非解析径向轴承支承转子系统非线性动力特性分析

Nomenclaturex,y,x ·, y·-displacement and velocity of rotor-x,-y,x-·,-y·-displacement and velocity of rotor , di mension less¨x,¨y-acceleration of rotor¨-x,¨-y-acceleration of rotor ,di mensionlessω-rotating speed of rotor-ω-rotating speed of rotor ,di mensionlessx,y,z-Cartesian coordinates-x,-y,-z-Cartesian coordinates ,di mensionless2m-mass of rotorg-acceleration of gravityG-weight of rotor ,di mensionlesse=e2x e2y-mass eccentricity of rotorex,ey-mass eccentricity of rotor in thexan…     

变推力作用下的柔性旋转飞行器动力学建模

The dynamic response of a flexible spinning vehicle with the varying thrust was investigated. The varying thrustwas modeled as a series of simple harmonic components superimposed on a constant thrust. The analytical solutions forlongitudinal motion were obtained by combining the motion equations and boundary conditions, and then, the transversebending of rocket was examined solved by considering a coupled forcing vibration with varying parameters. Numericalsolutions for a rocket with end-varying thrust were studied. It is shown that the lateral vibrations and motion attitudes ofrocket depend on the frequencies of varying thrust to great extent, and an important phenomenon, beating, maybe take place.The proposed approach is more accurate and efficient in comparison to those standard numerical techniques.     

柔性转轴动力学分析与拍振现象

In this paper,the intrinsic behavior of rotating Euler-Benoulli flexible shafts was studied due to coupled bending and torsional vibratuions,the equations of motion of the shaft with unbalanced eccentricity and visous material damping were derived by the Hamilton principle.The numerical solution was obtained using the perturbation approach and mode-assuming method.The influences of the coupled vibrations between the benging and torsion.the rotaing speed,material damping and the slenderness ratio of the shaft were analyzed.It is clearly shown that the beating phenomena can occur when the interaction of torsion and flexure is considered.     

非线性方程孤子-混沌双解的物理意义,泛量子理论和非线性数学的某些应用

某些非线性方程中存在混沌-孤子双解,其具有波粒二象性等物理意义.然后探讨了孤子的量子理论,一方面发展孤子理论为量子化的;另一方面用孤子方法量子化.量子孤子化就对应泛量子理论.最后讨论非线性数学的某些应用.非线性数学是演化、相变等必不可少的条件.数学和物理、化学、天文、生物等的非线性应该共同发展.     

一类带有Newman边界条件的非线性抛物方程的解的爆破和整体存在

通过构造辅助函数和利用最大值原理,得到了非线性抛物方程(g(u))t=▽.(a(u)b(x)c(t)▽u)+h(t)f(u)的解的爆破和整体存在的充分条件,给出了爆破时间的上界和爆破速率的上估计以及整体存在解的上估计.     

一类具有非线性发生率的时滞病毒模型Hopf分支

研究了一类具有Beddington-DeAngelis非线性发生率的时滞病毒动力学模型。以时滞为参数,研究了模型的Hopf分支,得到时滞病毒模型的局部稳定性和产生局部Hopf分支的充分条件。最后,给出仿真实例,验证了理论分析结果的正确性。     

存在轴承径向游隙的三自由度齿轮动力学混沌与分叉研究

综合考虑齿轮时变啮合刚度、齿面间隙、轴承游隙和啮合综合误差等多种非线性因素影响,建立三自由度直齿轮振动模型,并对模型进行无量纲化处理。采用4阶变步长Runge－Kutta法对齿轮模型微分方程进行求解,得到齿轮在轴承径向游隙变化时运动的分岔图、相图和Poincaré映射图。发现随着轴承游隙的变小,系统响应也经历了从混沌态到稳态再到混沌态的历程,其中发生了倍周期分岔的现象。给出了系统的分岔值,得到了系统混沌形成的过程。     

Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control

We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.