearing-rotor system is caused by strong nonlinearity of oil film forces with respect to the displacements and velocities of the center of the rotor. A method consisting of a predictor-corrector mechanism and Newton-Raphson method is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of the bearing-rotor system. Meanwhile the dynamic coefficients of bearing are obtained. The nonlinear unbalance periodic responses of the system are obtained by using Poincaré-Newton-Floquet method and a combination of predic- tor-corrector mechanism and Poincaré-Newton-Floquet method. The local stability and bifuration behaviors of periodic motions are analyzed by the Floquet theory. Chaotic motion of long term dynamic behaviors of the system is analyzed with power spectrum. The numerical results reveal such complex nonlinear behaviors as periodic, quasi-periodic, chaotic, jumped and coexistent solutions.
文摘Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.
文摘综述了输液管系统的各类物理模型及其相应的数学模型,在流体满足基本假设条件下,对于管道内径远远小于管道长度的直管和曲管,详细叙述了梁模型管动力学数学模型的建模过程以及建模方法,针对在水动压力作用下以及管道短而且薄的情形,综述了壳模型的输液管道的动力学方程。在此基础上,概述了近几年来输液管道的非线性振动、稳定性、分岔与混沌、特别是管道控制的研究现状,并对今后的发展趋势作了分析和预测。综观非线性动力学理论的发展历程可以发现选取研究对象和典型的数学模型是至关重要的。对于低维的非线性系统,常常选用Van der Pol、Duffing、Mathieu、Lorenz等典型系统来进行研究工作的。通过本文可以看出,对于研究高维非线性系统动力学,流诱发输液管的动力学问题是非常典型的模型之一,它有着容易理解的工程背景、包含了梁和壳的振动问题,并且它的数学模型相对简单,然而却能包含非常复杂的非线性动力学现象,同时容易解释数学方法得到的结果易对应到工程中的实际现象。本文希望通过对输液管动力学模型及其非线性动力学和控制研究现状的综述,建立高维非线性动力学的分析模型,以便发展高维非线性动力学的分岔与混沌理论,同时建立相应的控制理论基础。
