惯性式冲击振动落砂机周期倍化分岔的反控制

在不改变惯性式冲击振动落砂机系统平衡解结构的前提下,考虑碰撞振动系统的Poincaré映射的隐式特点以及经典的映射周期倍化分岔临界准则给反控制带来的困难,基于不直接依赖于特征值计算的周期倍化分岔显式临界准则,研究了落砂机系统周期倍化分岔的反控制.论文首先对落砂机系统施加线性反馈控制,得到受控闭环系统的Poincaré映射,并应用不直接依赖于特征值计算的周期倍化分岔显式临界准则,获得了系统发生周期倍化分岔的控制参数区域.然后应用中心流形-正则形方法分析了周期倍化分岔的稳定性.最终采用数值仿真验证了在任意指定的系统参数点通过控制能产生稳定的周期倍化分岔解.     

基于倍周期分岔的系统混沌参数区域预测

提出了利用倍周期分岔原理寻求系统的混沌参数区域的方法。该方法根据动力系统的一些基本理论，从倍周期分岔途径出发，通过解析方法，得到了Holmes型Duffing系统的混沌参数区域，并通过数值仿给以了验证。     

外激励作用下亚音速二维壁板的复杂响应研究

研究了亚音速流中二维壁板在外激励作用下的复杂响应问题。采用迦辽金方法将非线性运动控制方程离散为常微分方程组,采用数值方法进行计算,研究了壁板系统的复杂响应。应用最大李亚普诺夫指数和庞加莱截面方法对系统的运动性质进行了判定。结果表明,系统随着参数的变化呈现出复杂的响应,系统的周期运动与混沌运动会相间出现;系统由周期运动进...     

参激屈曲梁的倍周期分岔和混沌运动的实验研究

本文对一端固定一端滑动承受轴向简谐载荷的屈曲梁的非线性响应进行了实验。研究了其基本参数共振和主参数共振两种情况，揭示了系统的倍周期分岔和混沌运动等复杂动力学行为。在某些情况下，混沌吸引子和周期吸引子共存，另一些则存在间歇混沌。给出了响应的时间历程、相图、频率谱和Ｐｏｉｎｃａｒｅ映射     

分段线性非线性振子的倍周期分叉和混沌研究

对一类分段线性非线性振子的动力学进行了研究，发现随分叉参数的改变，系统存在非常丰富的振荡态。并通过倍周期分叉过程进入混进入混沌状态，表现出与一维Ｌｏｇｉｓｔｉｃ映射非常似的振荡模式。     

轴向流作用下均布非线性弹簧支承二维壁板的复杂响应

考虑刚性导流段和尾流段对流场的影响,建立轴向流作用下二维板的非线性流固耦合运动控制方程,用有限差分法对控制方程进行离散。为了克服差分网格较多时带来的计算规模较大的问题,对控制方程用主模态缩减法缩减自由度,然后对离散方程进行数值积分,得到系统的复杂响应,分析其分岔和混沌特性。计算结果表明,以来流流速幅值和阻尼参数为可变参数时,系统具有极其复杂的动态响应,通过分岔图、相图和庞加莱截面图等方法判断了系统多种形式的周期、拟周期和混沌运动,在以来流流速幅值为可变参数时,系统一开始经由周期倍化分岔的方式进入混沌;在以阻尼系数为可变参数时,经由倒周期倍化分岔的方式从混沌运动退回到周期振动。     

转子—轴承系统发生动静件碰摩时的混沌路径

分析了一个由油膜轴承支承的转子系统在发生动静件碰摩时的振动特性。转子转速与不平衡量被用来作为控制参数以研究进入和离开混沌区域的各种路径以及系统的各种形式的周期、拟周期与混沌运动。结果证明碰摩转子系统在进入和离开混沌区域时可经由倍周期分岔、阵发性和拟周期路径，以及一种由周期运动直接到混沌状态的突发路径。     

两自由度机械臂λ^2=1下的Hopf分岔与混沌研究

研究了一类周期系数力学系统因周期运动失稳而产生Hopf分岔及混沌问题.首先根据拉格朗日方程给出了该力学系统的运动微分方程,并确定其周期运动的具有周期系数的扰动运动微分方程,再根据Floquet理论建立了其给定周期运动的Poincaré映射,根据该系统的特征矩阵有一对复共轭特征值从-1处穿越单位圆情况,分析该Poincaré映射不动点失稳后将发生次谐分岔、Hopf分岔、倍周期分岔,而多次倍周期分岔将导致混沌.并用数值计算加以验证.结果表明,随着分岔参数的变化,系统的周期运动可通过次谐分岔形成周期2运动,进而发生Hopf分岔形成拟周期运动,并再次经次谐分岔、倍周期分岔形成混沌运动.     

干摩擦振动系统响应计算方法研究综述

首先讨论了两固体接触表面间的干摩擦力模型,重点介绍了滞迟摩擦模型方面的研究工作;然后,论述了含有各种干摩擦环节的振动系统简谐、随机和冲击激励下的响应计算方法,着重讨论了基于滞迟恢复力模型的响应计算方法,并对各种计算方法的特点进行了评述.最后,指出了干摩擦振动系统响应计算方法亟待解决的一些重大问题.      

干摩擦系统在基础位移冲击激励下的特性

本文给出了具有软化弹簧特性的干摩擦隔振系统隔离基础位移冲击激励的理论分析和结果,分析结果表明干摩擦隔冲系统远优于线性阻尼系统,隔冲效果很明显.     

Studies on Bifurcation and Chaos of a String-Beam Coupled System with Two Degrees-of-Freedom

In this paper, research on nonlinear dynamic behavior of a string-beam coupled system subjected to parametric and external excitations is presented. The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam coupled system. The Galerkin's method is employed to simplify the governing equations to a set of ordinary differential equations with two degrees-of-freedom. The case of 1:2 internal resonance between the modes of the beam and string, principal parametric resonance for the beam, and primary resonance for the string is considered. The method of multiple scales is utilized to analyze the nonlinear responses of the string-beam coupled system. Based on the averaged equation obtained here, the techniques of phase portrait, waveform, and Poincare map are applied to analyze the periodic and chaotic motions. It is found from numerical simulations that there are obvious jumping phenomena in the resonant response–frequency curves. It is indicated from the phase portrait and Poincare map that period-4, period-2, and periodic solutions and chaotic motions occur in the transverse nonlinear vibrations of the string-beam coupled system under certain conditions. An erratum to this article is available at .     

Synchronisation and Chaos in a Parametrically and Self-Excited System with Two Degrees of Freedom

Vibration analysis of a non-linear parametrically andself-excited system of two degrees of freedom was carried out. The modelcontains two van der Pol oscillators coupled by a linear spring with a aperiodically changing stiffness of the Mathieu type. By means of amultiple-scales method, the existence and stability of periodicsolutions close to the main parametric resonances have beeninvestigated. Bifurcations of the system and regions of chaoticsolutions have been found. The possibility of the appearance ofhyperchaos has also been discussed and an example of such solution hasbeen shown.     

Note on Chaos in Three Degree of Freedom Dynamical System with Double Pendulum

The nonlinear response of a three degree of freedom vibratory system with double pendulum in the neighbourhood internal and external resonances is investigated. The equations of motion have bean solved numerically. In this type system one mode of vibration may excite or damp another one, and for except different kinds of periodic vibration there may also appear chaotic vibration. To prove the character of this vibration and to realise the analysis of transitions from periodic regular motion to quasi-periodic and chaotic, the following have been constructed: bifurcation diagrams and time histories, phase plane portraits, power spectral densities, Poincaré maps and exponents of Lyapunov. These bifurcation diagrams show many sudden qualitative changes, that is, many bifurcations in the chaotic attractor as well as in the periodic orbits.     

Estimating the Largest Lyapunov Exponent in a Multibody System with Dry Friction by using Chaos Synchronization

Using the properties of chaos synchronization, the method for estimating the largest Lyapunov exponent in a multibody system with dry friction is presented in this paper. The Lagrange equations with multipliers of the systems are given in matrix form, which is adequate for numerical calculation. The approach for calculating the generalized velocity and acceleration of the slider is given to determine slipping or sticking of the slider in the systems. For slip–slip and stick–slip multibody systems, their largest Lyapunov exponents are calculated to characterize their dynamics.The project supported by the National Natural Science Foundation of China (10272008 and 10371030) The English text was polished by Yunming Chen     

Nonlinear Oscillations in a System with Dry Friction

The case is examined where the right-hand side of the equations of motion is discontinuous. Attraction only in the stick domain ensures existence of periodic oscillations. Sufficient stability conditions for the periodic solution of a nonlinear system with dry friction are established__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 110–116, April 2005.     

The Discrete Models on a Frictional Single Degree of Freedom System

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Simulation of the Onset of Nonstationarity and Chaos in a Hydrodynamic System Governed by a Small Number of Degrees of Freedom

The hypothesis of the onset of nonstationarity and chaos in a hydrodynamic system as a result of the nonlinear interaction of a small number of degrees of freedom is verified experimentally with reference to fluid convection in a toroidal channel. Regimes of motion of a fluid medium which correspond qualitatively to the Lorenz model are obtained experimentally. These include steady-state regimes, their bifurcations, nonuniqueness and instability, unsteady periodic and stochastic regimes. The spectral and statistical characteristics of the and unsteady processes are investigated, the nature of the onset of chaos is analyzed, and the results are compared with calculations. The mathematical model of the problem is refined.     

Periodic and Non-Periodic Oscillations of a Class of Hysteretic Two Degree of Freedom Systems

The equations governing the response of hysteretic systems to sinusoidal forces, which are memory dependent in the classical phase space, can be given as a vector field over a suitable phase space with increased dimension. Hence, the stationary response can be studied with the aids of classical tools of nonlinear dynamics, as for example the Poincaré map. The particular system studied in the paper, based on hysteretic Masing rules, allows the reduction of the dimension of the phase space and the implementation of efficient algorithms. The paper summarises results on one degree of freedom systems and concentrates on a two degree of freedom system as the prototype of many degree of freedom systems. This system has been chosen to be in 1:3 internal resonance situation. Depending on the energy dissipation of the elements restoring force, the response may be more or less complex. The periodic response, described by frequency response curves for various levels of excitation intensity, is highly complex. The coupling produces a strong modification of the response around the first mode resonance, whereas it is negligible around the second mode. Quasi-periodic motion starts bifurcating for sufficiently high values of the excitation intensity; windows of periodic motions are embedded in the dominion of the quasi-periodic motion, as consequence of a locking frequency phenomenon.     

Numerical Simulation of the Flow in the Carotid Bifurcation

Pulsatile flow through the three-dimensional carotid artery bifurcation has been studied using the artificial-compressibility method. The part of the flow with large inertia bifurcates and creates a very steep velocity gradient on the divider walls. The flow near the nondivider walls slows down because of dilation of the cross section and strong adverse pressure gradient. The secondary flow in the bifurcation region, which is similar to the Dean vortex in a curved pipe, is strong and very complex. The region of separation is not closed for the cases of steady and pulsatile flow. The extent of this region is small and the streamlines are smooth except in the decelerating phase of systole. The change of common-internal bifurcation angle (25°± 15°) for fixed internal–external bifurcation angle of 50° has more effect on the shear on the bifurcation-internal carotid wall and less effect on the shear on the common-internal carotid wall. The mean wall shears are not sensitive to the input flow-rate waveform for constant mean flow, but the maximum wall shears are. Received 3 January 1997 and accepted 11 April 1997     

Homoclinic Twist Bifurcation in a System of Two Coupled Oscillators

We analyse the dynamics of two identical Josephson junctions coupled through a purely capacitive load in the neighborhood of a degenerate symmetric homoclinic orbit. A bifurcation function is obtained applying Lin's version of the Lyapunov–Schmidt reduction. We locate in parameter space the region of existence of n-periodic orbits, and we prove the existence of n-homoclinic orbits and bounded nonperiodic orbits. A singular limit of the bifurcation function yields a one-dimensional mapping which is analyzed. Numerical computations of nonsymmetric homoclinic orbits have been performed, and we show the relevance of these computations by comparing the results with the analysis.