类Pade逼近方法在二维非线性振动系统的应用

提出一种求解强非线性系统同异宿轨道解析解的改进类Pad\'{e}逼近方法, 该方法在分析带有扰动参数的系统时无需预先限定参数的取值范围. 首先研究了具有三次非线性项的系统,分析其产生同宿或异宿轨道时参数的取值范围, 分别提出直接体现参数的同宿及异宿解的设解通式, 据此获得了一类强非线性下的自治系统方程的同宿及异宿解. 其次, 对于非自治系统, 研究了具有三次非线性项系统的强迫振动, 直接考虑扰动参数对整个系统的影响, 得到了满足同(异)宿边界条件的周期解. 最后, 构造了两种不同形式的异宿解, 从而减少了保守系统异宿解的计算量. 借助数值模拟验证了该方法的有效性及精确性.      

A general metrology of stress on crystalline silicon with random crystal plane by using micro-Raman spectroscopy

The requirement of stress analysis and measurement is increasing with the great development of heterogeneous structures and strain engineering in the field of semiconductors. Micro-Raman spectroscopy is an effective method for the measurement of intrinsic stress in semiconductor structures. However, most existing applications of Raman-stress measurement use the classical model established on the (001) crystal plane. A non-negligible error may be introduced when the Raman data are detected on surfaces/cross-sections of different crystal planes. Owing to crystal symmetry, the mechanical, physical and optical parameters of different crystal planes show obvious anisotropy, leading to the Raman-mechanical relationship dissimilarity on the different crystal planes. In this work, a general model of stress measurement on crystalline silicon with an arbitrary crystal plane was presented based on the elastic mechanics, the lattice dynamics and the Raman selection rule. The wavenumber-stress factor that is determined by the proposed method is suitable for the measured crystal plane. Detailed examples for some specific crystal planes were provided and the theoretical results were verified by experiments.     

Experimental study on the local similarity scaling of the turbulence spectrum in the turbulent boundary layer

The streamwise fluctuating velocity in the turbulent boundary layer is measured under approximately medium Reynolds Number by hot wire in order to investigate the scaling properties of the overlapped turbulent spectrum among energy-containing area, inertial subrange and dissipation range based on FFT analysis. The experiment indicates that the high Reynolds flow reported before is not indispensable to produce −1 scaling. So far as the measured position is provided with much higher spatial resolution and enough closing to the wall, −1 scaling is determinate to exist when approaching medium Reynolds. The scaling ranges are supposed to begin at inner scale and end in outer scale, which reveals the local similarity of the energy spectrum over the energy-containing eddies near the wall. In the logarithmic area (y ⁺ > 130), −5/3 scaling occurs in the energy spectrum, while moving away from the wall with Reynolds numbers increasing, the inertial subrange extends to the lower wavenumbers. On the condition k ₁ η ≫ 0.1, the curves of the turbulence spectrum in the logarithmic layer are superposed, which expresses the similarity of turbulence energy distributed in Komogorov scaling area and exhibits local isotropy characteristics by virtue of the viscous dissipation. Supported by the National Natural Science Foundation of China (Grant Nos. 10832001 and 10872145), the Program for New Century Excellent Talents in Universities of Education Ministry of China, and the Plan of Tianjin Science and Technology Development (Grant No. 06TXTJJC13800)     

Visualization of Lagrangian fluid transport of a vortex ring based on time-resolved PIV

Journal of Visualization - We carry out experiments on vortex ring flows submerged underwater which are generated by a pulsatile circular jet with the stroke ratio of 10. The pulsatile Reynolds...     

Predetermined control of turbulent boundary layer with a piezoelectric oscillator

With a piezoelectric(PZT) oscillator, the predetermined controls of the turbulent boundary layer(TBL) are effective in reducing the drag force. The stream-wise velocities in the TBL are accurately measured downstream of the oscillator driven by an adjustable power source. The mean velocity profiles in the inner and outer scales are reported and the skin friction stresses with different voltage parameters are compared. Reduction of integral spatial scales in the inner region below y+of 30 suggests that the oscillator at work breaks up the near-wall stream-wise vortices responsible for high skin friction. For the TBL at Reθof 2183, the controls with a frequency of 160 Hz are superior among our experiments and a relative drag reduction rate of 26.83% is exciting. Wavelet analyses provide a reason why the controls with this special frequency perform best.     

Effects of single synthetic jet on turbulent boundary layer

The turbulent boundary layer (TBL) is actively controlled by the synthetic jet generated from a circular hole. According to the datasets of velocity fields acquired by a time-resolved particle image velocimetry (TR-PIV) system, the average drag reduction rate of 6.2% in the downstream direction of the hole is obtained with control. The results of phase averaging show that the synthetic jet generates one vortex pair each period and the consequent vortex evolves into hairpin vortex in the environment with free-stream, while the reverse vortex decays rapidly. From the statistical average, it can be found that a low-speed streak is generated downstream. Induced by the two vortex legs, the fluid under them converges to the middle. The drag reduction effect produced by the synthetic jet is local, and it reaches a maximum value at x⁺=400, where the drag reduction rate reaches about 12.2%. After the extraction of coherent structure from the spatial two-point correlation analysis, it can be seen that the synthetic jet suppresses the streamwise scale and wall-normal scale of the large scale coherent structure, and slightly weakens the spanwise motion to achieve the effect of drag reduction.     

壁面湍流发卡涡包空间模态的TRPIV实验研究

运用高时间分辨率粒子图像测速(Time-resolved PIV简称TRPIV),测量得到平板湍流边界层流向/法向平面内瞬时速度矢量空间分布的时间序列;采用空间局部平均速度结构函数的概念,识别和提取湍流边界层中大尺度发卡涡包结构的空间特征。发现在湍流边界层中不同法向位置多个正负发卡涡包结构同时交替存在。这些分布在不同法向高度的发卡涡包结构之间通过倾斜的涡量剪切层相联系,构成了湍流边界层中内、外区紧密相连、相互作用的一种稳态的分布方式。     

TBM滚刀刀圈与岩石的滑动磨损实验研究

硬岩隧道掘进机(TBM)的滚刀刀圈在破岩过程中面临剧烈的磨损,对TBM的掘进效率及施工成本影响巨大。为了深入研究全断面隧道掘进机滚刀刀圈的磨损机理,本文在M-200型磨损试验机上模拟了TBM滚刀刀圈与岩石的磨损行为。基于实验数据,验证了磨粒磨损引起的磨损量与摩擦距离的线性关系,分析了岩石硬度、摩擦系数和润滑对磨粒磨损速率的影响。实验结果表明,在大载荷下,磨损形式将由单纯的磨粒磨损转化为磨粒磨损与疲劳磨损共同存在的形式,并且计算了疲劳磨损量,进而对比了磨粒磨损量与疲劳磨损量的大小。结论:硬度、摩擦系数越大,滚刀刀圈磨损越严重;润滑对降低磨损有重要作用;在大载荷作用下,磨损状态将由磨粒磨损转化为磨粒磨损和疲劳磨损共存的状态。上述研究结果可以为TBM滚刀刀圈设计及施工提供一定的参考。     

基于双线性位移模式数字图像相关方法的误差分析及应用

探讨数字图像相关方法测试结果的误差分布规律对提高该方法的测试精度具有重要意义。本文从理论上分析了基于双线性位移模式数字图像相关方法的子区变形场测试误差分布规律,结果表明,当试件的真实变形可由双线性位移模式描述时,变形场最大测试误差通常出现在子区的边界或节点处。因此,若试件发生均匀拉伸等常应变变形,可利用相关系数选取一个最优子区,认为测得最优子区中心应变为试件真实应变。零变形实验验证了该测试方法的可靠性。最后对手机导光板试件在单轴拉伸载荷下的数字图像进行分析,并利用本文方法测试了其弹性常数。     

On the pricing of American contingent claims under transaction costs and multiple risky assets

This paper addresses the hedging problem of American Contingents Claims (ACCs) in the framework of continuous-time Itô models for financial market. The special feature of this paper is that in the financial market the investor has to face fixed and proportional transaction costs when trading multiple risky assets. By using the auxiliary martingale approach and extending the results of Cvitanic and Karatzas [Cvitanic J, Karatzas I. Hedging and portfolio optimization under transaction costs: a martingale approach. Math Finance 1996;6:135–65] on pricing European contingent with transaction costs in the single-stock market, an arbitrage-free interval [h_low, h_up] is identified, and the end points are characterized by auxiliary martingales and stopping times in terms of auxiliary stochastic control problems. Here h_up and h_low are so-called the upper hedging price and the lower hedging price.