一类Cohen-Grossberg型BAM脉冲神经网络周期解的存在性和全局指数稳定性

利用Lyapunov泛函、不等式方法及Poincaré映射,建立了一类具有混合时滞的Cohen-Grossberg型BAM脉冲神经网络周期解的存在性和全局指数稳定性的充分性判据。     

转子—非圆轴承系统非线性动力学行为的研究

非线性油膜力数据库方法获得非圆滑动轴承的非线性油膜力,利用 Runge-Kutta法、Poincaré映射和频谱图对刚性 Jeffcott转子—椭圆轴承系统在较宽参数范围内的分叉和非线性动力学行为进行研究。得到了系统在某些参数域的分叉图、时间历程、频谱图、相图、Poincaré映射图。研究结果表明:在特定参数范围内系统存在倍周期分叉、Hopf分叉、解的跳跃、K-T周期解、概周期运动和混沌运动等非线性动力学行为。      

一类中立型高维周期微分系统的周期解

文中利用指数型二分法,结合不动点定理考虑如下形式的中立型高维周期系统: 苦d/dt[x(t)+cx1]=A(t,x(t))x(t)+f(t,x1),得到其T-周期解存在的充分性条件,所得结论改进或推广了早先文献中周期解存在的相应结论。     

一类变系数混合时滞细胞神经网络周期解的存在性和全局指数稳定性

应用Mawhin连续性定理和不等式方法,给出了一类变系数混合时滞细胞神经网络周期解存在和指数稳定的充分条件。该结论对神经网络的设计具有重要的参考价值。     

时滞BAM神经网络周期解的存在唯一性

研究了一类具有变系数及状态依赖时滞或分布时滞的BAM神经网络模型的周期解存在唯一性问题,利用不动点定理获得了周期解的存在唯一性条件,并应用数例说明结论的有效性。     

两端固支输流管的稳定性和混沌运动分析

本文详细讨论了两端固支输流管在其支承简谐运动激励下的稳定性及混沌运动,推导了管道运动方程,运用相平面图,Lyapunov指数,Poincare映射以及运动时间历程等分析手段重点考察了系统参数u(流体流速）和n(激振频率）变化对管道运动的影响,结果表明,在所研究的系统中存在发生混沌运动的参数区域,而且发现有3条通向混沌运动的途径,即：（1）周期倍化;（2）间歇阵发混沌;（3）概周期运动。     

考虑中介轴承波纹度的双转子系统的非线性振动

针对考虑中介轴承波纹度的双转子模型,应用转子动力学理论和拉格朗日方程建立系统的运动方程,采用数值方法求得系统的非线性振动响应,并分析了转速、波纹度最大幅值、波纹度波数和波纹度初始幅值对系统动力学行为的影响规律.结果表明:波纹度对高、低压转子动力学行为的影响规律基本一致,随着转速的增加,高、低压转子的运动表现为周期运动与非周期运动交替变化,在较低转速区可能发生概周期及混沌运动.随着波纹度最大幅值的增大,系统可由周期运动演化为周期2运动、概周期运动及周期4运动,表明波纹度最大幅值增大时不利于系统的安全平稳.当波数为滚动体数的整数倍时,系统可能出现概周期及混沌等复杂非周期运动.随着波纹度初始幅值的增大,系统表现为概周期运动与混沌运动交替出现,但波纹度初始幅值相对较大时转子系统的振动幅值相对较小.      

高阶中立型无穷时滞微分方程的周期解

阐明了利用Fourier级数理论,研究高阶常系数中立型无穷时滞微分方程的周期解问题,获得了周期解存在性和唯一性的充分必要条件.     

一类具有分布时滞和离散时滞中立型积分微分方程周期解

考虑了具有分布和离散时滞的方程tt dd t x(t)(-)B(t,s)x(s)ds =C(t,s)x(s)ds +i=l(t,x(t -(t)))+b(t) ∫-∞ A(t,x(t))x(t)+ ∫-∞ ∑giτi周期解的存在性问题。文章通过利用线性系统的指数二分性和 Krasnoselskii不动点定理得到了1上述方程周期解存在唯一的充分条件,结论推广和改进了已有文献的结果,并通过一个例子说明该结果的优越性。     

非线性不平衡转子轴承系统周期解的预测

本文提出一种对非线性不平衡转子轴承系统周期解进行预测的新型算法,它利用系统周期解的稳态及瞬态信息,反解雅可比矩阵,实现对系统周期解的预测追踪,并利用反解得出的雅可比矩阵,求得系统周期解的Floquet乘子以判别其非线性稳定性。文中以刚性不平衡转子轴承系统为例,实现了周期解的预测追踪及非线性稳定性判别,说明了新算法的有效性。      

时滞细胞神经网络平衡点的全局指数稳定性研究

利用常数变易法和变量替换的方法，研究了具有时滞的细胞神经网络平衡点的奎局指数稳定性，给出了网络平衡点的全局指数稳定性的充分判据。     

Exponential Time-varying Sliding Mode Control for Large Angle Attitude Eigenaxis Maneuver of Rigid Spacecraft

An eigenaxis maneuver strategy with global robustness is studied for large angle attitude maneuver of rigid spacecraft. A sliding mode attitude control algorithm with an exponential time-varying sliding surface is designed, which guarantees the sliding mode occurrence at the beginning and eliminates the reaching phase of time-invariant sliding mode control. The proposed control law is global robust against matched external disturbances and system uncertainties, and ensures the eigenaxis rotation in the presence of disturbances and parametric uncertainties. The stability of the control law and the existence of global siding mode are proved by Lyapunov method. Furthermore, the system states can be fully predicted by the analytical solution of state equations, which indicates that the attitude error does not exhibit any overshoots and the system has a good dynamic response. A control torque command regulator is introduced to ensure the eigenaxis rotation under the actuator saturation. Finally, a numerical simulation is employed to illustrate the advantages of the proposed control law.     

电动力绳系周期解求解及稳定性控制

电动力绳系姿态摆动动力学方程具有非线性特点,且姿态摆动状态直接影响着空间任务能否正常进行。首先,基于哑铃模型及偶极子地磁场模型假设,推导了在倾斜圆轨道上运行的电动力绳系姿态动力学方程。其次,给出了利用摄动法和不动点迭代法相互配合的数值方法求解该非线性方程周期解的过程及解的稳定性判断准则,并针对不稳定周期解提出了相应的稳定性控制策略。最后,通过数值仿真分析,得到了姿态摆动运动的周期解图像,验证了周期解求解算法的有效性,并对不稳定周期解实现了稳定性控制。     

A multi-order method for predicting stability of a multi-delay milling system considering helix angle and run-out effects

In this paper, a multi-delay milling system considering helix angle and run-out effects is firstly established. An exponential cutting force model is used to model the interaction between a work-piece and a cutting tool, and a new approach is presented for accurately calibrating exponential cutting force coefficients and cutter run-out parameters. Furthermore, based on an implicit multi-step Adams formula and an improved precise time-integration algorithm, a novel stability prediction method is proposed to predict the stability of the system. The involved time delay term and periodic coefficient term are integrated as a comprehensive state term in the integral response which is approximated by the Adams formula. Then, a Floquet transition matrix with an arbitrary-order form is constructed by using a series of matrix multiplication, and the stability of the system is determined by the Floquet theory. Compared to classical semi-discretization methods and full-discretization methods, the developed method shows a good performance in convergence, efficiency, accuracy, and multi-order complexity. A series of cutting tests is further carried out to validate the practicability and effectiveness of the proposed method. The results show that the calibration process needs a time of less than 5 min, and the stability prediction method is effective.     

Linear stability analysis of interactions between mixing layer and boundary layer flows

The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed.The mixing layers include wake,shear layer and their combination.The mean velocity profile of confluent flow is taken as a superposition of a hyperbolic and exponential function to model a mixing layer and the Blasius similarity solution for a flat plate boundary layer.The stability equation of confluent flow was solved by using the global numerical method.The unstable modes associated with both the mixing and boundary layers were identified.They are the boundary layer mode,mixing layer mode 1 (nearly symmetrical mode) and mode 2 (nearly anti-symmetrical mode).The interactions between the mixing layer stability and the boundary layer stability were examined.As the mixing layer approaches the boundary layer,the neutral curves of the boundary layer mode move to the upper left,the resulting critical Reynolds number decreases,and the growth rate of the most unstable mode increases.The wall tends to stabilize the mixing layer modes at low frequency.In addition,the mode switching behavior of the relative level of the spatial growth rate between the mixing layer mode 1 and mode 2 with the velocity ratio is found to occur at low frequency.     

挤压油膜阻尼器-滑动轴承-转子系统非线性动力特性的数值分析及实验研究

 采用非线性模型,研究挤压油膜阻尼器 -滑动轴承 -转子系统的运动稳定性和分岔特性。利用有限元离散变分不等原理和基于线性规划余原理的迭代方法,求解自由边值条件下的油膜力。采用模态综合技术中的缩减系统线性自由度的方法,并提出基于 Newmark法的预估 -校正 -局部迭代的方法,求解系统响应。采用 Poincaré映射法,将周期解的确定转化为 Poincaré截面上不动点的确定,然后分析不动点的稳定性。最后通过实验转子,从实验与数值计算进行对比分析,验证了挤压油膜阻尼器的减振特性及其提高系统运动稳定性的特性,同时也说明了上述方法可以有效地分析这类系统的局部非线性动力特性。     

高机动性飞机大迎角全局稳定性研究

为了研究高机动性飞机大迎角时的全局稳定性,建立了飞机的非线性动力学方程和气动力模型。应用微分方程定性理论,通过对算例的分析,讨论了目前飞机设计中常用的稳定性判据(如(C_(nβ))_(dyn)和LCDP等)与平衡点处线化矩阵特征值之间的关系。结果表明这些判据可以从飞机在特定状态下的线化矩阵经简化得到。因此,它们只能预测大迎角的局部稳定性。若考虑全局稳定性则必须用本文所给的方法进行。最后,指出了平衡点和周期吸引子与机翼摇晃、偏离和尾旋之间的关系,并用时间过程作了验证。