刚性弹侵彻动力学中的第三无量纲数

采用侵彻阻力的一般表达式,计及速度一次项和减速度效应导致的附加虚拟质量项,利用量纲分析方法,明确定义控制刚性弹侵彻过程的第三无量纲物理量,即阻尼函数ξ.针对一般凸形弹头的侵彻问题开展分析,得到一般化的无量纲侵彻深度的计算公式;同时给出多个常用弹形的形状参数.针对已公开发表的不同弹形、靶材和撞击速度的侵彻实验数据,考察有无阻尼函数的理论预期,分析结果与实验数据一致.     

桥墩柔性防撞装置的静力学模型研究

文章利用一个简单模型,分析了我国自主研发的桥梁柔性防撞装置的基本静力学性能.即分析研究了装置分别在平动、转动以及平动转动耦合时的结构响应.构建物理模型:两个刚性的椭圆型结构箱梁环绕在桥墩上,箱梁之间由均布弹簧圈支撑连接.研究表明:1)纯平动下,无量纲化弹性反力与平动方向不一致,可以分解为垂直方向上两个分力,分别与各自方向上的无量纲位移近似认为是线性关系,外力通过椭圆中心时需要外扭矩平衡装置,无量纲平衡扭矩与无量纲位移平方成正比;2)纯转动下,转角很小时,无量纲扭矩为转角的三次方函数.此外,文章还定性的分析了平动转动同时发生时的力学性能,即:平动对扭矩转角关系的影响、转动对力位移关系的影响.     

流变学中的 Deborah 数

流变学所考虑的对象,可以说介于固体和流体之间. 固体力学中考虑介质的变形,流体力学则考虑介质的流动,流变介质既有流动又有变形. 创立流变学的是美国的宾厄姆 (C.E.Bingham 1878$\sim$1945, 也翻译为宾汉),他把流变学定义为``流动和变形 的学科'. 但是, 他为流变学起的名词 rheology 却是``流 rheo 的学问 logy', 他为流变学会的会徽上写上了希腊文``一切皆流'. 我不清楚在中文里,``流变学'这个词是怎样确定下来的, 大概是``约定俗成'吧. 最早正式出版的流变学中文书为袁龙蔚(1928$\sim$2004) 编著的<流变学概论>(1961年, 上海科技出版社) . 汉语术语``流变学'体现了``既流又变'的性质. 流变学中有个无量纲数 Deborah 数, 是以色列学者 M. Reiner (1886$\sim$1976)引进的, 这个数的定义为松弛时间与观测时间之比,它刻画了``像流体那样流动'的程度. 形象化地说, Deborah数很小, 则介质变形是主要的, 这个数很大, 则流动是主要的. 极而言之, 固体变而不流,则 Deborah 为零. 流体在流, 说变形已不合适, 则 Deborah 数为无穷大. Deborah 的汉译, 《力学名词》(科学出版社,1993年)和《流变学词 汇》(科学出版社, 1990)都是``德博拉'. 这个 Deborah 是圣经中一个女先知的名字,现也作为女子常用名字. 在圣经通用的版本中, 女先知 Deborah 译为``底波拉'. Reiner 引进的无量纲数以 Deborah 命名, 因为这个女先知说, 在上帝面前, 大山也会流动. 有趣的是, 圣经的现代翻译(英文,中文)里, 查不到``山会流'的说法, 而 Reiner则认为, 英文翻译得不确切, 没有忠实于圣经旧约的原文------希伯来语 (注意: Reiner 是以色列人). 圣经 (教会内规定版本) 上有关的话为: 士师记,第5章, 5:``山见耶和华的面就震 动', 相应的英文为 Judges, 5.5:``The mountains quaked before the Lord.' Reiner 关于 Deborah 数的短文见 Physics Today, vol 17, No.1, p62.     

三参量固体模型粘弹性输流管道的动力特性分析

推导了三参量固体模型粘弹性输流管道的振动微分方程 ,计算了在不同无量纲松弛系数和弹性常数比下管道的无量纲临界流速和无量纲自振复频率 ,并给出了前三阶复频率与流速的关系 .计算结果表明 ,质量比、无量纲松弛系数及无量纲弹性常数比对输流管道的动力特性均有影响 .     

线弹簧和转动弹簧支承粘弹性圆柱体的动力特性

对线、转动弹簧支承三参量模型粘弹性圆柱体轴向流动中的特征方程进行了推导,运用Matlab软件求解了其在轴向流动中的前三阶复频率.给出了当质量比β、量纲为一的延滞时间α和弹性系数比λ一定时,改变量纲为一的弹簧刚度a和转动弹簧b的情况下,三参量模型粘弹性圆柱体的前三阶模态量纲为一的复频率的实部及虚部与流速ν之间的关系曲线图;并分析了量纲为一的弹簧刚度对圆柱体动力特性的影响.研究结果表明:三参量模型粘弹性圆柱体分别处于两端固定和两端自由状态的两种特殊情况:两种情况下,第一阶模态的临界发散速度几乎相同,但当圆柱体两端自由时,第三阶模态发散的无量纲临界流速明显小于两端固定的圆柱体.且当ν=0时,两种情况下的前三阶复频率的虚部都相等.     

基于深部监测的滑坡动态特征分析

通过引力作用下理想气体流体力学方程组的无量纲化, 以空间尺度因子代 换时间参数, 根据量纲理论\Pi定理, 在方程中用与尺度因子对应的统计量物理 为度量单位, 从理论上推导出流体力学微分方程组的分离变量形式, 获得一组具有 分形结构特征一阶微分方程组. 引力作用下理想气体统计特征参量相对于空间尺度因子的一 般函数形式具有广义分形的结构特征, 这个结果表明局域性流体力学微分方程能够作为统计分 形结构的动力学基础.     

弹性地基上转动FGM梁自由振动的DTM分析

基于Euler-Bernoulli梁理论,利用广义Hamilton原理推导得到弹性地基上转动功能梯度材料(FGM)梁横向自由振动的运动控制微分方程并进行无量纲化,采用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,计算了弹性地基上转动FGM梁在夹紧-夹紧、夹紧-简支和夹紧-自由三种边界条件下横向自由振动的无量纲固有频率,再将控制微分方程退化到无转动和地基时的FGM梁,计算其不同梯度指数时第一阶无量纲固有频率值,并和已有文献的FEM和Lagrange乘子法计算结果进行比较,数值完全吻合。计算结果表明,三种边界条件下FGM梁的无量纲固有频率随无量纲转速和无量纲弹性地基模量的增大而增大;在一定无量纲转速和无量纲弹性地基模量下,FGM梁的无量纲固有频率随着FGM梯度指数的增大而减小;但在夹紧-简支和夹紧-自由边界条件下,一阶无量纲固有频率几乎不变。     

基于无量纲分析的法向恢复系数模型研究

作为描述接触碰撞过程能量损失的重要参量,恢复系数的深入研究对于提升现有接触碰撞力模型预测性能、准确描述接触碰撞现象,并进一步探明其对机械系统整体动态特性影响规律方面具有重要作用.鉴于现有恢复系数模型计算精度的局限性,本文基于无量纲分析方法,提出了一种考虑材料特性与初始碰撞速度的新型恢复系数模型.具体实施过程如下:首先,利用有限元软件ABAQUS建立弹性球-理想弹塑性基底法向接触碰撞数值仿真模型,分别从最小网格尺寸设置与接触碰撞能量转换角度验证了所建模型的有效性;基于此模型开展多工况下的数值模拟研究,分析不同材料弹塑性参数与初始碰撞速度对接触碰撞响应的影响;在此基础上,引入无量纲化参数E*/(ρv_nc²)与σ_y/E*,寻找恢复系数与弹塑性参数及初始碰撞速度间的函数关系;进一步结合Johnson塑性碰撞理论,反向推算获取屈服速度与材料属性的映射关系,最终建立无量纲化恢复系数新模型;通过与低速试验数据、高速有限元模拟结果的对比,验证了新模型的预测精度和泛化性能.     

基于SVD理论的可观测度分析方法的几个反例

常用的可观测度（DOO）分析方法有估计误差协方差矩阵的特征值和特征向量法和可观测性矩阵的奇异值分解（SVD）方法,前者需要在滤波结束之后进行,而后者不需要进行滤波运算就可直接用于分析整个系统的可观测度。但在利用SVD方法分析系统各个状态的可观测度时,为比较不同状态变量可观度的大小,需要对系统状态进行无量纲化处理,文章通过反例说明在利用变量代换方法进行无量纲化处理时,变换前后状态可观测度分析的结果不一致,原因在于SVD方法对于状态空间坐标系的拉伸变换不具有不变性。     

接触引起的'刚度增加'现象的机理

研究了转子和定子碰摩时振幅的跳跃现象,利用响应相位特征解释了接触诱发‘刚度增加'的机理.当转子与定子之间的间隙足够大时,转子在临界转速达到最大振幅,然后迅速衰减.如果与定子发生接触或碰撞,它们之间的接触将在很宽的速度范围得以维持,即便是转速已经远离临界转速.这一现象也称为‘刚度增加'或‘硬化'(stiffness increase Or stiffening).研究结果表明,形成该现象的机理足由于接触的作用,使得激励与振动响应的相位差保持在小于π/2的范围内.并且振幅跳跃与相位跃迁相伴出现.实验结果也验证了这一结论.     

Symmetrization of Lagrangian gas dynamic in dimension two and multidimensional solversSymétrisation de la dynamique des gaz en dimension deux et solveurs multidimensionnels

We propose a new formulation of multidimensional Euler equations in Lagrange coordinates as a system of conservation laws associated with free-divergent constraints. This formulation leads to a natural class of entropic Lagrangian schemes, based on a multidimensional node solver. For the sake of simplicity the study is done in 2D, but most of the ideas can be generalized in 3D. To cite this article: B. Després, C. Mazeran, C. R. Mecanique 331 (2003).     

Potential waves in one dimension

Some properties of one-dimensional potential waves are discussed. In particular it is shown that wave equations of this kind admit an infinity of local conservation laws with densities and fluxes depending on the fields only. This set of conserved quantities has a simple structure. In some cases this structure can be made explicite by means of a principle of conserved flux.A close relation between this set of conserved quantities and solutions of the hodograph equations has been found.     

Structural optimization in truth dimensionOptimisation structurale dans la dimension de vérité

Optimization theory has advanced considerably during the last three decades as is illustrated by a vast number of published books, surveys, and papers concerning this subject. An optimal decision under uncertainty conditions is dependent on the Engineer's objectives, which may be not known with certainty or represented by natural language. To deal with this problem, in this paper, a new approach based on coupling the existing knowledge of experts and numerical results obtained from traditional optimization techniques is presented using non-conventional logic. To cite this article: C. Tran, C. R. Mecanique 330 (2002) 609–614.     

Steady-state countercurrent flow in one dimension

Two phase countercurrent steady-state flow through permeable media in one dimension is discussed. For steady-state countercurrent flow in water wet porous media, a saturation profile is predicted with the water saturation decreasing in the direction that the water phase is flowing. The de la Cruz and Spanos equations predict that the Muskat relative permeability curves for countercurrent flow will be less than the Muskat relative permeability curves for steady-state cocurrent flow. This result has immediate implications regarding the use of external drive techniques to determine relative permeabilities based on the Buckley-Leverett theory and Muskat's equations. These equations and current experimental evidence involving countercurrent flow indicate that Muskat's equations do not adequately describe the multiphase flow of immiscible fluids.     

Multiscale Higuchi’s fractal dimension method

Nonlinear Dynamics - We investigate the closed-loop control of a circular cylinder showing lock-in phenomena due to vortex-induced vibrations (VIV). The control action was implemented by a...     

Analytical expressions for odd-order anisotropic tensor dimension

According to the symmetries of the matter, the number of coefficients needed to define a tensorial relation varies. It is well known that in linear elasticity the number of generic coefficients varies from 21, for a complete anisotropic material, to 2, in case of isotropy. In a previous contribution, we provided analytical expressions that give the number of generic anisotropic coefficients in any anisotropic system for an even-order tensor. In the present note, we aim at extending the previous results to the case of odd-order tensors. As an illustration, the dimension of any anisotropic system for third-order piezoelectricity tensors and of the fifth-order coupling tensors of Mindlin's strain-gradient elasticity are determined.     

On the Mindlin microelasticity in one dimension

Mindlin's microelasticity theory is reduced to the one-dimensional setting to examine its prediction of the response of microstructured materials on a pulse loading. The one-dimensional setting requires a minimal number of additional material parameters. Since analytical solutions may be found only in highly simplified asymptotic cases, numerical simulations are performed by means of a finite-volume numerical scheme modifying the wave-propagation algorithm. The calculated response of a material described by the Mindlin microelasticity is compared then with the corresponding response of an “equivalent” periodic laminate.     

Capillary fingering: Percolation and fractal dimension

We present experimental and theoretical results concerning immiscible displacements (drainage) in 2-dimensional permeable media. When capillary forces are predominant, the injected fluid presents very thin fingers and the Representative Elementary Volume concept cannot be used for describing the partial saturations. The purpose of this paper is to show how this classical concept can be replaced by a statistical approach based on fractal geometry.Communication presented at the International Symposium on the Stochastic Approach to Subsurface Flow, Montvillargenne 4–7 June 1985.