基于小波变换模极大的爆破震动信号奇异谱分析

系统论述了基于小波变换模极大(WTMM)的多分形奇异谱计算方法。利用此方法对某一典型的岩石爆破震动信号进行分析,给出了分段函数Z(q,a)、尺度指数(q)以及奇异谱f()的分布曲线,说明了信号的多分形特征,认为信号的突变主要集中在1的奇异指数上,而信号的奇异指数也主要集中在0.28～0.72之间;并提出了对于岩石爆破震动信号几乎是处处奇异的重要结论。     

小问题

349.如图所示的细长杆正方形框架,边长为a,各杆的El相同.图1(a)和图1(b)中作用力均沿AC方向,但是作用力方向不同.问两种情况下系统失稳的临界力各是多少?(a)(b)图1统系350.亦笛二奏拉格朗日方程中.当主动力有势且拉氏函数不显含某一广义量守恒的物理意义,坐标时,存在广义动量守恒.关于广义动涌堂本蕊妹平劫时愉素纬的动量守佰竺在系统定轴转动时为系统的动量矩守恒.那么是否存在的动量与动量矩以某种组合方式出现的真正的“广义”小问题@王灿星$浙江大学力学系 @高云峰$清华大学工程力学系…     

结构主动控制的LQG/LTR改进方法

提出一种改进的LQG／LTR(Linear Quadratic Gaussian synthesis with a Loop Transfer Recovery)结构主动控制方法，一种新的补偿器结构被用于回路传输恢复(LTR)。这个补偿器有以下优点：(1)它是开环稳定的；(2)它能保证整个闭环系统的稳定性；(3)更重要的是．对于相同的回路传输恢复度，它所需要的增益要小于传统LQG／LTR方法的基于观测器的控制器增益。还有，就是这个新的补偿器比传统的基于观测器要有较好的恢复性能。最后，数值算例验证了本文方法的有效性。     

Asymptotic method for singular perturbation problem of ordinary difference equations

This paper is taken up for the following difference equation problem(P,)(L,y)_k≡εy(k 1) a(k,ε)y(k) b(k,ε)y(k-1)=f(k,ε)(1≤k≤N-1),B_1y≡-y(0) c_1y(1)=a,B_2y≡-c_2y(N-1) y(N)=βwhereεis a small parameter,c_1,c_2,a,βconstants and a(k,ε),b(k,ε),f(k,ε)(1≤k≤N)functions of k andε.Firstly,the case with constant coefficients isconsidered.Secondly,a general method based on extended transformation is given tohandle(P.)where the coefficients may be variable and uniform asymptotic expansionsare obtained Finally,a numerical example is provided to illustrate the proposed method.     

Ⅱ型缺口试样应力场和应力场强度因子

1.前言对于理想的无限大Ⅱ型试样,应力场和应力场强度因子都有解析解。Hiroshi Tada等人给出了计算有限长度Ⅱ型试样K_Ⅱ的公式: F(a/b)=[1.30-0.65a/6+0.37(a/b)~2+0.28(a/b)~3]/(1-a/b)~1/2 (1) 其中,a和b分别表示裂纹和试样的长度,B是试样的厚度,P是外载荷。保持试样的长度和外载荷不变,按公式(1)计算,K_Ⅱ随裂纹长度a的变化,如图2中的曲线Ⅱ所示。结果表明,K_Ⅱ并不随a的增大而单调地增大,这和理想的无限大Ⅱ型试样的结果K_Ⅱ=τ(πa)~1/2相矛盾。另外,对Ⅱ型缺口试样的实验也表明,导致材料断     

Rotating electroosmotic flows in soft parallel plate microchannels

We present a theoretical investigation of rotating electroosmotic flows(EOFs) in soft parallel plate microchannels. The soft microchannel, also called as the polyelectrolyte-grafted microchannel, is denoted as a rigid microchannel coated with a polyelectrolyte layer(PEL) on its surface. We compare the velocity in a soft microchannel with that in a rigid one for different rotating frequencies and find that the PEL has a trend to lower the velocities in both directions for a larger equivalent electrical double layer(EDL) thickness λFCL(λFCL = 0.3) and a smaller rotating frequency ω(ω 5).However, for a larger rotating frequency ω(ω = 5), the main stream velocity u far away from the channel walls in a soft microchannel exceeds that in a rigid one. Inspired by the above results, we can control the EOF velocity in micro rotating systems by imparting PELs on the microchannel walls, which may be an interesting application in biomedical separation and chemical reaction.     

裂纹面受剪力作用的板的应力强度因子

考虑一个在ξ-η平面内一等厚度(厚度为h)的无限大板,在η=0,|ξ|≤a处有一条裂纹,如图1所示。在裂纹表面承受单位长度的剪力Q。为了方便,引入无量纲坐标,x=ξ/a,y=η/a。本文参照Wang解含裂纹板受扭的方法,采用了计及横向剪切变形影响的Reissner的薄板弯曲理论。根据该理论,需要求解挠曲函数w(x,y)的四阶偏微分方程(对于本题是双调和方程)和应力     

THE WEAK DAMPED OSCILLATION IN A RANDOM MEDIUM

The paper gives a solution of the random differential equation with random coefficient,that is (?)(t) K~2(t)x(t)=-εf(x,t),where K(t)is a random process and ε is adamp coefficient,it is a little parameter.     

Markovian risk process

A Markovian risk process is considered in this paper,which is the gener- alization of the classical risk model.It is proper that a risk process with large claims is modelled as the Markovian risk model.In such a model,the occurrence of claims is described by a point process {N(t)}_(t≥0) with N(t) being the number of jumps during the interval(0,t]for a Markov jump process.The ruin probabilityΨ(u)of a company facing such a risk model is mainly studied.An integral equation satisfied by the ruin probability functionΨ(u)is obtained and the bounds for the convergence rate of the ruin probabilityΨ(u)are given by using a generalized renewal technique developed in the paper.     

A SPECTRAL RESOLVING METHOD FOR ANALYZING LINEAR RANDOM VIBRATIONS WITH VARIABLE PARAMETERS

This paper is a development of ref. [1]. Consider the following random equation: in which excitation I(t) and response Z(t) are both random processes, and it is proposed that they are mutually independent. Suppose that I(t)=a(t)I·(t), a(t) is a known function of time and I·(t) is a stationary random process. In this paper, the spectral resolving form of the random equation stated above, the numerical solving method and the solutions in some special cases are considered.     

基于响应面法的五心底结构形状优化

三心底结构是国防、航空及航天等领域经常采用的结构,其旋转母线是由三段弧线组成的,对应着三个圆心,故得名三心底。三心底结构可调整的参数变量少,优化潜力小。根据三心底的形状推广出五心底结构,增加可调整的参数变量,然后对其进行优化。将响应面方法与模型参数化相结合,建立了以结构重量为目标及以结构强度为约束的形状优化模型。根据结...     

圆板非线性振动有限元分析的一种迭代方法

同时考虑横向振动和板平面内的运动,用3节点有限元研究均匀圆板的轴对称大振幅非线性振动,构造了一个避免发散加速收敛的平均迭代法,并将计算结果与文献的已有结果做了比较。     

多变量单元结构共振解耦动力优化设计方法

针对截面多变量单元结构的动力优化问题，建立了带频率约束的结构动力优化设计模型，对隐式非线性频率约束函数进行Taylor近似展开，给出了截面多变量单元频率梯度函数显式表达式，基于Kuhn-Tucker条件构建迭代算法，其中拉格朗日乘子通过建立联合方程组求解，形成了含多变量单元共振解耦优化设计方法。以矩形截面单元结构为算例的结果表明，所给单元多变量算法具有良好的准确性；截面变量对频率的贡献存在主次之分，区分指标可采用梯度值；次要变量的修正因子迭代中可采用定值，且其下限应尽可能降低，利于节约成本。本文工作对多变量复杂截面结构动力优化设计可提供理论指导，提高结构动力优化方法的适用性。     

Independent continuous mapping for topological optimization of frame structures

Based on the Independent Continuous Mapping method (ICM), a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements: the weak material element method and the tiny section element method. Three criteria (no structural singularity, no violated constraints and no change of structural weight) are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.The project supported by the National Natural Science Foundation of China (10472003) and Beijing Natural Science Foundation (3042002) The English text was polished by Yunming Chen.     

The parameter perturbation method on elastic wave equation in inhomogeneous medium

I.IntroductionTheelasticwaveininhomogeneousmediumiscomplicatedbecauseofthediffracting,scattering,andtransmutingofthewavetapes.Exceptforsomesimpleandregularmediummode1s,thesolutionofelasticwavehasnotbeengotyet.Nowadays,theresearchoftheelasticwavescattering…     

Numerical solution of the Klein–Gordon equation via He’s variational iteration method

In this paper, we present the solution of the Klein--Gordon equation. Klein--Gordon equation is the relativistic version of the Schrödinger equation, which is used to describe spinless particles. The He’s variational iteration method (VIM) is implemented to give approximate and analytical solutions for this equation. The variational iteration method is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. Application of variational iteration technique to this problem shows rapid convergence of the sequence constructed by this method to the exact solution. Moreover, this technique reduces the volume of calculations by avoiding discretization of the variables, linearization or small perturbations.     

A combined approach of EFGM and precise algorithm in time domain solving viscoelasticity problems

In this paper, element free Galerkin (EFG) method is combined with a precise algorithm in the time domain for solving viscoelasticity problems. By expanding variables at discretized time intervals, an initial boundary value problem is converted into a series of recurrent boundary value problems which can be conveniently solved by EFG/EFG-FE with a self-adaptive computing process. There is no requirement of iteration for the solution of non-linear cases. Satisfactory numerical results are obtained for both static and dynamical viscoelasticity problems.     

计算圆板大振幅非线性振动频率的平均刚度法

本文用平均刚度法研究圆板大振幅非线性振动的频率问题，导出了相应的非线性广义特征值方程，构造了一种避免发散并能加速收敛的加权平均迭代法，计算结果与Ｋａｎｔｏｒｏｖｉｃｈ时间平均法的解十分吻合。     

Determining the natural frequencies of highly inhomogeneous shells of revolution with transverse strain

A method of studying the natural vibrations of highly inhomogeneous shells of revolution is developed. The method is based on a nonclassical theory of shells that allows for transverse shear and reduction. By separating variables, the two-dimensional problem is reduced to a sequence of one-dimensional eigenvalue problems. The inverse iteration method is used to reduce these problems to a sequence of inhomogeneous boundary-value problems solved by the orthogonal sweep method. The capabilities of the method are illustrated by solving certain representative problems and comparing their solutions with those obtained using the three-dimensional theory of elasticity, the classical theory of shells, and the refined Timoshenko model __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 38–47, September 2007.     

离散变量结构形状优化设计的综合算法

提出一种离散变量结构形状优化设计的方法,该方法在优化过程中将两类变量统一考虑,根据两类变量的相对差商值确定搜索的变量;并且对形状变量施加了运动极限的限制,从而保证了收敛速度快,收敛平稳;将该算法应用于几个经典的结构优化算例：运算结果显示了该方法计算效率高,优化效果也比较满意．