Vibrational hydrodynamic interaction between a sphere and the boundaries of a cavity

A new type of vibrational lift force [1] acting on a spherical body oscillating in a viscous fluid near a rigid boundary is experimentally investigated. The interaction between the body and the cavity boundary creates a repulsion force which is capable of holding a heavy body in the gravity field at a certain distance from the floor and a light body at a certain distance from the ceiling. The repulsion force appears at a distance comparable with the Stokesian boundary layer thickness and increases as the surface is approached. Outside the viscous interaction range, the repulsion force is replaced by an attraction force which decays with distance. Dimensionless parameters governing the vibrational interaction are found and threshold curves, corresponding to the transition of bodies of different densities to the “suspended” state, are plotted as functions of a dimensionless frequency. The dependence of the repulsion and attraction forces on the distance between the body and the wall is studied.     

Negative linear compressibility of generic rotating rigid triangles

The compressibility properties of systems consisting of generic rotating rigid triangles are analyzed and discussed.It is shown that these systems which are usually associated with auxeticity can exhibit strongly anisotropic properties for certain conformations, which may give rise to the anomalous property of negative linear compressibility(NLC), that is, the system with particular geometry will expand along one direction when loaded hydrostatically. It is also shown that through carefully choosing the geometric features(i.e. the dimensions and the alignment of the rotating triangles as well as the angles between them) and the direction along which the linear compressibility is measured, one may control the magnitude and range of the NLC. All this provides a novel but effective method of manufacturing the systems which can be tailored to achieve particular values of NLC to fit particular practical applications.     

含铰接杆系结构几何非线性分析子结构方法

将细长杆系结构按长度方向划分为多个子结构,由于在子结构坐标系下的节点位移均是小位移,可以将子结构内部自由度凝聚到边界. 考虑到子结构端面在变形过程中保持为刚性截面,将端面节点自由度进一步凝聚到端面形心点,这样每一个子结构就减缩成形式上只有两个节点的广义梁单元,大大减缩了自由度. 大位移大转动是细长杆系结构产生几何非线性效应的一个重要原因,基于共旋坐标法,建立了随单元一起运动的随动坐标系,推导了子结构单元的节点力平衡方程及其切线刚度阵. 同时,考虑到工程机械中细长杆系结构含有相互铰接的刚体加强块,给出了非独立自由度节点力转换到独立参数下的广义节点力及其导数. 最后,通过履带式起重机的副臂工况算例,给出了其在不同载荷下的臂架结构位移,验证了方法的正确性.      

四节点二十四自由度平板壳单元几何刚度矩阵显式解析式的推演算法研究

几何刚度矩阵的推演是结构几何非线性有限元分析的重点和难点之一。推导几何刚度矩阵显式解析表达式成为简化非线性有限元列式,提高分析效率的关键。本文在协同转动法框架下,基于刚体运动法则对四节点二十四自由度的平板壳单元几何刚度矩阵显式解析式进行了推导和讨论;分析了悬臂梁大转动、不同壁厚条件下简支圆柱形屋顶空间大变位两个经典算例。研究结果表明：（1）几何刚度矩阵的显式计算公式不仅为板壳结构几何非线性列式提供了方便而且具有良好的精度;（2）推导的几何刚度矩阵适用于各类型四边形二十四自由度平板壳单元模型;（3）与数值积分相比,采用解析形式的几何刚度矩阵可以显著提高非线性响应计算效率。     

对平面运动刚体加速度瞬心问题的进一步讨论

讨论了与加速度瞬心相关的几个问题,进一步深化了对加速度瞬心概念的理解．     

刚性弹丸撞击下混凝土板侵彻极限深度与痂斑极限厚度经验公式的验算

为了估算混凝土板在外来飞射体撞击下的侵彻极限深度与痂斑极限厚度,总结了以往试验与理论研究成果,评价了几种有代表性的经验公式,对4种具有不同特征参数的导弹撞击混凝土板时的侵彻极限深度与痂斑极限厚度进行了对比。结果表明,现有的经验公式估算侵彻极限深度的差异不大,而估算痂斑极限厚度有时差异较大。     

勒让德伪谱法求解三维刚体摆姿态运动最优控制问题

研究伪谱法求解三维刚体摆姿态运动最优控制问题. 针对三维刚体摆这类含有约束的力学模型,提出了基于勒让德伪谱法的三维刚体摆姿态最优控制方法. 利用插值逼近设计了三维刚体摆姿态运动最优控制算法,得到了三维刚体摆的姿态最优控制轨迹,并结合松弛参数来控制插值点的取值,寻找满足的可行解. 仿真结果表明,基于勒让德伪谱法的最优控制算法使得三维刚体摆能以较小的误差运动到期望的末端姿态,且计算速度快,能够获得精度较高的控制输入量.     

Weakly Terminal Objects in Quasicategories of $\mathbb{SET}$ Endofunctors

The quasicategory ℚ of all set functors (i.e. endofunctors of the category of all sets and mappings) and all natural transformations has a terminal object – the constant functor C₁. We construct here the terminal (or at least the smallest weakly terminal object, which is rigid) in some important subquasicategories of ℚ – in the quasicategory of faithful connected set functors and all natural transformations, and in the quasicategories of all set functors and natural transformations which preserve filters of points (up to cardinality κ).Mathematics Subject Classifications (2000) 18A22, 18A25.Libor Barto: This work was completed with the support of the Grant Agency of the Czech Republic under the grant 201/02/0148; supported also by MSM 113200007.     

A round ball uniquely minimizes gravitational potential energy

We give a proof following Carleman that among measurable bodies in of mass and density at most 1, a round ball of unit density uniquely minimizes gravitational potential energy.

     

NUMERICAL SIMULATION OF BENARD CONVECTION IN A CLOSED RECTANGLE (Ⅱ)——THREE-DIMENSIONAL CASE

In the paper, numerical simulation is performed for Benard convection in a closed three-dimensional rectangle with non-slippery bound. Numerical results show that when Rayleigh number Ra<3.6×104, Benard convection is steady, and when Ra≥3.6×104 it is unsteady and irregular. The cross sections and correlation coefficients of various fields are studied, and it is found that the external correlation scales of flow decrease as Ra increases when Ra≥ 7.5×104. Moreover, statistical analyses show that the Taylor inner scales (λv,λθv and so on) also decrease as Ra increases, and that the changing rates of λv and λθv with height are very different to each other in the vicinity of upper and lower bounds. Furthermore, statistical analyses show that the computed Nusselt number Nu is close to the lower limit of many experimental values, and in the transient region of flow pattern d1gNu/d1gRa is relatively greater than that in other region. In addition, other statistical quantities of the fields of temperat