多自由度非线性振动系统的多频分叉

本文研究自治和非自治多目由度非线性振动系统当其线化系统有多个特征值同时经过虚轴时产生的多频分叉问题,提出了用于分析多频分叉问题的平均摄动解法,得到了在共振和非共振情形的多频分叉渐近摄动解和稳定性判据,我们还将本文方法用在分析机车轮对动力系统的Hopf分叉中和Van der PolDuffing耦合非线性振子的双频分叉中。     

一类具有二维分叉方程的积分方程的分叉

本文研究一类含参数的非线性积分方程的分叉问题,其中的积分算子的线性化算子在分叉值点处有二维零空间。利用Liapunov-Schmidt约化方法和基于系统的对称性的群论方法,得到了周期分叉解存在的充分条件。     

一维相对论振子运动的研究

该文运用椭圆积分的理论，给出了一维相对论振子运动的解析解以及振子的振动周期. 指出相对论振子的振动周期不但与振子的固有性质有关，而且还与振子的振幅有关.     

非线性振动系统的异宿轨道分叉,次谐分叉和混沌

在参数激励与强迫激励联合作用下具有van der Pol阻尼的非线性振动系统,其动态行为是非常复杂的.本文利用Melnikov方法研究了这类系统的异宿轨道分叉、次谐分叉和混沌.对于各种不同的共振情况,系统将经过无限次奇阶次谐分叉产生Smale马蹄而进入混沌状态.最后我们利用数值计算方法研究了这类系统的混沌运动.所得结果揭示了一些新的现象.     

非线性弹性梁在谐波激励下的次谐和超次谐响应

本文研究受横向周期载荷作用的梁的动力响应,梁的本构关系具有三次非线性项·　轴向载荷作用下已屈曲的梁受到横向激励后,谐波是不稳定的,将分叉出次谐波、超次谐波,以Ｍｅｌｎｉｋｏｖ法确定了次谐轨道、超次谐轨道产生的条件·     

附加非线性振子的双稳态电磁式振动能量捕获器动力学特性研究

随着微机电科技的进步,利用环境振动进行系统自供电已经成为目前非线性动力学研究的热点.将质量-弹簧-阻尼系统与双稳态振动能量捕获系统相结合,提出了附加非线性振子的双稳态电磁式振动能量捕获器,建立系统的力学模型及控制方程.通过数值仿真研究了简谐激励下质量比和调频比发生变化时附加非线性振子的双稳态电磁式振动能量捕获器的动力学响应.通过与附加线性振子双稳态系统的对比,获得了上述参数对附加非线性振子的双稳态电磁式振动能量捕获器发生大幅运动的影响规律,显示出附加非线性振子的双稳态电磁式振动能量捕获器的优越性,并获得了附加非线性振子的双稳态电磁式振动能量捕获器发生连续大幅混沌运动的最优参数配合.上述研究结果为双稳态电磁式振动能量捕获系统的相关研究提供了理论基础.     

用图像研究非线性迭代模型

用蛛网图、迭代函数图、周期分叉图以及分布直方图等几何图像研究了L og istic模型的迭代轨道,研究了非线性迭代轨道进入混沌状态的条件.     

带有同号截距和负斜率的一维不连续分段线性映射的边界碰撞分叉曲线

本文研究一维带有同号截距的分段线性映射动力系统的边界碰撞分叉问题.根据截距的位置关系,将问题分成两类,并采用Leonov方法来研究边界碰撞分叉曲线.另外确定了边界碰撞分叉曲线和flip分叉曲线所围成的周期区域.研究结果表明,当分段线性映射具有同号截距时,其具有非常丰富的周期结构.     

具有参数及受迫激励的二阶系统的次谐波与混沌解

具有受迫激励的二阶非线性振子由次谐波分叉导致混沌,已有许多文献讨论过。而具有脉冲非线性参数激励的二阶系统的次谐分叉现象曾由徐皆苏等作过系统讨论。本文则讨论在实际中更有价值的两种激励同时作用的二阶系统     

势阱深度对双稳态电磁发电系统发电性能的影响研究

电磁式振动能量捕获技术从单稳态系统发展到多稳态系统,拓宽了响应频带,增大了输出电压,能够获得较好的发电性能.以附加线性振子的双稳态电磁式振动能量捕获器为研究对象,主要研究了势阱深度对双稳态系统发电性能的影响,并基于最优发电性能下的势阱深度,研究了双稳态系统结构参数中质量比与调频比对系统发电性能的影响.通过数值仿真结果说明,在外部激励频率为低频时:势阱深度较大时,双稳态系统的振子只能在一个阱内发生小幅振动运动;当势阱深度小到一定程度时,双稳态系统的振子跨过势垒在两个阱间内发生大幅混沌运动或周期运动,其优于小幅振动运动时的平均输出功率.通过数值模拟,得到双稳态系统具有较高的发电性能下的最优质量比、调频比以及阻尼比参数.     

Three-parametric robot manipulators with parallel rotational axes

The paper deals with asymptotic motions of 3-parametric robot manipulators with parallel rotational axes. To describe them we use the theory of Lie groups and Lie algebras. An example of such motions are motions with the zero Coriolis accelerations. We will show that there are asymptotic motions with nonzero Coriolis accelerations. We introduce the notions of the Klein subspace, the Coriolis subspace and show their relation to asymptotic motions of robot manipulators. The asymptotic motions are introduced without explicit use of the Levi-Civita connection.     

On Optimum Propulsion by Means of Small Periodic Motions of a Rigid Profile II. Optimization of the Period and Numerical Results

We present some numerically calculated optimum thrust generating small amplitude periodic motions of a rigid profile in an inviscid imcompressible fluid. The motions considered consist in general of both a heaving and a pitching part and have common period. Apart from the prescribed thrust, the motions have to satisfy the demand that the contribution to the total thrust of the suction at the leading edge not exceed a given number and are furthermore subjected to a constraint on their amplitude. Solutions of an analogous optimization problem for pure heaving motions are also discussed. Furthermore, the problem of optimizing the period of the motions is considered.     

Periodic motions in a simplified brake system with a periodic excitation

In this paper, periodic motions for a simplified brake system under a periodical excitation are investigated, and the motion switchability on the discontinuous boundary is discussed through the theory of discontinuous dynamical systems. The onset and vanishing of periodic motions are discussed through the bifurcation and grazing analyses. Based on the discontinuous boundary, the switching planes and the basic mappings are introduced, and the mapping structures for periodic motions are developed. From the mapping structures, the periodic motions are analytically predicted and the corresponding local stability and bifurcation analysis is completed. Periodic motions will be illustrated for verification of analytical predictions. In addition, the relative force distributions along the displacement are illustrated for illustrations of the analytical conditions of motion switchability on the discontinuous boundary.     

Planetenbewegungen des Flaggenraumes

In [8] the author gave a report on some properties of flag space motions, especially of the composition of screw motions or rotations in flag space. Planet motions more generally are motions which can be composed by two one-parameter-groups. These motions are investigated with respect to their orbits, their multiple ways of construction and the tubular surfaces they can determine. Some of them yield tubular screw surfaces, some others move every sphere the way that it again envellopes a sphere. These motions, which have no Euclidean counterpart, determine non-trivial, kinematically generated LIE-transformations in flag space.     

Some features of the deceleration of an inhomogeneous ball in the air

A model of the deceleration of an inhomogeneous ball acted upon by the drag of the air is discussed, taking into account the interaction of the translational and rotational motions. The problem is reduced to analysing a non-linear second-order dynamical system. The steady motions of the ball, including self-oscillatory and self-rotation motions, are obtained. The bifurcation values of the parameters defining these motions are determined. The corresponding phase portraits are constructed and an interesting interpretation of them is given.     

The orbital stability of periodic motions of a Hamiltonian system with two degrees of freedom in the case of 3:1 resonance

The problem of the orbital stability of periodic motions, produced from an equilibrium position of an autonomous Hamiltonian system with two degrees of freedom is considered. The Hamiltonian function is assumed to be analytic and alternating in a certain neighbourhood of the equilibrium position, the eigenvalues of the matrix of the linearized system are pure imaginary, and the frequencies of the linear oscillations satisfy a 3:1 ratio. The problem of the orbital stability of periodic motions is solved in a rigorous non-linear formulation. It is shown that short-period motions are orbitally stable with the sole exception of the case corresponding to bifurcation of short-period and long-period motions. In this particular case there is an unstable short-period orbit. It is established that, if the equilibrium position is stable, then, depending on the values of the system parameters, there is only one family of orbitally stable long-period motions, or two families of orbitally stable and one family of unstable long-period motions. If the equilibrium position is unstable, there is only one family of unstable long-period motions or one family of orbitally stable and two families of unstable long-period motions. Special cases, corresponding to bifurcation of long-period motions or degeneration in the problem of stability, when an additional analysis is necessary, may be exceptions. The problem of the orbital stability of the periodic motions of a dynamically symmetrical satellite close to its steady rotation is considered as an application.     

Multiple bifurcation trees of period-1 motions to chaos in a periodically forced,time-delayed,hardening Duffing oscillator

In this paper, bifurcation trees of periodic motions in a periodically forced, time-delayed, hardening Duffing oscillator are analytically predicted by a semi-analytical method. Such a semi-analytical method is based on the differential equation discretization of the time-delayed, nonlinear dynamical system. Bifurcation trees for the stable and unstable solutions of periodic motions to chaos in such a time-delayed, Duffing oscillator are achieved analytically. From the finite discrete Fourier series, harmonic frequency-amplitude curves for stable and unstable solutions of period-1 to period-4 motions are developed for a better understanding of quantity levels, singularity and catastrophes of harmonic amplitudes in the frequency domain. From the analytical prediction, numerical results of periodic motions in the time-delayed, hardening Duffing oscillator are completed. Through the numerical illustrations, the complexity and asymmetry of period-1 motions to chaos in nonlinear dynamical systems are strongly dependent on the distributions and quantity levels of harmonic amplitudes. With the quantity level increases of specific harmonic amplitudes, effects of the corresponding harmonics on the periodic motions become strong, and the certain complexity and asymmetry of periodic motion and chaos can be identified through harmonic amplitudes with higher quantity levels.     

C-半群的渐近概周期运动

讨论了Banach空间上C-半群的渐近概周期（AAP）运动,给出C-半群的渐近概周期运动的若干等价条件,进而得到C-半群的弱渐近概周期（WAAP）运动的等价条件.     

Dynamics of a model of two delay-coupled relaxation oscillators

This paper investigates the dynamics of a new model of two coupled relaxation oscillators. The model replaces the usual DDE (differential-delay equation) formulation with a discrete-time approach with jumps. Existence, bifurcation and stability of in-phase periodic motions is studied. Simple periodic motions, which involve exactly two jumps per period, are found to have large plateaus in parameter space. These plateaus are separated by regions of complicated dynamics, reminiscent of the Devil’s Staircase. Stability of motions in the in-phase manifold are contrasted with stability of motions in the full phase space.     

Sliding and transversal motions on an inclined boundary in a periodically forced discontinuous system

In this paper, sliding and transversal motions on the boundary in the periodically driven, discontinuous dynamical system is investigated. The simple inclined straight line boundary in phase space is considered as a control law for such a dynamical system to switch. The normal vector field for a flow switching on the separation boundary is adopted to develop the analytical conditions, and the corresponding transversality conditions of a flow to the boundary are obtained. The conditions of sliding and grazing flows to the separation boundary are presented as well. Using mapping structures, periodic motions of such a discontinuous system are predicted, and the corresponding local stability and bifurcation analysis of the periodic motion are carried out. Numerical illustrations of periodic motions with and without sliding on the boundary are given. The local stability analysis cannot provide the proper prediction of the sliding and grazing motions in discontinuous dynamical systems. Therefore, the normal vector fields of periodic flows are presented, and the normal vector fields on the switching boundary points give the analytical criteria for sliding and transversality of motions.