相对论Birkhoff系统的平衡稳定性

研究相对论Birkhoff系统的平衡稳定性.给出相对论Birkhoff自治系统、半自治系统和非自治系统的平衡方程、受扰运动方程和一次近似方程;给出判定平衡稳定性的一次近似方法及其判据;讨论相对论Birkhoff系统平衡稳定性和经典Birkhoff系统平衡稳定性的关系.给出实例以说明方法的应用 关键词： 相对论 Birkhoff系统 平衡稳定性 一次近似方法     

中国古籍中的初态敏感性和混沌

本文收集《尚书》、《礼记》、《汉书》、《指月录》、苏轼诗等古籍中关于初态敏感性的形象描述,还列举了《庄子》、《白虎通》、《五灯会元》等古籍中出现的混沌一词.     

超临界轴向运动梁横向非线性振动频域分析

数值方法研究超临界速度下轴向运动梁横向非线性振动前两阶固有频率.通过对非平凡平衡位形做坐标变换,建立超临界轴向运动梁的标准控制方程,一个积分-偏微分非线性方程.利用有限差分法数值离散梁两端简支边界下控制方程,计算轴向运动梁中点的横向振动位移,并将计算结果作为时间序列,运用离散傅立叶变换得到超临界轴向运动梁横向振动的频率...     

轴向加速运动黏弹性梁受迫振动中的混沌动力学

研究了黏弹性轴向运动梁在外部激励和参数激励共同作用下横向振动的混沌非线性动力学行为. 引入有限支撑刚度, 并考虑黏弹性本构关系取物质导数, 同时计入由梁轴向加速度引起的沿径向变化的轴力, 建立轴向运动黏弹性梁横向非线性振动的偏微分-积分模型. 通过Galerkin截断方法研究了外部激励的频率和因速度简谐脉动引起的参数激励的频率在不可通约关系时轴向运动连续体的非线性动力学行为, 并对不同截断阶数的数值预测进行了对比. 基于对控制方程的Galerkin截断, 得到离散化的常微分方程组, 使用四阶Runge-Kutta方法求解. 基于此数值解, 运用非线性动力学时间序列分析方法, 通过Poincaré 映射, 观察到轴向运动梁随扰动速度幅值的倍周期分岔现象, 并比较了有无外部激励对倍周期分岔的影响. 分别在低速以及近临界高速运动状态下, 从相平面图、Poincaré 映射以及频谱分析的角度识别了系统中存在的准周期运动形态. 关键词： 轴向运动梁 非线性 混沌 分岔     

Synchronization of spatiotemporal chaos in complex networks via backstepping

A backstepping approach is proposed for the synchronization of chain networks of multi-spatiotemporal chaotic systems with topologically equivalent structures. The synchronization of multi-spatiotemporal chaotic systems is implemented by adding the control only to a terminal node, and the controller is designed via a corresponding update law. The control law is applied to spatiotemporal Gray-Scott systems. Numerical results demonstrate the effectiveness and the feasibility of the proposed approach.     

Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices

In this paper,Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated.Firstly,the equations of motion of discrete nonholonomic systems are introduced for regular and irregular lattices.Secondly,for cases of the two lattices,based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates,we present the quasi-extremal equation,the discrete analogues of Noether identity,Noether theorems,and the Noether conservation laws of the systems.Thirdly,in cases of the two lattices,we study the Mei symmetry in which we give the discrete analogues of the criterion,the theorem,and the conservative laws of Mei symmetry for the systems.Finally,an example is discussed for the application of the results.     

Application of canonical coordinates for solving single-freedom constraint mechanical systems

This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conserva-tive and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this re-lation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.     

车路耦合非线性振动高阶Galerkin截断研究

将移动车辆模型化为运动的两自由度质量-弹簧-阻尼系统,道路模型化为立方非线性黏弹性地基上的弹性梁,并将路面不平度设定为简谐函数．通过受力分析,建立车路非线性耦合振动高阶偏微分方程．采用高阶Galerkin截断结合数值方法求解耦合系统的动态响应．首次研究不同截断阶数对车路耦合非线性振动动态响应的影响,确定Galerkin截断研究车路耦合振动的收敛性．研究结果表明,对于软土地基的沥青路面,耦合振动的动态响应,需要150阶以上的截断才能达到收敛效果．并通过高阶收敛的Galerkin截断研究了系统参数对车路耦合非线性振动动态响应的影响.     

Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition

One of the important issues in the system identification and the spectrum analysis is the frequency resolution, i.e., the capability of distinguishing between two or more closely spaced frequency components. In the modal identification by the empirical mode decomposition (EMD) method, because of the separating capability of the method, it is still a challenge to consistently and reliably identify the parameters of structures of which modes are not well separated. A new method is introduced to generate the intrinsic mode functions (IMFs) through the filtering algorithm based on the wavelet packet decomposition (GIFWPD). In this paper, it is demonstrated that the GIFWPD method alone has a good capability of separating close modes, even under the severe condition beyond the critical frequency ratio limit which makes it impossible to separate two closely spaced harmonics by the EMD method. However, the GIFWPD-only based method is impelled to use a very fine sampling frequency with consequent prohibitive computational costs. Therefore, in order to decrease the computational load by reducing the amount of samples and improve the effectiveness of separation by increasing the frequency ratio, the present paper uses a combination of the complex envelope displacement analysis (CEDA) and the GIFWPD method. For the validation, two examples from the previous works are taken to show the results obtained by the GIFWPD-only based method and by combining the CEDA with the GIFWPD method.     

《理论力学Ⅰ,Ⅱ》评介

评介梅凤翔和尚玫编著《理论力学Ⅰ,Ⅱ》.首先概括该书4篇共22章的主要内容.然后分析该书的主要特点,具体包括专题性内容覆盖一些通常不在本科生教材中出现的知识,对基本内容的处理有独到之处,历史背景资料充分翔实等.