Void formation and growth in a class of compressible solids

A new class of compressible elastic solids, which includes the Blatz-Ko material as a special case, is proposed. A closed-form solution is constructed and studied for a bifurcation problem modeling void formation in this class of compressible elastic solids. The relation between the void-formation condition and the material parameters is obtained analytically. An energy comparison of the void-formation deformation and the homogeneous expansion deformation is carried out.     

井眼剪切带分叉研究

井眼基本破坏形式是由于不稳定性造成的井眼岩石崩落坍塌和剪切带。井眼破坏的非均匀性采用传统的理论和方法不能得到较好的解释和预测。采用材料的分叉分析方法和变形局部化的数值模拟研究 ,可望对井眼失效的机理分析、预测和控制提供新的思路     

Chaos in parametric resonance flow at water-mercury interface

In the electrochemical system with liquid-liquid interface, intense local convections by the resonance with potential pulses take place. Therefore, with laser beam scattering, temporal movement of the water-mercury interface was observed. As a result, the scattering efficiency showed non-linear oscillation.

Such non-linear response could be controlled by potential pulse height. As the potential height was increased, new scattering peaks in the oscillation emerged, which was expected of a kind of bifurcation phenomenon. From these results, phase portrait, Poincarè section, correlation dimension of the strange attractor and the largest Lyapunov exponent of the trajectories were obtained. Consequently, it was concluded that all the parameters indicate chaotic behavior of the resonance flow.     

对称双弹簧振子系统的横振动的主共振与分岔

采用渐进法求近似解并用四阶Runge-Kutta法求数值解进行验证,分析和讨论了对称双弹簧振子受迫横振动周期解的多值性和振幅跳跃现象;绘制系统的分岔图研究系统拓扑结构随参数f0的变化,分析系统进入混沌的道路。结合对系统的Lyapunov指数、相轨图及Poincare映射的分析验证了上述结论,最后给出了系统的Lyapunov维数谱。     

Jeffcott转子系统分岔点预测

首先简述了一种用于转子轴承系统的稳定性量化分析方法,即首先利用数值积分对高维非线性转子系统进行解耦,将Rn轨线映射为一系列R1映像轨线,然后在R1观察空间中定义轨线的稳定裕度,根据轨线稳定裕度利用灵敏度技术预测动力系统的分岔点。最后,对一个单跨转子模型试验台建立了动力学方程,并利用上述方法通过2个算例预测了系统发生分岔的参数值和分岔特性。预测结果与直接数值积分法在庞加莱截面得到的分岔参数值基本一致,但由于该方法利用了灵敏度技术,所以其分岔点的搜索过程比直接数值积分法中的试探法要快得多。     

线性时滞状态反馈下Stuart-Landau系统的多周期解

对一个stuart-landau系统引入时滞状态反馈,研究时滞对非线性系统动力行为的影响。发现时滞可使系统出现周期振动,与无时滞系统不同之处在于有多个周期吸引子共存的现象。从理论上预测由时滞导致的动力学行为,得到周期解的解析形式。随着时滞量的变化,周期解个数及其稳定性发生变化。并通过对比周期解的数值解和解析解,数值验证多周期吸引子共存的现象。这些结果对控制系统的振动和系统同步等有着潜在的应用价值。     

端部约束悬臂输流管道的非线性动力学特性

针对悬臂端受线性弹簧支承和扭转弹簧约束的约束悬臂输流管道,采用分岔图、相平面图、Poincare截面和Lyapunov指数等非线性振动的数值仿真方法,研究其在自激-参数激励-外激励联合激励作用下的非线性动力学特性,分析系统出现周期和混沌运动响应的参数条件,揭示其通向混沌的途径,探寻各参数对输流管道振动特性的影响规律和各参数之间的相互制约关系.数值仿真结果表明,管道系统随质量比、端部约束刚度和管道粘弹性系数的不同,分别呈现周期、概周期、阵发性和混沌运动多种响应形式,系统通过倍周期分岔或阵发性进入混沌,通过倍周期倒分岔脱离混沌.     

Y型分叉冠状动脉血管中血液流动对血栓形成的影响

为研究Y型分叉血管中血液流动对血栓形成的影响,根据黏性流体稳定流动的Navier-Stokes方程,建立了冠状动脉分叉血管中血液流动的数学模型,并采用计算流体力学(computational fluid dynamics,CFD)的方法,数值模拟了不同Y型分叉冠状动脉血管中血液流动情况,并考虑了分叉角度、血液黏度、入口血流初始速度对血流速度场、壁面剪应力、壁面压强的影响.结果表明:分叉角度越小成栓可能性越大,存在最易成栓的血流速度,但血液黏度对血柱形成的影响不大.     

Bifurcation analysis for an SMIB power system with series capacitor compensation associated with sub-synchronous resonance

In this paper,an introduction to the bifurcation theory and its applicability to the study of sub-synchronous resonance (SSR) phenomenon in power system are presented. The continuation and bifurcation analysis software AUTO97 is adopted to investigate SSR for a single-machine-infinite-bus power system with series capacitor compensation. The investigation results show that SSR is the result of unstable limit cycle after bifurcation. When the system exhibits SSR, some complex periodical orbit bifurcations, such as torus bifurcation and periodical fold bifurcation, may happen with the variation of limit cycle. Furthermore, the initial operation condition may greatly influence the ultimate state of the system. The time-domain simulation is carried out to verify the effectiveness of the results obtained from the bifurcation analysis.     

A perturbation-incremental scheme for studying Hopf bifurcation in delayed differential systems

A new method, called perturbation-incremental scheme (PIS), is presented to investigate the periodic solution derived from Hopf bifurcation due to time delay in a system of first-order delayed differential equations. The method is summarized as three steps, namely linear analysis at critical value, perturba- tion and increment for continuation. The PIS can bypass and avoid the tedious calculation of the center manifold reduction (CMR) and normal form. Meanwhile, the PIS not only inherits the advantages of t...