Impulsive Control for T-S Fuzzy Model Based Chaotic Systems Consisting of Van der Pol Oscillators Coupled to Linear Oscillators

This paper proposes an impulsive control scheme for chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators （VDPL） based on their Takagi-Sugeno （T-S） fuzzy models. A T-S fuzzy model is utilized to represent the chaotic VDPL system. By using comparison method, a general asymptotical stability criterion by means of linear matrix inequality （LMI） is derived for the T-S fuzzy model of VDPL system with impulsive effects. The simulation results demonstrate the effectiveness of the proposed scheme.

Time Delay Induced Oscillation: An Example on a Class of <i>n</i>Coupled Van Der Pol Oscillators Model with Delays

In this paper, a class of n coupled van der Pol oscillator model with delays is considered. By employing an analysis approach, some sufficient conditions to guarantee the existence of stability and oscillations for themodel are obtained. Examples are provided to demonstrate the results.

Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling

In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays.

Collective Behavior of a Ring of Van Der Pol Oscillators under Gaussian and Random Coupling Schemes

The collective behavior of a ring of coupled identical van der Pol oscillators is numerically studied in this work. Constant, gaussian and random distributions of the coupling parameter along the ring are considered. Three values of the oscillators constant are assumed in order to cover from quasilinear to nonlinear dynamic performance. Single and multiple coupled frequencies are obtained using power spectra of the long term time series. Phase portraits are obtained from numerical simulations, and the coupled behavior is analyzed, compared and discussed.

基于耦合Van der Pol-Duffing系统的微弱信号检测研究

传统方法检测微弱信号具有一定的困难,利用混沌振子对微弱信号敏感以及对强噪声具有良好免疫力的特性,提出基于耦合Van der Pol-Duffing振子系统检测微弱信号的新方法。对比不同参数下耦合系统的动力学行为,通过分岔图和二分法确定临界阈值,保证阈值搜索速度和阈值精度。阐述基于相图的微弱信号检测原理,通过从混沌态到周期态的转变成功检测淹没在强噪声中的微弱信号,信噪比门限达到–30 d B。同时考察不同精度幅值下噪声对系统状态的影响,不同频率信号以及相移对检测的影响。仿真结果表明,该耦合系统在强噪声条件下对微弱信号敏感,用于检测微弱信号是可行的。

A NEW WAKE OSCILLATOR MODEL FOR PREDICTING VORTEX INDUCED VIBRATION OF A CIRCULAR CYLINDER

This article proposes a new wake oscillator model for vortex induced vibrations of an elastically supported rigid circular cylinder in a uniform current. The near wake dynamics related with the fluctuating nature of vortex shedding is modeled based on the classical van der Pol equation, combined with the equation for the oscillatory motion of the body. An appropriate approach is developed to estimate the empirical parameters in the wake oscillator model. The present predicted results are compared to the experimental data and previous wake oscillator model results. Good agreement with experimental results is found.

参数激励耦合系统的复杂动力学行为分析

分析了耦合van der Pol振子参数共振条件下的复杂动力学行为.基于平均方程,得到了参数平面上的转迁集,这些转迁集将参数平面划分为不同的区域,在各个不同的区域对应于系统不同的解.随着参数的变化,从平衡点分岔出两类不同的周期解,根据不同的分岔特性,这两类周期解失稳后,将产生概周期解或3-D环面解,它们都会随参数的变化进一步导致混沌.发现在系统的混沌区域中,其混沌吸引子随参数的变化会突然发生变化,分解为两个对称的混沌吸引子.值得注意的是,系统首先是由于2-D环面解破裂产生混沌,该混沌吸引子破裂后演变为新的混沌吸引子,却由倒倍周期分岔走向3-D环面解,也即存在两条通向混沌的道路:倍周期分岔和环面破裂,而这两种道路产生的混沌吸引子在一定参数条件下会相互转换.

并列双圆柱涡激振动的经验性模型研究

建立一种新的预报并列双圆柱涡激振动响应的经验性模型,根据特定间距比条件下旋涡脱落频率出现分支的现象,提出以两个具有不同固有频率的尾流振子来共同描述结构的近壁尾涡动力特性,同时两个振子均满足van der Pol方程,进而得到结构振子和流体振子的耦合方程组。使用该模型分别对中高质量比和低质量比的并列圆柱涡激振动问题进行数值计算,结果表明,结构的位移响应和最大振动幅值等变化规律与实验结果趋势一致,数值基本吻合。

海洋热塑性增强管(RTP)涡激振动数值计算

基于Van der Pol尾流振子模型和多体系统传递矩阵法(transfer matrix method for multibody systems,MSTMM),建立了可以快速预测海洋热塑性增强管(reinforced thermoplastic pipe, RTP)振动特性和涡激振动响应的动力学模型.仿真结果与ANSYS软件仿真结果以及文献实验数据对比,验证了本文模型的准确性.研究了考虑RTP立管刚性接头,不同顶张力,不同来流分布等情况对RTP立管涡激振动响应的影响.计算结果表明:流速越大,立管涡激振动激发出的模态越高;立管涡激振动主要受低阶模态控制;立管的刚性接头对立管的湿模态影响较小,但是对较高阶模态为主所激发出的涡激振动振幅分布影响较大;剪切流对沿立管轴向的涡激振动振幅分布影响较大,低流速能量小所引起的涡激振动幅值较小,但是当剪切流流速达到能激发出较高阶模态时,相比同等流速的均匀流所引起的涡激振动振幅要大.

立管涡激振动高阶响应研究（英文）

由于高阶响应对结构涡激振动存在显著影响,文中在考虑其影响的前提下利用经典Van der Pol尾流振子模型研究了立管在均匀流中的涡激振动特性。在尾流振子与结构模型的相互作用中同时考虑了一阶响应和高阶响应的影响,从而推导了一种考虑了一阶—高阶响应的涡激振动模型。并在此基础上,分析了考虑位移、速度和加速度三种不同右端耦合项作用下的响应特性。此外,还针对不同的质量阻尼比,比较了考虑高阶响应影响和未考虑高阶响应影响情况下系统的涡激振动特性。结果表明,考虑一阶—高阶响应的理论模型能更精确地反映该系统的振动特性。尾流振子和立管的运动幅值都有一定程度的增大。尽管计算结果显示高阶响应比一阶响应小若干个量级,但是不可以忽视高阶响应,因为它对一阶响应存在明显的影响。

柱体结构涡激振动数值计算

为了研究柱体结构的涡激振动特性预测方法,首先基于Van der Pol尾流振子模型建立了弹性支撑单自由度柱体的涡激振动模型。然后基于计算流体力学(CFD)方法、结构动力学理论以及嵌套网格技术,同时考虑弹性支撑柱体来流向和横向振动,建立了柱体结构的涡激振动高保真仿真模型。通过与国外文献实验数据对比,验证了两种模型的准确性。计算结果表明,在低质量比情况下,Van der Pol尾流振子模型在约化速度较小区域计算误差很大,在柱体振幅最大值附近误差较小,基本上可以捕捉到柱体的涡激振动特性,可以用于工程上快速预测柱体结构的涡激振动特性;在低质量比、高质量比以及指定的约化速度范围内,采用CFD方法和嵌套网格技术,可以避免由于柱体振幅较大引起的网格畸变和负网格问题,且可以获得较好的计算精度和详细的流场信息,但计算效率相比Van der Pol尾流振子模型较低。

抑制柱体结构涡激振动的非线性能量阱减振装置优化设计

为了抑制柱体结构的涡激振动(Vortex induced vibration,VIV)问题,该文基于Van der Pol尾流振子模型、结构动力学理论和优化算法,建立了非线性能量阱(Nonlinear energy sink,NES)减振装置优化设计仿真模型。采用Van der Pol尾流振子模型,将其与二维弹性支撑柱体结构动力学方程结合,建立二维弹性支撑柱体单自由度涡激振动预报模型,并与文献实验数据对比,验证了模型的准确性;在模型中嵌入NES控制模型,完成NES作用下的单自由度柱体VIV预测模型,并将其与优化算法相结合,通过优化算法改变非线性能量阱的参数,设计出对柱体涡激振动抑制效果满足设计要求的非线性能量阱;通过仿真分析优化后的NES结构参数对柱体涡激振动的抑制效果和机理。案例优化结果表明,在Ur=5.5时,NES作用下的柱体振幅减小了66.39%,减振效果明显。同时,该文采用优化方法获得的NES结构参数符合实际生产要求,确保了实物生产设计的可能性。

非线性涡激力模型气动参数识别新方法

基于非线性最小二乘法提出识别单自由度经验非线性涡激力模型气动参数新方法。通过同伦分析法获得涡振响应二阶解析解,基于该解构造非线性拟合目标函数并采用遗传算法识别出在给定参数区间内的最优拟合结果。分别用光滑信号及有噪信号进行数值验证,结果表明该方法具有可行性及较好稳定性,并运用该方法识别出流线型闭口箱梁断面的涡激力气动参数。

Phenomenological model for torsional galloping of an elastic flat plate due to hydrodynamic loads

This study investigates the torsional galloping phenomenon, an instability type flow-induced oscillation, in an elastic stru-cture due to hydrodynamic loads into the water current. The structure applied here is a rectangular flat plate with an elastic axis in its mid-chord length. The elasticity is provided by torsion spring. The flat plate has only one degree of freedom which is rotation in pure yaw about its axis. It is observed that as the current speed is higher than a critical velocity, the flat plate becomes unstable. The instability leads to torsional galloping occurrence, as a result of which the flat plate begins to yaw about the elastic axis. By testing two different chord lengths each with several torsion spring rates, the flat plate behavior is investigated and three different responses are recognized. Then, a phenomenological model is developed with the original kernel in the form of the van der Pol-Duffing equa-tion. The model explains these three responses observed experimentally.

水平两结构组合体系的解耦条件及其解析解

由于耦合效应使多结构组合体系的控制分析和计算变得很复杂,故本文着意讨论了水平两结构组合体系的一般解耦条件;并进一步推导了一类线性双自由度Van der Pol模型的解析解。同时,通过数值分析研究了可分离型组合体系的控制机理。

Koopman analysis of nonlinear systems with a neural network representation

The observation and study of nonlinear dynamical systems has been gaining popularity over years in different fields.The intrinsic complexity of their dynamics defies many existing tools based on individual orbits,while the Koopman operator governs evolution of functions defined in phase space and is thus focused on ensembles of orbits,which provides an alternative approach to investigate global features of system dynamics prescribed by spectral properties of the operator.However,it is difficult to identify and represent the most relevant eigenfunctions in practice.Here,combined with the Koopman analysis,a neural network is designed to achieve the reconstruction and evolution of complex dynamical systems.By invoking the error minimization,a fundamental set of Koopman eigenfunctions are derived,which may reproduce the input dynamics through a nonlinear transformation provided by the neural network.The corresponding eigenvalues are also directly extracted by the specific evolutionary structure built in.

预测传热管涡致振动的改进尾流振子模型

针对传热管的漩涡脱落诱发振动问题,在经典尾流振子模型的基础上,提出一种用于预测传热管涡致振动的改进尾流振子模型。计算结果与实验结果的对比显示,该模型能较好地模拟传热管涡致振动的重要特性。首先,通过研究发现,采用联合的位移耦合和加速度耦合模式,能较好地模拟柱体振动与漩涡脱落间的相互作用;其次,经典尾流振子模型中定义的经验参数为定常数,但通过分析发现,其经验参数应根据具体的结构参数来确定;最后,对改进的尾流振子模型所预测的结果与通过流固耦合数值模型计算得到的结果进行了对比分析,结果显示改进的尾流振子模型的结果与双向流固耦合模拟得到的结果吻合较好,说明尾流振子模型用于传热管的漩涡脱落诱发振动是可行的、合理的。