共查询到18条相似文献,搜索用时 156 毫秒
1.
2.
非线性切换系统具有广泛的工程背景,而传统的非线性理论不能直接用来解决其中的问题,因而成为当前国内外热点和前沿课题之一. 目前相关工作大都是围绕固定时间或单状态切换开展的,而实际工程系统大都属于多状态切换问题,同时多状态切换涉及到更为丰富的动力学行为. 本文基于两广义BVP 振子,通过引入双向切换开关,构建了双状态切换下的非线性动力学模型,进而研究状态切换导致的各种运动模式及其相应的产生机制. 应用非光滑系统的Poincaré映射理论,推导了双状态切换下的Lyapunov 指数的计算公式,结合子系统的分岔分析,得到了切换系统随分岔参数变化的动力学演化过程及其相应的最大Lyapunov 指数的变化情况. 得到了双状态切换条件下系统存在着各种形式的振荡行为,分析了诸如周期突变等现象及通往混沌的倍周期分岔道路,揭示了不同运动模式的产生机制及倍周期序列的本质. 与固定时间切换和单状态切换系统不同,双临界状态切换系统存在着更为丰富的非线性现象,其主要原因在于双状态切换会产生更多的切换点,且切换点的位置更加多变. 同时切换系统的倍周期分岔序列与光滑系统中的倍周期分岔序列不同,切换系统的倍周期分岔序列只对应于切换点数目的成倍增加,而其相应的周期一般不对应于严格的周期倍化过程. 相似文献
3.
4.
非光滑动力系统Lyapunov指数谱的计算方法 总被引:8,自引:1,他引:8
对 n 维非光滑(刚性约束和分段光滑)动力系统引进局部映射,利用 Poincaré映射分析方法得出了非光滑系统 Lyapunov 指数谱的通用计算方法.以一类刚性约束的非线性动力系统为例,给出了 Lyapunov 指数谱随参数大范围变化的规律,并与相应的 Poincaré映射分岔图进行对照,验证了上述通用计算方法的正确性和有效性. 相似文献
5.
本文从理论上描述了线性迭代函数系统(LIFS)产生分形、分岔和混沌行为的数学基础,分析讨论了BAHAR方程产生分岔和混沌的机制,给出计算机仿真结果。研究表明,分形、分岔和混沌行为不仅在非线性迭代函数系统(NIFS)中表现得非常丰富,而且在线性迭代函数系统(LIFS)中表现得也非常丰富。 相似文献
6.
以四自由度迟滞非线性随机振动模型为研究对象,以速度和位移立方的模型来模拟振动系统的迟滞非线性力,并以Monte Carlo法模拟随机位移激励,对迟滞非线性随机系统的动力学特性进行分析.通过系统的Poincare截面、分岔图及最大Lyapunov指数分析了系统迟滞非线性力各参数对系统混沌状态的影响.研究表明,非线性刚度系数对振动系统混沌状态的影响较小,线性阻尼项和线性刚度项次之,而非线性阻尼项的影响最为明显.不仅证明了非线性振动系统随机混沌振动现象的存在,更重要的是可以为非线性振动系统参数的合理取值提供理论依据. 相似文献
7.
功能度量法是基于可靠度的结构优化设计中评估概率约束的一种方法,其改进均值(AMV)迭代格式具有简洁、高效的优点,但对一些非线性功能函数搜索最小功能目标点时可能陷入周期振荡或混沌解,本文利用混沌反馈控制的稳定转换法对功能度量法的AMV迭代格式实施收敛控制.首先展示一些功能函数应用功能度量法AMV格式迭代计算产生了周期解和混沌解现象,并对迭代算法进行了混沌动力学分析.然后利用稳定转换法对功能度量法迭代失败的参数区间进行混沌控制,使嵌入周期和混沌轨道的不稳定不动点稳定化,获得了稳定收敛解,实现了迭代解的周期振荡、分岔和混沌控制. 相似文献
8.
9.
10.
结构可靠度分析FORM迭代算法的混沌控制 总被引:1,自引:1,他引:0
利用混沌控制原理对FORM收敛失败进行控制. 理清了全局性和局部性两类混沌反馈
控制各种方法的内在联系,说明稳定转换法和自适应调节法属于全局混沌反馈控制
方法,自适应调节法可视为稳定转换法的特例. 参
数调节混合法不过是松弛牛顿法的另一种表达形式,它们都属于局部混沌反馈控制方法. 阐
明了混沌反馈控制表达式与工程力学收敛控制迭代算法的对应关系. 也揭示了这些迭代算法
收敛控制措施的功效和局限性. 提出了一个以稳定转换法为主联合松弛牛顿法的混
沌反馈控制方法,对可靠度分析FORM迭代算法实现了周期振荡、分岔和混沌控制. 相似文献
11.
Fuzzy reliability analysis can be implemented using two discrete optimization maps in the processes of reliability and fuzzy analysis. Actually, the efficiency and robustness of the iterative reliability methods are two main factors in the fuzzy-based reliability analysis due to the huge computational burdens and unstable results. In the structural fuzzy reliability analysis, the first-order reliability method (FORM) using discrete nonlinear map can provide a C membership function. In this paper, a discrete nonlinear conjugate map is proposed using a relaxed-finite step size method for fuzzy structural reliability analysis, namely Fuzzy conjugate relaxed-finite step size method fuzzy CRS. A discrete conjugate map is stabilized using two adaptive factors to compute the relaxed factor and step size in FORM. The framework of the proposed fuzzy structural reliability method is established using two linked iterative discrete maps as an outer loop, which constructs the membership function of the response using alpha level set optimization based on genetic operator, and the inner loop, implemented for reliability analysis using proposed conjugate relaxed-finite step size method. The fuzzy CRS and fuzzy HL-RF methods are compared to evaluate the membership functions of five structural problems with highly nonlinear limit state functions. Results demonstrated that the fuzzy CRS method is computationally more efficient and is strongly more robust than the HL-RF for fuzzy-based reliability analysis of the nonlinear structural reliability problems. 相似文献
12.
Lyapunov exponents, defined as exponential divergent or convergent rate of initially infinitely close solution trajectories, have been widely used for diagnosing chaotic systems, as well for stability analysis of nonlinear systems. Although calculated from the evolution of disturbance vectors associated with the flow, Lyapunov exponents are not associated with any specific directions, and such evolutions are driven by the dynamics in all directions in the state space. It is desirable to explore the asymptotic behaviors of the dynamic systems along certain specific directions and the specific dynamics driving such behaviors. In this paper, the Lyapunov exponents are modified. The modified Lyapunov exponents can indicate the exponential divergent or convergent rates in certain directions, which are driven by the dynamics in the same directions. The existence and the invariance to the initial conditions of the proposed modified exponents are proven mathematically. The algorithm for calculating the modified Lyapunov exponents from mathematical models is also developed. A wide range of case studies, from classical nonlinear dynamic systems to engineering systems, are presented to demonstrate the proposed modified Lyapunov exponents, and the indications of the modified exponents are also discussed. The proposed modified Lyapunov exponents can reveal additional insights into the system dynamics to the conventional Lyapunov exponents. Such information can be instrumental for stability control design. 相似文献
13.
14.
A study is made of the dynamics of oscillating systems with a slowly varying parameter. A slowly varying forcing periodically crosses a critical value corresponding to a pitchfork bifurcation. The instantaneous phase portrait exhibits a centre when the forcing does not exceed the critical value, and a saddle and two centres with an associated double homoclinic loop separatrix beyond this value. The aim of this study is to construct a Poincaré map in order to describe the dynamics of the system as it repeatedly crosses the bifurcation point. For that purpose averaging methods and asymptotic matching techniques connecting local solutions are applied. Given the initial state and the values of the parameters the properties of the Poincaré map can be studied. Both sensitive dependence on initial conditions and (quasi) periodicity are observed. Moreover, Lyapunov exponents are computed. The asymptotic expressions for the Poincaré map are compared with numerical solutions of the full system that includes small damping. 相似文献
15.
In this paper, a Fourier expansion-based differential quadrature (FDQ) method is developed to analyze numerically the transverse nonlinear vibrations of an axially accelerating viscoelastic beam. The partial differential nonlinear governing equation is discretized in space region and in time domain using FDQ and Runge–Kutta–Fehlberg methods, respectively. The accuracy of the proposed method is represented by two numerical examples. The nonlinear dynamical behaviors, such as the bifurcations and chaotic motions of the axially accelerating viscoelastic beam, are investigated using the bifurcation diagrams, Lyapunov exponents, Poincare maps, and three-dimensional phase portraits. The bifurcation diagrams for the in-plane responses to the mean axial velocity, the amplitude of velocity fluctuation, and the frequency of velocity fluctuation are, respectively, presented when other parameters are fixed. The Lyapunov exponents are calculated to further identify the existence of the periodic and chaotic motions in the transverse nonlinear vibrations of the axially accelerating viscoelastic beam. The conclusion is drawn from numerical simulation results that the FDQ method is a simple and efficient method for the analysis of the nonlinear dynamics of the axially accelerating viscoelastic beam. 相似文献
16.
Nonlinear oscillations and chaotic motions in a road vehicle system with driver steering control 总被引:5,自引:0,他引:5
The nonlinear dynamics of a differential system describing the motion of a vehicle driven by a pilot is examined. In a first step, the stability of the system near the critical speed is analyzed by the bifurcation method in order to characterize its behavior after a loss of stability. It is shown that a Hopf bifurcation takes place, the stability of limit cycles depending mainly on the vehicle and pilot model parameters. In a second step, the front wheels of the vehicle are assumed to be subjected to a periodic disturbance. Chaotic and hyperchaotic motions are found to occur for some range of the speed parameter. Numerical simulations, such as bifurcation diagrams, Poincaré maps, Fourier spectrums, projection of trajectories, and Lyapunov exponents are used to establish the existence of chaotic attractors. Multiple attractors may coexist for some values of the speed, and basins of attraction for such attractors are shown to have fractal geometries. 相似文献
17.
树形多体系统非线性动力学的数值分析方法 总被引:4,自引:0,他引:4
研究了树形多体系统大线性动力学分析的数值方法,利用多体系统的正则方程及其线性化程,给出了多体系统Lyapunov指数和Poincare映射的计算方法,该算法具有较好的计算精度和通用性,既适用于说明该算法的有效性,并对该系统的动力学行为进行分析,最后用算例说明该算法的有效性,并对该系统的动力学特征(周期解、准周期解、分岔、混沌以及通往混沌的道路等)进行了分析。 相似文献