一类大气非线性动力热力学反应-扩散系统解的稳定性态

研究了一类大气非线性系统. 利用大气非线性热力动力学理论, 讨论了大气非线性强迫耗散系统的速度、温度和湿度所满足的非线性反应-扩散系统, 再利用微分方程Lyapunov稳定性理论, 得到了大气非线性反应-扩散系统在均匀定态解邻域内的微扰解. 最后由系统的控制参数的变化, 得到了大气非线性强迫耗散系统有关的物理量的有序-无序-有序状态的转化过程, 从而可以预报和预测相应的局部大气非线性强迫耗散系统的稳定性态.     

弹簧螺旋摆系统非线性振动的理论研究

运用牛顿第二运动定律对弹簧螺旋摆系统建立了模型方程,该方程为一组非线性微分方程,表明该系统具有复杂的非线性特征.理论分析表明,当系统固有的振动频率和摆动频率之比为2时,自由振动的弹簧螺旋摆系统存在内共振现象,数值求解结果证实了这一结论.并认为在一般情况下,弹簧螺旋摆系统的自由振动可能是准周期的.     

一种光电载荷非线性隔振装置的研究

针对光电载荷对隔振性能的需求,提出一种采用菱形连杆机构作为负刚度组件,具有高静、低动刚度特点的非线性隔振器（简称菱形HSLDS隔振器）。采用静力学分析方法,建立了隔振器数学模型,研究了刚度参数设定以及非线性调节方法;利用谐波平衡法（HBM）求解动力学方程,分析了各参数对隔振性能的影响关系;采用动力学仿真软件ADAMS及实物样机对理论模型与结论进行了验证。测试结果表明:菱形HSLDS隔振器具有较方便的参数调整能力,零位刚度及刚度非线性可通过拉簧参数与连杆参数进行设定、优化,隔振的刚度非线性优化程度受主隔振器阻尼以及零位刚度参数影响。相比于传统线性隔振器,菱形HSLDS具有显著的非线性隔振优势,可较好地满足光电载荷隔振需求。     

Universality and hysteretic dynamics in rapid fracture

Experiments in the dynamic fracture of brittle polyacrylamide gels show that a single-crack state undergoes a hysteretic transition to the microbranching instability with a characteristic activation time. Quantitative measurements also indicate that features such as crack front inertia, self-focusing of microbranches, and the appearance of front waves are universal attributes of dynamic fracture.     

垂直振动激发下颗粒物质的能量耗散

本文对垂直振动激发下的铜和玻璃珠两种密集颗粒样品,通过实时测量样品盒的加速度和振台对它的作用力,研究了样品的平均耗散功率.实验发现该耗散功率在给定振动强度下随振动频率的变化曲线是一个峰值在几十赫兹的宽峰结构,在给定频率下随强度的变化具有幂率规律,其幂值小于简谐受迫振动模型的幂值2.这些结果将有助于研究测定颗粒流体和气体的迁移系数,以及它们在不同运动模式下的能耗差异.     

Coarsening dynamics of striped patterns in thin granular layers under vertical vibration

The process of pattern formation in granular layers was experimentally studied. Ten layers of granular materials inside a vacuum container were placed under a vertical vibration of A sin2pi f t. Control parameters were the dimensionless acceleration Gamma = A(2pi f)(2)/g and vibration frequency f. When the system was quenched from a flat pattern state to a striped pattern state by instantly increasing Gamma, there were more than 10(4) periods before a full steady striped pattern appeared. This nonequilibrium and nonsteady process showed dynamic scaling behavior. The growth exponent of the characteristic length scale of the ordered domain was 0.25, which agrees with that of the Swift-Hohenberg system.     

一类时变非线性振动系统的同步控制方法

对于一类非自治的非线性振动系统，设计了控制方法并建立了相应的派生系统，使得派生系统能与原系统达到同步.利用Lyapunov稳定性理论证明了两个系统在一定条件下可以达到同步，给出了耦合参数的选择条件.对于含参数激励与强迫激励的Mathieu方程以及拟周期激励的Duffing方程进行了实际的仿真计算，证明了派生系统可以与原系统的拟周期、混沌运动快速实现同步. 关键词： 派生系统 同步 差别方程     

Influence of the diffusion current on the hysteretic behavior in the system of coupled Josephson junctions

The detailed investigation of the phase dynamics and the I–V curves in the system of coupled Josephson junctions have been carried out. The superconducting, quasiparticle, diffusion, and displacement currents have been calculated as functions of the total current through the system. The role of the diffusion current in the formation of the I–V curves has been studied and the influence of this quantity on the I–V curve branching and the magnitude of the return current has been revealed. The calculation results agree qualitatively with the experimental data.     

Modelling the vertical grating-waveguide coupler for the description of its nonlinear symmetry-breaking dynamics

We propose a new scheme to observe the symmetry-breaking dynamics of two counter-propagating beams in a Kerr-type nonlinear waveguide coupler. Using a grating to couple light at normal incidence upon the waveguide allows for a single-beam geometry. The ability of the grating to couple light symmetrically is demonstrated on the basis of a linear coupled-mode approach especially adapted to vertical coupling. The nonlinear symmetry-breaking dynamics is studied analytically.     

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     

Research on performance indices of vibration isolation system

Power flow transmissibility is proposed as a performance index to evaluate the performance of isolation system. It is defined as the ratio of the power flow input into the equipment and the power flow transmitted into the receiver. Based on a simple vibration isolation system, its relationship with other performance indices is given by theoretical and numerical analysis. The results show that power flow transmissibility can reflect the response characteristics of the whole isolation system effectively. In addition, power flow transmissibility can be estimated easily according to vibration acceleration level difference and does not involve the measurement of power flow. Furthermore, the influences of several parameters such as the damping, loss factor and stiffness of isolator on power flow transmissibility are analyzed.     

基于迟滞应力应变关系的非线性声学检测理论与方法研究

本文将传统PM(Preisach-Mayergoyz)模型由一维介质拓展到二维介质,引入迟滞细观弹性单元概念,得到迟滞变化的应力应变关系.并采用一阶有限差分方程进行了声场计算和分析,发现空间声场中含有明显的高阶奇次谐波成分.对接收到的全波信号进行滤波、放大、时间反转后加载到接收换能器对应阵元上再进行发射,观察到高次谐波在微损伤区域实现聚焦.这为利用非线性高次谐波检测微损伤提供了可能的途径,也为疲劳损伤等缺陷的早期检测提供了理论和方法依据.     

Some comments on nonlinear dynamics

I summarize here the remarks made at the closing of the Conference and Research Workshop: Perspectives on Nonlinear Dynamics, held in Trieste in July 2007.      

A perspective on nonlinear dynamics

We present a brief report on the conference, a summary of the proceedings, and a discussion on the field of nonlinear science studies and its current frontiers.     

Two-dimensional front dynamics and spatial solitons in a nonlinear optical system

Two-dimensional fronts and coarsening dynamics with a t{1/2} power law are analyzed experimentally and theoretically in a nonlinear optical system of a sodium vapor cell with single-mirror feedback. Modifications of the t{1/2} power law are observed in the vicinity of a modulational instability leading to the formation of spatial solitons of different sizes. The experimental and numerical observations give direct evidence for the locking of fronts as the mechanism of soliton formation. A phenomenological equation for the dynamics of the domain radius explains the observed behavior.     

基于MATLAB的非线性振动系统临界阻尼的研究

用MATLAB研究了非线性振动系统临界阻尼的性质,提出了非线性振动系统临界阻尼的计算公式和临界阻尼状态下系统的运动方程,并与数值解进行了比较.     

一个简单延迟非线性系统的动力学行为及混沌同步

分析一个简单二阶延迟系统的Hopf分支和混沌特性, 包括分支点、分支方向和分支周期解的稳定性, 解析求出退延迟情况下, 这个系统的相轨线方程; 通过数值计算并绘制分岔图, 揭示系统存在由倍周期通向混沌的道路; 利用单路线性组合信号, 反馈控制实现系统的部分完全同步; 利用主动-被动与线性反馈的联合, 实现系统的完全同步; 设计和搭建系统的电子实验线路, 并从实验中观测到与理论分析或数值计算相一致的结果. 关键词： 延迟非线性系统 电路实验 Hopf分支 混沌     

热超声键合换能系统动力学特性的非线性检验

根据实际超声换能系统的振动测试，提出了热超声键合换能系统动力学特性的非线性检验方法，利用基于相空间重构的替代数据法，通过对换能杆末端的实测数据进行正确替代，并用非线性动力学的理论来检验其是否具有非线性.通过实验对超声换能杆末端轴向、俯仰、横向的振动时间序列的关联维数进行了准确的计算，从而清晰地描述了上述三个方向的动力学特性.所提出的方法有利于更好地认识超声键合换能系统，为建立更加合理的非线性动力学模型奠定良好的理论基础，有很好的应用价值. 关键词： 超声键合 时间序列 相位随机化 替代数据