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1.
In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories. The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on. 相似文献
2.
基于Matlab仿真软件,考虑弹性水击对水轮机调节系统的影响,建立弹性水击水轮机微分代数模型,并与调速器和发电机共同构成水轮机调节系统非线性模型。在此基础上运用非线性动力学分叉理论对PID调速器参数进行Hopf分叉行为研究,得出PID参数三维分叉曲面、二维分叉曲线及稳定域,并通过对时域图、相轨迹图等的综合分析,得到取不同调速器参数时系统的非线性动力学特性,为机组PID参数选择提供理论依据。最后通过系统仿真得出,在小扰动下线性模型和非线性模型均能适用,在大扰动下非线性模型能更真实地反映机组动态特性。 相似文献
3.
Nomenclaturex,y,x ·, y·-displacement and velocity of rotor-x,-y,x-·,-y·-displacement and velocity of rotor , di mension less¨x,¨y-acceleration of rotor¨-x,¨-y-acceleration of rotor ,di mensionlessω-rotating speed of rotor-ω-rotating speed of rotor ,di mensionlessx,y,z-Cartesian coordinates-x,-y,-z-Cartesian coordinates ,di mensionless2m-mass of rotorg-acceleration of gravityG-weight of rotor ,di mensionlesse=e2x e2y-mass eccentricity of rotorex,ey-mass eccentricity of rotor in thexan… 相似文献
4.
Simplest normal forms of generalized Neimark-Sacker bifurcation 总被引：1，自引：0，他引：1
The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system.
It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation are expressed in polar coordinates,
then all odd order terms must, in general, remain in the normal forms. In this paper, five theorems are presented to show
that the conventional Neimark-Sacker bifurcation can be further simplified. The simplest normal forms of generalized Neimark-Sacker
bifurcation are calculated. Based on the conventional normal form, using appropriate nonlinear transformations, it is found
that the generalized Neimark-Sacker bifurcation has at most two nonlinear terms remaining in the amplitude equations of the
simplest normal forms up to any order. There are two kinds of simplest normal forms. Their algebraic expression formulas of
the simplest normal forms in terms of the coefficients of the generalized Neimark-Sacker bifurcation systems are given. 相似文献
5.
基于MATCONT的电力系统电压稳定分岔及控制仿真试验 总被引：1，自引：0，他引：1
介绍了电力系统ODE模型中引起电压失稳的常见分岔类型及分岔控制的基本概念;运用基于Matlab的数值分岔分析软件MATCONT对一个经典单机—动态负荷系统进行了分岔分析,验证了PQ动态负荷模型系统存在着鞍结分岔(SNB)现象,而RL动态负荷模型系统并无分岔现象产生.为延迟PQ动态负荷模型系统的鞍结分岔点,在原系统中引入了线性状态反馈控制和SVC控制两种分岔控制方法.MATCONT仿真结果显示,这两种控制方法均能够有效延迟鞍结分岔,从而提高系统的电压稳定性,并可通过选择合理的反馈控制器增益及SVC增益获得理想的分岔控制效果. 相似文献
6.
彭解华 《邵阳学院学报(社会科学版)》2001,23(2):24-29
参量激励下的Duffing-van der Pol系统是一个多参数的非线性系统,本文研究了该系统的二参数共振分叉问题,利用多尺度方法得到了系统的一次近似平均方程和分叉响应方程.分析了分叉方程的解及其在二分叉参数平面上的分布.研究了零解的稳定性. 相似文献
7.
This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to describe the low-frequency vibration of the drum brake, applied the centre manifold theory to simplify the system, and obtained the LCO amplitude by calculating the normal form of the simplified system at the Hopf bifurcation point. It is indicated that when the friction coefficient is smaller than the friction coefficient at the bifurcation point, the amplitude decreases; whereas with a friction coefficient larger than the friction coefficient of bifurcation point, LCO occurs. The results suggest that it is applicable to suppress the LCO amplitude by changing systematic parameters, and thus improve the safety and ride comfort when applying brake. These findings can be applied to guiding the design of drum brakes. 相似文献
8.
引入二次多项式平方轮胎模型,选取合适的状态变量,建立了四轮转向汽车四维非线性动力学系统,应用中心流形定理对其进行了降维处理并转换为中心流形上的一阶约化系统.应用非线性分岔和稳定性理论对均匀路面工况的稳定性进行了分析,并在Matlab/Simulink中进行了仿真.结果表明：随着车速和前轮转角的增加,高维四轮转向汽车奇异点处会发生鞍结分岔,该分岔会导致汽车失稳. 相似文献
9.
通过对非线性电路的理论分析,得出了非线性电路平衡状态的稳定性准则。即在非线性电路中,若平衡点处的动态电阻Rd为正,或当Rd为负时满足RdR1,则该点所表示的平衡状态是不稳定的。 相似文献
10.
嵌岩桩非线性动力学特性 总被引：1，自引：0，他引：1
The nonlinear dynamic characteristics of a pile embedded in a rock were investigated. Suppose that both the materials of the pile and the soil around the pile obey nonlinear elastic and linear viscoelastic constitutive relations. The nonlinear partial differential equation governing the dynamic characteristics of the pile was first derived. The Galerkin method was used to simplify the equation and to obtain a nonlinear ordinary differential equation. The methods in nonlinear dynamics were employed to solve the simplified dynamical system, and the time-path curves, phase-trajectory diagrams, power spectrum, Poincare sections and bifurcation and chaos diagrams of the motion of the pile were obtained. The effects of parameters on the dynamic characteristics of the system were also considered in detail. 相似文献