共查询到15条相似文献,搜索用时 156 毫秒
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针对一类具有非线性刚度、非线性阻尼的非线性相对转动系统, 应用耗散系统的拉格朗日原理建立在组合谐波激励作用下非线性相对转动系统的动力学方程. 构造李雅普诺夫函数, 分析相对转动系统的稳定性, 研究自治系统的分岔特性. 应用多尺度法求解相对转动系统的非自治系统在组合激励作用下的分岔响应方程. 最后采用数值仿真方法, 通过分岔图、时域波形、相平面图、Poincaré截面图等研究外扰激励、系统阻尼、 非线性刚度对相对转动系统经历倍周期分岔进入混沌运动的影响.
关键词:
相对转动
组合激励
分岔
混沌 相似文献
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本文以一类典型的相对转动振动系统为研究对象,研究激励引起的系统混沌运动和安全域侵蚀,并对系统施加时滞位置反馈来抑制这两类复杂动力学行为.首先,利用Melnikov函数法获得相对转动系统的混沌运动及安全盆侵蚀的激励振幅阈值;其次,通过讨论时滞反馈系统的Hopf分岔条件获得适用于Melnikov函数法的控制参数取值范围,进而利用Melnikov函数法获得时滞受控系统的全局分岔必要条件;最后,利用四阶Rung-Kutta法和点映射法数值模拟了时滞受控系统动力学行为随参数的演变,从而验证解析结果的有效性.研究发现:在正的增益系数和较短的时滞量下,时滞位置反馈能够有效抑制相对转动系统的混沌运动和安全盆侵蚀现象. 相似文献
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研究一类具有异宿轨道的非线性相对转动系统的分岔与混沌运动. 应用耗散系统的拉格朗日方程建立一类组合谐波激励作用下非线性相对转动系统的动力学方程. 利用多尺度法求解相对转动系统发生组合共振时满足的分岔响应方程并进行奇异性分析, 得到了系统稳态响应的转迁集. 根据相对转动系统异宿轨道参数方程, 求解了异宿轨道的Melnikov函数, 并给出了系统发生Smale马蹄变换意义下混沌的临界条件. 最后采用数值方法, 通过分岔图, 最大Lyapunov指数图, 相轨迹图和庞加莱截面图研究系统参数对混沌运动的影响. 相似文献
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研究一类具有同宿轨道、异宿轨道的相对转动非线性动力系统的混沌运动. 建立具有非线性刚度、非线性阻尼和外扰激励作用的一类两质量相对转动非线性动力系统的动力学方程. 利用Melnikov方法讨论了系统的全局分岔和系统进入混沌状态的可能途径,给出了系统发生混沌的必要条件,并利用最大Lyapunov指数图,分岔图,Poincare截面图和相轨迹图进一步分析了系统的混沌行为.
关键词:
相对转动
非线性动力系统
混沌
Melnikov方法 相似文献
5.
建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性.
关键词:
相对转动
准周期参激
时滞反馈
极限环 相似文献
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研究一类非线性相对转动系统在负载Coulomb摩擦效应下的混沌运动行为. 根据Lagrange方程建立一类含非线性负载Coulomb摩擦阻尼的两个质量相对转动系统的动力学方程. 利用Cardano公式讨论自治系统的特征值, 在此基础上, 应用待定系数法给出系统同宿轨道的存在性, 并借助Silnikov定理研究了系统的混沌行为. 最后数值模拟了给定参数下系统的混沌运动, 并给出在Coulomb摩擦阻尼变化下系统由周期、倍周期通向混沌的途径, 验证了理论分析的正确性. 相似文献
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建立具有一般非线性弹性力、广义摩阻力和谐波激励的一类相对转动非线性动力系统的动力学方程. 对相对转动非线性自治系统进行定性分析,通过构造Lyapunov函数研究自治系统奇点的稳定性. 运用多尺度法求解谐波激励下非自治系统在几种不同共振响应下的近似解,同时分析了主振系统稳态运动的稳定性.
关键词:
相对转动
非线性动力系统
Lyapunov函数
稳定性 相似文献
11.
建立了一类具有Mathieu-Duffing振子的两质量相对转动系统的非线性动力学方程. 应用多尺度法求解该系统发生主共振-基本参数共振的分岔响应方程,并通过奇异性分析得到系统稳态响应的转迁集. 利用Melnikov方法讨论系统在外激扰动和参激扰动变化下的全局分岔和系统进入混沌状态的可能途径,得到外激和参激幅值变化下系统可能出现多次通向混沌的道路,获得系统发生混沌的必要条件. 最后采用数值方法验证了理论研究的有效性.
关键词:
相对转动
Mathieu-Duffing振子
混沌
Melnikov方法 相似文献
12.
Hopf bifurcation control for a coupled nonlinear relative rotation system with time-delay feedbacks 下载免费PDF全文
This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time- delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1:1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution. 相似文献
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Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation 下载免费PDF全文
This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincar map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using non-feedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to period-motions by adding an excitation term. 相似文献
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The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example. From the Lyapunov stability theory, sufficient conditions for choosing control parameters to guarantee chaos control are derived. Several experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances. 相似文献
15.
Hysteresis-induced bifurcation and chaos in a magneto-rheological suspension system under external excitation 下载免费PDF全文
The magneto-rheological damper(MRD) is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom(2-DOF) MR suspension system was established first, by employing the modified Bouc–Wen force–velocity(F –v) hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface.The largest Lyapunov exponent(LLE) was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density(PSD) diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy(K entropy) were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system. 相似文献