饱和地基上含刚核弹性圆板的竖向振动分析

基于作者提出的饱和土弹性波动方程，研究了饱和地基上含刚核弹性圆板在竖向集中谐和力作用下的振动特性。首先应用Hankel积分变换求解该饱和土波动方程，然后按混合边值条件建立起一组描述含刚核弹性圆板振动的对偶积分方程，并将其化为第二类Fredholm积分方程进行数值求解。文末给出了含刚核弹性圆板在饱和地基上振动的阻抗函数随无量纲频率a0的变化曲线，并考察了土的渗透系数，弹性板含刚域的大小以及板的柔度等参数对阻抗函数的影响，得出了一些有意义的结论。     

超薄油膜润滑的分子动力学模拟Ⅰ．刚性分子模型

分子量级超薄油膜的润滑特性与流体润滑及边界润滑的都有所不同，而且在超薄油膜中也同样存在着润滑剂的流动。因此，利用分子动力学方法模拟了超薄油膜中的压力流动，模拟中采用了刚性分子流体模型，重点研究固体壁面对流动的影响，结果表明，当油膜厚度远比流体分子“直径”大时，模拟所得速度剖面和流量均与流体力学的理论值基本一致；随着油膜厚度逐渐变薄，压力流动或动压流因受到固体壁面的阻碍作用而不断减小；当油膜厚度减小到几个分子直径量级时，两固体壁面之间的流体分子发生固化或晶体化，由此而导致压力流动消失。这可能是流体动力润滑向边界润滑转化的机理之一。由这些研究结果可见，分子动力学模拟在薄膜润滑研究中具有广阔的应用前景。     

Renewal of basic laws and principles for polar continuum theories （XI）——consistency problems

Some consistency problems existing in continuum field theories are briefly reviewed. Three arts of consistency problems are clarified based on the renewed basic laws for polar continua. The first art discusses the consistency problems between the basic laws for polar continua. The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua. The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body. The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them. In the meantime, these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories.     

Theory of inverted pendulum with follower force revisited

The effect of the type of springs on the equilibrium states of an inverted pendulum is examined. The angular and linear eccentricities of the follower force are taken into account __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 126–137, June 2007.     

Dynamic Behavior of Multilink Pendulums under Follower Forces

The results from studies of the dynamic behavior of a double pendulum under the action of a follower force are analyzed. It is pointed out that bifurcations and catastrophes of equilibrium states may occur at some values of the parameters. Differential equations are presented which describe the plane-parallel motion of a pendulum with an arbitrary number of links and angular and linear eccentricities of the follower force whose orientation depends on one parameter. The basic problems of dynamics of pendulums with different number of links are formulated __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 3–35, June 2005.     

旋转倒立双摆摆起控制量的动态设计变量优化

倒立摆的摆起过程是复杂的非线性力学与控制的综合问题,当力学模型和参数确定时,寻求有效方法计算控制律函数是实现摆起的关键。本文以倒立双摆模型为研究对象,将动态设计变量优化方法引入对摆起开环控制律的分析,编制计算机程序进行数值仿真,确定了控制律函数与状态量随时间变化的状态,为复杂强非线性系统的控制提出了一种有效方法。     

SYMPLECTIC STRUCTURE OF POISSON SYSTEM

When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform.Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the midpoint scheme. Numerical results show the effectiveness of the nonlinear transform.     

The dynamics of coupled planar rigid bodies. II. Bifurcations,periodic solutions,and chaos

We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.     

大型沉井结构施工力学模型的研究

大型沉井结构是当今应用较广的基础工程，由于沉井结构的规模大，工区土层复杂，存在有许多不确定性因素。使得施工过程的力学模型比较难确定。迄今尚缺乏可供借鉴的理论研究。由于施工的关键是保证沉井的均匀下沉，控制终沉和防止突沉，为此，建立合适的施工力学模型以预测下沉量和开挖量之间的关系就十分必要，考虑到混凝土沉井在土体中下沉时，其本身的变形很小，可以忽略其影响，本文从多自由度刚体运动的角度，建立沉井下沉过程的动态力学模型。为验证所建模型的正确性，本文对一实际工程进行了数值仿真计算。并将计算结果与实测结果进行了对比。结果表明，所建立的力学模型能较好地反映沉井下沉的工程实际，因而可以应用该模型对沉井下沉进行预测分析。从而有助于指导沉井的实际施工。     

ANALYSIS OF AN INCOMPRESSIBLE RUBBER WEDGE CONTACTING WITH A RIGID NOTCH

I. INTRODUCTION It is well known that rubber materials are much more important in modern society. It is, therefore,not surprising that a sizable number of investigations have been concerned with the rubber materials.Considerable attention has been paid …