On reachable set bounding for discrete-time switched nonlinear positive systems with mixed time-varying delays and disturbance

This paper addresses the reachable set bounding for discrete-time switched nonlinear positive systems with mixed time-varying delays and disturbance, which contains switched linear positive systems as a special case. By resorting to a new method that does not involve the common Lyapunov–Krasovskii functional one, explicit criteria to ensure any state trajectory of the system converges exponentially into a prescribed sphere are obtained under average dwell time switching. The results can then be extended to more general time-varying systems. Finally, two numerical examples are used to demonstrate the effectiveness of the obtained results.     

热力学数据对1, 3-丁二烯燃烧特性的影响

基于G4方法, 计算了1,^{3-丁二烯框架燃烧反应机理中102个物种的热力学数据, 并考察了振动非谐性、 频率校正因子以及受阻内转动对结果的影响. 结果表明, 考虑振动非谐性或采用不同的频率校正因子, 对热力学数据的影响不大; 考虑内转动后, 对热力学数据有较大影响. 而且考虑内转动后, 得到的热力学数据与实验热力学数据吻合得更好. 用所得热力学数据模拟了1,3-丁二烯的绝热燃烧温度以及点火延迟时间, 结果显示, 要得到可靠的绝热火焰温度, 对小分子(如CO和CO₂等)的热力学数据需要采用实验结果. 将用所得热力学数据模拟得到的点火延迟时间, 与机理本身的热力学数据所得点火延迟时间进行对比, 二者差别显著, 表明所得热力学数据主要通过改变一些反应的逆反应速率常数来影响点火延迟时间. 进一步确定了用所得热力学数据对点火延迟时间有显著影响的一些物种.}     

Dynamics of milling processes with variable time delays

A milling-process model with a variable time delay associated with each cutting tooth is presented in this article. The source of this variable time delay is the feed rate. The effect of the feed motion on the entry cutting angle, the exit cutting angle, and the amplitude of feed mark is also discussed. Loss-of-contact effects are also considered. The system dynamics is described by a set of delay differential equations with periodic coefficients and variable time delays. A semi-discretization scheme is presented for analyzing the stability of periodic orbits of this system. The analysis provides evidence of period-doubling bifurcations and secondary Hopf bifurcations. Good agreement is found between the numerical results obtained from this work and the results of related experimental studies.     

Measurement of energy release rate and energy flux of rapidly bifurcating crack in Homalite 100 and Araldite B by high-speed holographic microscopy

High-speed holographic microscopy is applied to take three successive photographs of fast propagating cracks in Homalite 100 or in Araldite B at the moment of bifurcation. Crack speed at bifurcation is about 540 m/s on Homalite 100, and about 450 m/s on Araldite B. From the photographs, crack speeds immediately before and after bifurcation are obtained, and it is found that discontinuous change of crack speed does not exist at the moment of bifurcation in the case of Homalite 100, but exists in the case of Araldite B. From the photographs, crack opening displacement (COD) is also measured along the cracks as a function of distance r from the crack tips. The measurement results show that the CODs are proportional to √r before bifurcation. After bifurcation, the CODs of mother cracks are proportional to √r, though the CODs of branch cracks are not always proportional to √r. The energy release rate is obtained from the measured CODs, and it is found that energy release rate is continuous at bifurcation point in both cases of Homalite 100 and Araldite B. Energy flux that shows the energy flow toward a crack tip is also obtained.     

V型缺口裂端的三维应力状态及约束分析

利用三维有限元方法，研究了有限厚度板中V型缺口根部穿透裂纹前沿的三维弹性应力场。对不同厚度、不同缺口张开角和裂纹长度对应力强度因子及裂尖附近的三维约束程度的影响进行了分析，同时还讨论了三维约束区的大小。研究结果显示：当缺口张开角小于60度时，不同缺口的应力强度因子和离面约束因子的分布基本一致，角度的影响不明显。应力强度因子是厚度的函数，板中面的应力强度因子随厚度的增加逐渐减小趋近干平面值，最大为1．08倍的平面值。当板厚超过15倍的缺口深度时，应力强度因子最大值将从中面转移至接近自由表面位置，距中面约0．4倍板厚。三维约束非常明显的区域在裂尖前沿约0.45倍厚度的范围内．二维到三维的过渡区在裂尖前沿1.5倍厚度的区域内；在中面上三维效应影响区最大，随着离中面距离的增加逐渐减小，在自由表面上降为0。     

周期波导中弹性波局部化问题的研究

基于弹性波传递矩阵方法，对周期波导中弹性波局部化问题进行了分析研究。根据互易性原理和能量地恒定律，给出了结构弹性波传递矩阵的一般表达式。采用两种求解局部化因子的计算方法，分别计算了谐和与失谐周期波导中的局部化因子，并对其进行了分析讨论。本文对周期波导中波传播与振动局部化的分析方法和计算结果可用于结构的优化设计。     

A DECAGONAL QUASICRYSTAL WITH AN ARC-SHAPED CRACK

A decagonal quasicrystal,which is weakened by an arc-shaped crack penetratingthrough the solid in the period direction,and which is subjected to remote uniform phonon stresses,is investigated by applying the complex variable method which is just developed by the authors.It is found that the phonon and phason stresses near the crack tips exhibit inverse square rootsingularities.The four complex stress functions characterizing the phonon and phason fields arederived.Explicit expressions for the phonon and phason stress intensity factors,crack openingdisplacements and energy release rate are also presented.     

中心裂纹圆盘应力强度因子的测试误差分析

本文在中心裂纹圆盘应力强度因子解析解的基础上,利用一阶微分法则,给出了与裂纹相对长度和加载角相关的应力强度因子(K 和K )的4个误差传递函数。这4个误差传递函数关于裂纹相对长度和加载角均是非线性的,它们既是误差分析的基础,又是合理确定裂纹相对长度和加载角的基础。分析结果表明,加载角的误差Δθ除了对纯 型K 的误差几乎没有影响,对纯 型K 影响较小外,对复合型K 、K 的误差均有较大影响。最后,本文建议裂纹相对长度的取值范围为0.4～0.6;还建议在复合型断裂试验时,必须依据对K 、K 的总体精度要求来严格控制加载角的精度。     

金属橡胶材料阻尼测试的一个新方法

金属橡胶材料是一种新型减振缓冲材料。本文提出了一个金属橡胶材料阻尼性能的测试方法。基于粘弹性阻尼耗能的基本原理,在给定应变激励函数的条件下,构造了一个等效应力响应函数,由滞环面积相等建立了一组包含实测应力响应和等效应力响应的等效耗能方程,将应变激励函数离散得到了损耗因子的计算表达式,由此可以通过实测应力方便地计算出损耗因子。该方法不仅便于对大阻尼材料的阻尼进行测试,而且具有精度高的优点。依据这一方法对金属橡胶材料进行了测试,测试结果表明我们开发的金属橡胶材料有很好的阻尼减振性能。     

负压爆炸载荷和数据采集间隔对弹性开孔板动应力集中的影响

基于ANSYS 7.0/LS-DYNA程序,对3 m3 m四边简支,厚度0.025 m,中心开有0.3 m0.3 m方孔的弹性板,在正压和负压三角爆炸载荷作用下的应力响应进行了分析,利用能量密度时间分布函数（TDFED）确定了动应力集中因子,并给出其计算步骤。计算结果表明计算总时间和数据采集时间间隔对动应力集中因子影响较大,而负压荷载影响较小。