Optimal sampling and range of measurement in displacement-only laser-speckle correlation

A statistical analysis of the subjective laser-speckle pattern is performed with emphasis on its spectral distribution. An optimal sampling resolution of the laser-speckle pattern is obtained using the Shannon sampling theorem. Experiments show that the displacement-only correlation using laser speckles is a reliable measurement as long as the sampling requirement is satisfied. Upper limits of measurement such as accuracy, measurable area and measurable deformation are discussed. A method of changing the measurement capabilities by adjusting the speckle-recording arrangement is also given.Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 23–June 1.     

Approximate sampling theorem for bivariate continuous function

An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution . The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation , a piece-wise linear function , and posseses an explicit computation formula . Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function .     

Data sampling and data recovery

The sampling theorem states that a continuous signal can always be reconstructed from an equi-spaced set of samples of the signal, as long as the sampling rate has been chosen in accordance with the Nyquist criterion, thus allowing economical use of sampling rate and data storage. The practical aspects of data reconstruction from such sets of samples are considered.     

The Mean Value Theorem and Converse Theorem of One Class the Fourth-Order Partial Differential Equations

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆａｍｏｕｓＡｓｇｅｉｒｓｓｏｎｍｅａｎｖａｌｕｅｔｈｅｏｒｅｍｈａｓａｎｓｗｅｒｅｄｔｈａｔｔｈｅＣａｕｃｈｙｐｒｏｂｌｅｍｓａｒｅｉｌｌ＿ｐｏｓｅｄｔｏｔｈｅｕｌｔｒａ＿ｈｙｐｅｒｂｏｌｉｃｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｏｆｔｈｅｓｅｃｏｎｄ＿ｏｒｄｅｒ(Δ2 ｘ-Δ2 ｙ)ｕ=0 . ( 1 )Ｔｈｅｒｅｓｕｌｔｃａｎｂｅｕｓｅｄｔｏｐｒｏｖｅｔｈｅｃｏｎｔｉｎｕａｔｉｏｎｏｆｔｈｅｓｏｌｕｔｉｏｎｓｏｆｔｈｉｓｅｑｕａｔｉｏｎ ( 1 ) .Ｓｏｉｔｉｓｉ…     

Signal reconstruction by random sampling in chirp space

Reconstruction by irregular sampling and sampling at rates below the Nyquist rate are important issues for the experimental characterization of dynamical systems. For the space of functions that can be approximated by chirps, we prove a reconstruction theorem by random sampling at arbitrary rates.     

结构可靠度分析中的最小方差抽样

重要抽样技术是结构可靠度分析活跃的发展方向之一。本文研究了以抽样方差最小为条件的重要抽样问题，给出了正态抽样分布函数有关参数的计算公式，分析和实际模拟表明，在以正态分布进行了抽样的前提下，应用优化的参数，可使抽样效率进一步提高。     

An Analytical Study of Free Convective Boundary-Layer Flow in Porous Media: The Effect of Anisotropic Diffusitivity

The effect of an anisotropic thermal diffusivity tensor on the free convective boundary-layer flow in porous media is studied. Convection is induced by a generally inclined, uniformly heated surface embedded in a fluid-saturated medium. A third-order boundary-layer theory is presented in order to obtain accurate information on the effect of anisotropy on the rate of heat transfer into the porous medium. It is shown that the thickness of the resulting leading order boundary-layer flow depends on the precise nature of the anisotropy. On the other hand, the anisotropic diffusivity does not induce a fluid drift in the spanwise direction, a result which is different from that obtained in our earlier study of the effects of an anisotropic permeability. It is found that the second order temperature field does not contribute to the overall rate of heat transfer. Finally, we show that the third-order correction to the leading-order rate of heat transfer is given in terms of an explicit formula.     

土的各向同性化变换应力方法

在不同方向的力学参数、结构特性及应力应变关系的不同为材料的各向异性, 建立能够反映这种复杂特性的强度准则、本构模型, 对于材料本构关系的研究具有重要的理论意义. 但材料的各向异性一直是其力学特性描述的难点, 对此, 郑泉水院士提出了各向同性化定理, 为后续研究解决材料的各向异性问题提供了方向及思路. 作者等针对土的应力诱导各向异性提出了变换应力方法, 这种方法同样遵循对材料进行各向异性问题各向同性化处理的思路, 与郑泉水院士的各向同性化定理是一脉相承的, 也是对各向同性化定理的发展. 本文旨在通过分析各向同性化定理与变换应力方法明确两者间的内在联系, 并以土材料的应力诱导各向异性处理为例, 说明在具体材料的各向异性处理过程中面临的现实问题以及变换应力方法是如何解决这些问题的. 分析并给出了变换应力方法应用时的三个合理假设, 推导出了具体的变换应力数学公式, 阐明了在考虑土的应力诱导各向异性的具体函数已经给出的情况下, 在构造土的弹塑性本构模型中采用变换应力方法的必要性.      

建筑结构基于巴斯金风速谱的系列风振响应的简明封闭解

针对巴斯金风速谱激励下的建筑结构顺风向振动响应表达式复杂的问题,提出了一种简明封闭解法.巴斯金随机谱广泛应用于描述脉动风、随机地震动和路面不平顺等各种随机激励,本文基于留数定理给出巴斯金风速功率谱的二次正交式.综合运用复模态法和虚拟激励法获得了建筑结构系列响应(位移、层间位移及其变化率)功率谱的统一形式的二次正交式,并根据谱矩的定义获得了建筑结构系列响应的方差和谱矩及绝对加速度方差的简明封闭解.运用本文方法对一8层建筑结构进行分析,并与传统虚拟激励法进行对比研究,表明本文所得封闭解正确,并可用于验证虚拟激励法在谱矩和方差分析时的精度和效率.由于本文方法含有复模态法,故可用于各类线性结构基于巴斯金谱的随机响应分析和基于动力可靠度及舒适度的动力优化分析.     

GENERALIZATION OF STEINER FORMULAFOR THE HOMOTHETIC MOTIONS ONTHE PLANAR KINEMATICS

The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.     

下穿铁路隧道爆破振动衰减规律研究

基于Heelan短柱药包理论,引入等效作用半径的概念,得到内部瞬时激励荷载作用下爆破峰值振动速度的衰减模型方程,并通过量纲分析进行验证。结合下穿隧道爆破工程,研究不同雷管段位及不同炮孔类型对应的爆破峰值振动速度的衰减规律。此外,讨论球形装药、柱状装药条件下改进公式的药量形式表达式,结果显示,利用等效作用半径作为拟合参考变量可以综合考虑不同雷管段位及不同炮孔类型对爆破振动规律的影响。统计数据表明,利用改进公式得到的拟合效果最优,可以为类似隧道爆破振动研究提供参考。     

一种基于能量法则的爆炸成形弹丸速度的工程计算方法

为了准确预报爆炸成形弹丸的速度,提出了以药型罩中所有内部微元都变处于流动状态的时刻作为爆炸成形弹丸成形结束的标志,并因此得出药型罩自身变形时所消耗的变形能应与使整个药型罩都处于流动状态的熔化能相等。在此基础上利用能量守恒原理,建立了爆炸成形弹丸速度的计算公式,并通过试验和数值模拟验证。实验和计算结果表明,本文中所建立的爆炸成形弹丸速度的计算公式具有较好的工程实用价值。     

Some new fixed point theorems in probabilistic metric spaces

ＳＯＭＥＮＥＷＦＩＸＥＤＰＯＩＮＴＴＨＥＯＲＥＭＳＩＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳｚｈｕＣｈｕａｎ－ｘｉ（朱传喜）（ＭａｔｈｅｍａｔｉｅｓＤｉｖｉｓｉｏｎ,Ｎａｎｃｈａｎｇ．Ｕｎｉｖｅｒｓｉｔｙ,Ｎａｎｃｈａｎｇ）（Ｒｅｃｅｉｖ...     

位移控制法测定阻力曲线的实验和分析研究

分析探讨了位移控制法测K_R-△α的原理方法、误差估计等问题。并通过实测,提出了新的拟合式。指出了自动检测的必要和可能。     

Assessment of turbulent spectral bias in laser Doppler velocimetry

A critical evaluation is made of the spectral bias which occurs in the use of a laser Doppler velocimeter (LDV). In order to accommodate the randomly sampled LDV data, statistical treatments of particle arrival times are needed. This is modeled as a doubly stochastic Poisson process which includes the intensity function of the velocity field. Three processing algorithms are considered for spectral estimates: the sample and hold method (SH), the modified Shannon sampling technique (SR), and the direct transform (RG). Assessment is made of these for varying data densities (0.05 ≤ d.d ≤ 5) and turbulence levels (t.i.=30%, 100%). The effects of the values of the Reynolds stress coefficients and the transversal standard deviation on the spectral contents were examined. As an improved version of the spectral estimator, the utility of POCS (the projection onto convex sets) has been tested in the present study. This algorithm is found useful to be in the region when d.d. ? 3.     

Fifth-order isotropic descartes tensor

Ｉｎｔｈｉｓｌｉｔｅｒａｔｕｒｅ [1 ] ,[2 ]ｏｒｄｅｒ 0～ 4ｉｓｏｔｒｏｐｉｃｄｅｓｃａｒｔｅｓｔｅｎｓｏｒ’ｓｅｘｉｓｔｅｎｃｅａｎｄｉｔｓｇｅｎｅｒａｌｒｅｐｒｅｓｅｎｔａｔｉｏｎｆｏｒｍｕｌａａｒｅｄｉｓｃｕｓｓｅｄ .Ｗｉｔｈｒｅｇａｒｄｔｏｏｒｄｅｒｋ ≥ 5(ｄｅｓｃａｒｔｅｓｔｅｎｓｏｒｏｒａｆｆｉｎｅｏｒｔｈｏｇｏｎａｌｔｅｎｓｏｒ) ,ｔｈｅｎｕｍｂｅｒ (3 ｋ)ｏｆｉｔｓｃｏｍｐｏｎｅｎｔｓｉｓｖｅｒｙｂｉｇ ,ａｎｄｉｔｓｓｔｒｕｃｔｕｒｅｉｓｖｅｒｙｃｏｍｐｌｉｃａｔｅｄ ,ｓｏｎｏｐａ…     

用功的互等定理求解矩形薄板的自然频率

从虚功原理出发，证明了薄板小挠度弯曲问题的功的互等定理，并由此推出了求解矩形薄板自然频率的公式．算例表明，该公式计算简便，精度较高．     

Variational principles and entropy production in creeping flow of non-newtonian fluids

The extension of Helmholtz—Korteweg's theorem to purely viscous non-Newtonian fluids yields a variational principle for steady creeping flow for a rather wide class of fluids. Only for a restricted subclass (Newtonian and power-law fluids) does the quantity to be minimized coincide with the total rate of entropy production. It is argued that the Helmholtz—Korteweg theorem is a purely mechanical result which has no significant thermodynamic content.     

Positive solutions to （n-1,1） m-point boundary value problems with dependence on the first order derivative

Using the extension of Krasnoselskii＇s fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green＇s function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.     

The application of graph theory to the limit analysis for torsion of thin-walled bars with complex cross-sections

Graph theory is employed in this paper as a means to establish the topological model of complex thin-walled cross-sections. On this basis, the upper and lower bound theorems of the plastic limit analysis are applied to the analysis of the plastic limit shear flows on the cross-section of thin-walled bars under St. Venant torsion. Corresponding mathematical programming problems are formulated and their duality is shown. After solving the linear programming problem corresponding to the lower bound theorem, the limit torsional moment of a thin-walled cross-section can be calculated according to the shear stress distribution in the limit state. The formula for calculating the limit torsional moment is given. Furthermore, the limit state of thin-walled cross-sections under St. Venant torsion is also discussed and the concept of the limit tree is introduced. A computer program has been developed by the author. Results calculated by the program for typical complex cross-sections are given.