一类非完整系统的全局镇定

当非完整系统只能局部转换为链式形式时, 由于存在变换奇异点集合, 针对链式系统所设计的全局反馈控制律只能局部镇定原非完整系统, 而且当期望状态接近奇异点时, 闭环系统的吸引区很小. 本文针对一类可局部转换为链式系统的非完整系统, 首先利用吸引区是状态空间中的一个不变集且与变换奇异点集不相交的条件导出了一个吸引区的不变子集, 然后给出了将系统状态从任意点驱动到吸引区不变子集内的开环控制算法, 最后结合开环控制和闭环控制得到一种混合控制算法. 该混合控制算法可以保证任意不在变换奇异点集合内的期望状态是全局渐近稳定的. 对平面两转动关节空间机器人的仿真结果证实了算法的有效性.     

基于小波模极大值的信号奇异性检测

小波分析近乎完美的数学特性受到各领域科学家和工程技术人员的青睐.文中讨论了基于小波模极大值的信号奇异性检测方法,该方法突破了傅立叶分析在时域和频域方面的局部化能力,信号的局部正则性可由其小波变换模随尺度参数的衰减特性来刻画,通过确定小波变换在细尺度下的局部模极大值来检测信号奇异性.实验表明,该方法能有效的、实用的.     

连续复小波变换在工程检测数据处理中的应用

通过对基桩检测信号进行多尺度一维连续复小波分解，得到局部模极大值线（local maximum line），计算模极大值线对应位置的Lipschitz指数值，从而综合判断信号的奇异点位置．由信号的奇异点位置很容易确定入射波、缺陷反射波、桩底反射波位置．这种分析方法可以实现对反射波测试数据更为灵活精细的分析，消除了由实测信号直接判读反射波到达时刻存在的潜在错误．最后给出了实测桩端部响应信号的分析实例，结果表明：复小波变换判断有效桩长和缺陷位置比实小波变换具有更好的精度．     

平面铰链五杆机构的奇异性研究

推导了平面铰链五杆机构的雅可比矩阵,得出机构处于奇异位置时的姿态,并给出了避免五杆机构奇异的方法:当五杆机构雅可比矩阵的行列式det(J)=0时,可使规划的轨迹远离工作空间的边界,避免该种奇异;当五杆机构雅可比矩阵的行列式det(J)→∞时,可选择合适的机构尺寸、合适的机构位姿形式或使规划的轨迹不通过奇异轨迹避免机构奇异.开发了五杆机构奇异轨迹的仿真软件,为五杆机构的设计提供了依据.     

啁啾对双曲正割脉冲光束空间强度分布的影响

从傍轴波动方程出发,给出了啁啾双曲正割脉冲光束在自由空间中的传输方程,研究了啁啾对双曲正割脉冲光束空间强度分布的影响。结果表明,在初始位置初始时刻啁啾对双曲正割脉冲光束空间强度的分布没有任何影响,但会影响脉冲前后沿的空间强度分布。当双曲正割脉冲光束传输以后,啁啾对双曲正割脉冲光束空间强度的分布影响很大,只要啁啾系数足够大,对于脉冲宽度大于一个甚至是几十个光波振荡周期的双曲正割脉冲光束同样存在空间奇异性。啁啾系数的大小和符号对双曲正割脉冲光束空间强度的分布有不同的影响。     

Increase of stress intensity near interface edge of elastic-creep Bi-material under a sustained load

The transition from small-scale creep to large-scale creep ahead of a crack tip or an interface edge with strong elastic stress singularity at the loading instant causes stress relaxation and the decrease of stress intensity in general. However, this study shows that the stress near the interface edge of bi-material with no or weak elastic stress singularity increases after the loading instant and brings about the stress concentration during the transition. In addition, the creep strain distribution of this bi-material after the loading instant is different from that occurred in the transition of an interface edge with strong elastic stress singularity or a crack tip (notch root). The criterion for the increase or decrease of stress intensity near the interface edge proved by the finite element method is proposed in this study. The stress intensity near the interface edge increases when the elastic stress singularity is lower than the creep stress singularity (λ^el < λ^cr) and vice versa.     

Analysis of Bimaterial Wedges Using a New Singular Finite Element

This paper is concerned with the singular stress field at the vertex of a bimaterial wedge under in-plane loading. The boundary value problem is initially formulated in terms of the complex function method. The eigenequations are obtained using the continuity conditions along the interface and the traction-free conditions along the free edges, leading to the development of explicit expressions for the singular stress and displacement fields for a general bimaterial wedge. These expressions are then used to develop a new singular finite element. This element enables the determination of the singular stress field and the associated stress intensity factors reliably and efficiently. To establish the validity of the method, test cases are examined and compared with existing solutions. The method is then applied to evaluate the effect of the wedge geometry and the elastic mismatch upon the resulting stress intensity factors.     

Orbit systematics in anisotropic Kepler problem

We revisit the Anisotropic Kepler Problem (AKP), which concerns with trajectories of an electron with anisotropic mass term in a Coulomb field. This is one of the most fundamental fields in Quantum Chaos. Nowadays various quantum systems are challenging us. Classical theories of these may have chaos. Quantum mechanics have developed from integrable cases and may have to be reformulated for such cases. AKP then serves as a suitable testing ground for quantum chaos. We first review a pioneering work by Martin Gutzwiller (J Math Phys (1977) 18:106). We shall show the systematics of the trajectories using ample figures from an extensive numerical analysis. Then we focus on the rolê of hyperbolic singularities and we comment on the approximations in an analytic formulation. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Stress concentration analyses of bi-material bonded joints without in-plane stress singularities

The problem of stress concentration in bi-material bonded joint is investigated under the condition of without stress singularities. Disappearance conditions of stress singularity near interface corners and edges are determined based on analyses of eigenvalue equations. Straight-side and curved interface of materials are designed for the bi-material models to avoid singular stress fields around the interface corner and edge. Assuming that one stress component or combined stresses are responsible for failure at or near the interface, the stress concentration becomes critical for the design of bi-material joints with higher interfacial strength. Numerical results show that the stress state near the interface depends strongly on both the interface geometry and the combination of materials, and stress concentration may always occurs at or near the interface. Emphasis is placed on the necessity for geometric optimization of an interface in order to design singularity-free junction with higher interfacial strength.     

基于小波变换的某重力拱坝背水坡转异裂缝序列的分析

裂缝转异诊断对分析大坝安全稳定运行有重要意义。将小波变换应用于大坝裂缝转异分析中,并结合某重力拱坝背水坡裂缝X18-1的实测数据,分别从小波系数图的过零点和极值点、多尺度下模极大值线及奇异性变化角度讨论其与裂缝转异时刻的关系,最终综合判断出裂缝的转异时刻。分析结果表明,小波系数图、模极大值线和奇异性均可反映裂缝的转异,但各自独立的诊断结果不完全相同,综合分析可准确判定裂缝的转异时刻,为裂缝转异诊断提供了新思路。