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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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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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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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对称双弹簧振子受迫、有阻尼横振动的混沌行为 总被引:4,自引:1,他引:3
对受周期外力驱动的对称双弹簧振子进行了研究,建立了系统的动力学方程,用线性稳定性分析方法讨论了平衡点附近邻域的稳定性,利用数值计算并结合多种分析方法,求解非线性方程和判断解的性质.通过改变系统参数,画出时域图、相图及分岔图等.计算分析和数值实验发现,这个简单的力学系统存在十分丰富的动力学行为(分岔、混沌).理论分析和数值实验结果一致. 相似文献
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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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针对Rssler系统平衡点的Hopf分岔,以Washout滤波器为控制器,详细讨论了控制器参数对Hopf分岔点位置、分岔类型以及周期解振幅的控制问题.首先根据Routh-Hurwitz判据计算了受控系统的参数空间稳定域,找出了对应的Hopf分岔边界,并由此分析了滤波器时间常数、线性控制增益对分岔点位置的影响.然后,引入NormalForm直接法方便地求出系统Hopf分岔Normal Form系数,由此确定出改变分岔类型和周期解振幅的控制器非线性增益选择原则.最后用数值计算验证了本文的结论. 相似文献
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建立了振动筛系统的动力学模型,推导出了其周期运动的Poincaré 映射,基于Poincaré 映射方法着重研究了系统Flip-Hopf-Hopf余维三分岔、三次强共振条件下的Hopf-Hopf余维三分岔以及三种非常规的混沌演化过程.研究结果表明,此两类余维三分岔点附近的动力学行为变得更加复杂和新颖,在分岔点附近出现了三角形吸引子、3T2环面分岔以及“五角星型”、“轮胎型”概周期吸引子,揭示了环面爆破、环面倍化以及T2环面分岔向混沌演化的过程,这些结果对于振动筛系统的动力学优化设计提供了理论参考.
关键词:
余维三分岔
非常规混沌演化
T2环面分岔')" href="#">T2环面分岔 相似文献
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研究了弹性轨道条件下,控制回路中位置反馈信号存在时滞的磁浮系统在亚谐轨道激励作用下的响应问题. 将动力学模型在平衡点处线性化,以时滞为分岔参数,得到了系统出现Hopf分岔的条件. 用中心流形约化方法得到了包含轨道扰动系统的Poincaré规范型. 用多尺度法从理论上推导了时滞磁浮系统的亚谐共振周期解,得到了自由振动的分岔响应方程,分析了周期解中自由振动项的存在条件,研究了控制参数和激励参数与周期解的关系. 最后用数值仿真的方法分析了时滞参数、控制参数对系统响应的影响,分析结果指出,使系统保持稳定的亚谐响应的时滞边界小于无扰动时的时滞边界,时滞参数不但可以抑制亚谐响应,还能够控制混沌的产生,而控制参数可以控制系统响应中自由振动项的出现和受迫振动的幅值,适当选择这些参数可以有效抑制亚谐振动响应.
关键词:
亚谐共振响应
位置时滞反馈控制
非自治磁浮系统
分岔 相似文献
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假设超晶格锯齿形沟道对粒子的作用等效为形状相似的周期场作用. 在经典力学框架内,引入正弦平方势,把粒子运动方程化为具有阻尼项和双频激励项的摆方程. 用Melnikov方法对单频激励系统的分叉与混沌进行分析;用Lyapunov方法对双频激励系统的稳定性进行讨论. 结果表明:在弱非线性情况下,双频激励系统存在局域不稳定,且这种不稳定将向全局扩展,直至混沌的出现;导致混沌的双频激励强度远小于单频激励强度;外加一个适当的超声场可望将这种敏感钝化,使系统的稳定性得到改善.
关键词:
超晶格
准周期激励
混沌
稳定性 相似文献
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针对随机相位作用的Duffing混沌系统, 研究了随机相位强度变化时系统混沌动力学的演化行为及伴随的随机共振现象. 结合Lyapunov指数、庞加莱截面、相图、时间历程图、功率谱等工具, 发现当噪声强度增大时, 系统存在从混沌状态转化为有序状态的过程, 即存在噪声抑制混沌的现象, 且在这一过程中, 系统亦存在随机共振现象, 而且随机共振曲线上最优的噪声强度恰为噪声抑制混沌的参数临界点. 通过含随机相位周期力的平均效应分析并结合系统的分岔图, 探讨了噪声对混沌运动演化的作用机理, 解释了在此过程中随机共振的形成机理, 论证了噪声抑制混沌与随机共振的相互关系. 相似文献
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Aline Souza de Paula Francisco Heitor Iunes Pereira-Pinto 《Journal of sound and vibration》2006,294(3):585-595
Pendulum is a mechanical device that instigates either technological or scientific studies, being associated with the measure of time, stabilization devices as well as ballistic applications. Nonlinear characteristic of the pendulum attracts a lot of attention being used to describe different phenomena related to oscillations, bifurcation and chaos. The main purpose of this contribution is the analysis of chaos in an experimental nonlinear pendulum. The pendulum consists of a disc with a lumped mass that is connected to a rotary motion sensor. This assembly is driven by a string-spring device that is attached to an electric motor and also provides torsional stiffness to the system. A magnetic device provides an adjustable dissipation of energy. This experimental apparatus is modeled and numerical simulations are carried out. Free and forced vibrations are analyzed showing that numerical results are in close agreement with those obtained from experimental data. This analysis shows that the experimental pendulum has a rich response, presenting periodic response, chaos and transient chaos. 相似文献
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The dynamical behaviors of a periodic excited oscillator with multiple time scales in the form that order gap exists between the frequency of the excitation and the natural frequency, are investigated in this Letter. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamics. Different types of bursting phenomena, such as fold/Hopf bursting, fold/Hopf/homoclinic bursting and Hopf/homoclinic bursting, are presented, the mechanism of which is obtained based on the bifurcations of the generalized autonomous system as well as the introduction of the so-called transformed phase portraits. Furthermore, the evolution of the bursting is discussed in details, in which one may find that when the two limit cycles caused by the Hopf bifurcations of the two related equilibrium points interact with each other, homoclinic bifurcation may occur, leading to the merge of the two cycles to form a large amplitude cycle. The homoclinic bifurcation may cause the two asymmetric bursters to merge into a symmetric enlarged burster, in which the large amplitude of the spiking state agrees well with the amplitude of the cycle caused by the homoclinic bifurcation. 相似文献
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Bifurcations and chaotic motions in the autonomous system of a restrained pipe conveying fluid 总被引:1,自引:0,他引:1
The stability and dynamics of a cantilevered pipe conveying fluid with motion-limiting constraints and a linear spring support have been investigated. Emphasis is placed on analyzing local qualitative behavior of the system in the neighborhood of a doubly degenerate point. Using some qualitative reduction methods of dynamical system theory, the four-dimensional differential equation of motion is reduced to a two-dimensional one, and then the possible motions of the pipe are predicted through analyzing bifurcations of the solution to the reduced equation of motion. The unfolding result is found to be in good agreement with the result obtained using the numerical method. It is also found that there exist the quasi-periodic motions and route to chaos through breakup of the quasi-periodic torus surface in some parameter region of the system, which differs from that of periodic-doubling bifurcation route found earlier in this system. Numerical simulations have been performed using the four-dimensional equation of motion to confirm the analytical results. 相似文献
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A two-degree-of-freedom system having symmetrically placed rigid stops and subjected to periodic excitation is considered. Such models play an important role in the studies of mechanical systems with clearances or gaps. The period-one double-impact symmetrical motion and its Poincaré map are derived analytically. Stability and local bifurcations of the period-one double-impact symmetrical motion are analyzed by the equation of Poincaré map. The routes from period-one double-impact symmetrical motion to chaos, via pitchfork bifurcations and period-doubling bifurcation, are studied by numerical simulation. Some non-typical routes to chaos, caused by grazing the stops and Hopf bifurcation of period two four-impact motion, are analyzed. Hopf bifurcations of period-one double-impact symmetrical and antisymmetrical motions are shown to exist in the two-degree-of-freedom vibratory system with two-sided stops. Interesting feature like the period-one four-impact symmetrical motion is also found, and its route to chaos is analyzed. It is of special interest to acquire an overall picture of the system dynamics for some extreme values of parameters, especially those which relate to the degenerated case of a single-degree-of-freedom system, and these analyses are presented here. 相似文献