关于准速度和准加速度表示的Appell方程

本文给出准速度和准加速度联合表示的一阶和二阶非完整系统的Appell方程的新形式,并将所得结果推广到变质量系统,最后举例说明新方程的应用。     

准坐标下的广义Mac-Millan方程

本文得到了适用于非线性非完整系统的广义Mac-Millan方程的准坐标表述,证明了与准坐标形式的广义Чаплыгин方程的等价性. ...     

冲击波作用下铝的准弹性卸载行为

根据一维应变冲击波的基本关系,将Cochran 等定义的有效剪切模量与准弹性卸载过程的纵波和体波声速关联起来,并藉此研究了冲击波作用下铝的准弹性卸载特性. 利用VISAR高压声速测量技术获得了LY12铝在20$\sim$100\,GPa压力下沿着准弹性卸载过程的有效剪切模量,结果表明LY12铝的有效剪切模量随卸载应力的下降而迅速下降. 采用与卸载应力成线性关系的方程对有效剪切模量进行了近似描述,该方程的斜率随初始冲击压力的增加而增加,体现了准弹性卸载行为的压力相关性. 将有效剪切模量结果与准静态实验结果进行了比较,由此分析了冲击波作用下准弹性卸载过程的可能物理机制. 应用有效剪切模量方程对6061铝合金的准弹性行为进行了模拟,计算结果与实验结果符合很好.      

准晶数学弹性力学和缺陷力学

对准晶数学弹性理论的基本概念和基本框架作了介绍,在此基础上分别针对目前已经发现的几类一维准晶、二维准晶和三维准晶讨论了其数学弹性的理论体系．为了求解准晶弹性的边值问题或初值一边值问题,还必须发展相应的方法论．物理工作者在研究准晶位错弹性问题中发展了Ｇｒｅｅｎ函数方法．针对一维与二维准晶弹性中几类问题提出了分解与叠加程序,这一程序的使用,使极其复杂的准晶弹性问题得到简化,进而引进位移函数或应力函数,把数目。庞大的准晶弹性基本方程化成一个或少数几个高阶偏微分方程,进一步使求解步骤大为简化．对三维立方准晶弹性也采用了类似步骤使求解过程大为简化．在以上化简的基础上,发展了准晶弹性的边值问题或初值一边值问题的复交函数方法和 Ｆｏｕｒｉｅｒ分析方法,求得了一系列准晶位错问题和裂纹问题的分析解（古典解）．在研究准晶弹性的边值问题古典解的同时,也讨论了同这些边值问题相对应的变分问题和广义解（弱解）以及这种弱解的数值方法──有限元法．在物理学家工作基础上开展的这些工作可以看作对经典数学弹性理论和方法、经典Ｖｏｌｔｅｒｒａ位错理论、普通结构材料断裂力学和经典有限元的某些发展．此外,还把一维六方准晶弹性动力学的结果与统计物理的某些     

准晶数学弹性力学和缺陷力学

对准晶数学弹性理论的基本概念和基本框架作了介绍,在此基础上分别针对目前已经发现的几类一维准晶、二维准晶和三维准晶讨论了其数学弹性的理论体系．为了求解准晶弹性的边值问题或初值一边值问题,还必须发展相应的方法论．物理工作者在研究准晶位错弹性问题中发展了Ｇｒｅｅｎ函数方法．针对一维与二维准晶弹性中几类问题提出了分解与叠加程序,这一程序的使用,使极其复杂的准晶弹性问题得到简化,进而引进位移函数或应力函数,把数目。庞大的准晶弹性基本方程化成一个或少数几个高阶偏微分方程,进一步使求解步骤大为简化．对三维立方准晶弹性也采用了类似步骤使求解过程大为简化．在以上化简的基础上,发展了准晶弹性的边值问题或初值一边值问题的复交函数方法和 Ｆｏｕｒｉｅｒ分析方法,求得了一系列准晶位错问题和裂纹问题的分析解（古典解）．在研究准晶弹性的边值问题古典解的同时,也讨论了同这些边值问题相对应的变分问题和广义解（弱解）以及这种弱解的数值方法──有限元法．在物理学家工作基础上开展的这些工作可以看作对经典数学弹性理论和方法、经典Ｖｏｌｔｅｒｒａ位错理论、普通结构材料断裂力学和经典有限元的某些发展．此外,还把一维六方准晶弹性动力学的结果与统计物理的某些      

Kirchhoff弹性杆分析动力学的准坐标表达

作为DNA的力学模型,依据Kirchhoff动力学比拟思想建立的弹性细杆的分析力学方法已从静力学深入到动力学。由于静力学平衡微分方程与刚体动力学相当,因此,弹性细杆动力学的分析力学方程必是以弧坐标和时间为双自变量的偏微分方程。以横截面的形心速度以及弯扭度和角速度沿主轴的分量为准速度,定义了准坐标,导出了准坐标的微分和变分运算的交换关系。从Hamilton原理出发,利用准坐标的微分和变分运算的交换关系,导出了Kirchhoff弹性杆动力学准坐标下的Boltzmann-Hamel方程,并由此导出Lanrange方程。指出了Boltzmann-Hamel方程显式即为弹性杆动力学的Kirchhoff方程。定义关于弧坐标和时间的正则变量和Hamilton函数,导出Boltzmann-Hamel方程的正则形式。本文结果是以弹性杆静力学和刚性杆动力学为其特例。作为例子,建立了垂挂的在重力作用下作平面运动的弹性细杆的动力学微分方程以说明本文方法的应用。     

P1波入射准饱和土的波型转换问题

针对各向同性准饱和土体中体波的传播问题,本文深入研究了P1波(第一纵波)入射土体时所出现的波型转换现象。在准饱和土波动方程的基础上,通过数值算例,找出标准参数土体模型的临界饱和度及波型转换角,并分析土体孔隙率、渗流系数、水压力和入射波频率等参数对该现象的影响。     

准静态变形破坏的近场动力学分析

基于近场动力学理论,提出新的更能反映非局部长程力特性的物质点间作用力函数,并通过在物质点运动方程中引入局部阻尼、构造分级加载算法和系统失衡判断准则,实现了采用统一的近场动力学模型和算法进行从准静态变形、裂纹萌生和扩展直至结构破坏全过程的连续模拟和准确定量计算。     

Poisson括号方法及其在准晶、液晶和一类软物质中的应用

对凝聚态物理学中的Poisson 括号及有关Lie群和Lie代数方法做了介绍. 同时介绍了在准晶、液晶和一类软物质研究中的应用.不仅介绍了推导以上物质的流体动力学方程或弹性-流体动力学方程, 也讨论了某些方程的解, 这种解还揭示了国外著名权威的经典解的错误.     

准静态离散元方法和线性粘弹性问题的模拟

离散元方法是近年发展起来的一种新数值方法,但原则上只能用于动态问题。从静力平衡条件出发建立了离散元系统的准静态演化方程并证明了系数矩阵具有对称正定、稀疏、带状分布等特点,适用于“有效列”方法求解,该解法比高斯消去法节省更多的内存和机时。通过引入广义Maxwell体的元间作用模型建立起线性粘弹性材料准静态响应的离散元模拟方法。该方法独立于传统动态离散元方法,是传统动态离散元方法的拓展,可望在更多领域获得应用。     

MINIMAL POLYNOMIAL MATRIX AND LINEAR MULTIVARIABLE SYSTEMS(Ⅰ)

part(Ⅰ)of this work is on the theory of minimal polynomial matrix and Part(Ⅱ)onthe applications of this theory to linear multivariable systems.In Part(Ⅰ).concepts of annihilating polynomial matrix and the minimal polynomialmatrix of a given linear transformation in a vector group are given and the concepts of thegenerating system and minimal generating system of an invariant subspace for a givenlinear transformation are given as well.After discussing the basic properties of theseconcepts the relations between them and the characteristic matrix corresponding to aninduced operator of a given linear transformation in any of its invariant subspace arestudied in detail.The characteristics of the minimal polynomial matrix for a given vectorgroup and the necessary and sufficient condition for the two generating systems to have thesame generating subspace is given.Using these results we can give the expression for the setof all B’s which makes the system x=Ax Bu a complete controllable system for a givenA.     

Reduced equilibrium equations for perfectly elastic materials

Sufficient conditions are given on the coordinate systems which enable reduced equilibrium equations to be derived for perfectly elastic materials involving deformations which depend in an essential way only on two of the three coordinates. Reduced equilibrium equations given previously for plane and axially symmetric deformations are special cases of the equations given here. These equations considerably reduce the calculations involved in investigating possible solutions of finite elasticity, either exact semi-inverse solutions or approximate perturbation solutions. Moreover a formula for the pressure function appearing in the reduced equilibrium equations is given which relates to the corresponding pressure function associated with the inverse deformation. This formula is similar to one given previously for fully three dimensional deformations.     

Interval finite element method and its application on anti-slide stability analysis

The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements are given. The sub-interval amount is discussed and the approximate computation formula is given. At the same time, the computational precision is discussed and some measures of improving computational efficiency are given. Finally, based on sub-interval perturbed finite element method and anti-slide stability analysis method, the formula for computing the bounds of stability factor is given. It provides a basis for estimating and evaluating reasonably anti-slide stability of structures.     

Technical Stability of Discontinuous Control Systems with a Continuous Set of Initial Perturbations

Conditions of technical stability in a given measure are derived for autonomous dynamic discontinuous-control systems for all possible initial states in a given domain of admissible initial perturbations of the output processes. The criteria formulated depend on the properties of the roots of the secular equation of a given quadratic form assigned to the control system under investigation     

Formulation and solution for inverse problem of nonholonomic dynamics

This paper presents a formulation and solution for the inverse problem ofnonholonomic dynamics:to find the form of nonholonomic constraints when someintegrals are given and to find the generalized reactive forces of constraint acting onthe system when the expression of the kinetic energy is given.An example is given toillustrate the application of the result.     

Some uses of Green's theorem in solving the Navier–Stokes equations

This paper gives a review of methods where Green's theorem may be employed in solving numerically the Navier–Stokes equations for incompressible fluid motion. They are based on the concept of using the theorem to transform local boundary conditions given on the boundary of a closed region in the solution domain into global, or integral, conditions taken over it. Two formulations of the Navier–Stokes equations are considered: that in terms of the streamfunction and vorticity for two-dimensional motion and that in terms of the primitive variables of the velocity components and the pressure. In the first formulation overspecification of conditions for the streamfunction is utilized to obtain conditions of integral type for the vorticity and in the second formulation integral conditions for the pressure are found. Some illustrations of the principle of the method are given in one space dimension, including some derived from two-dimensional flows using the series truncation method. In particular, an illustration is given of the calculation of surface vorticity for two-dimensional flow normal to a flat plate. An account is also given of the implementation of these methods for general two-dimensional flows in both of the mentioned formulations and a numerical illustration is given.     

NUMERICAL SOLUTIONS OF ONE–DIMENSIONAL MHD EQUATIONS BY A FLUCTUATION APPROACH

In this paper a higher-order Godunov method for one-dimensional solutions of the ideal MHD (magneto-hydrodynamics) equations is presented. The method uses a fluctuation approach and includes a new sonic fix and a new Roe averaging. After a short introduction the MHD equations in conservative form are given. The flux is rearranged such that the eigenstructure is not changed. This rearrangement allows full Roe averaging for any value of adiabatic index (contrary to Brio and Wu's conclusion). A new procedure to get Roe—averaged MHD fields at the interfaces between left and right states is then presented and some useful identities are given. Next the second-order-limited fluctuation approach is presented in full detail. The new sonic fix for MHD and the procedure for applying this fix to the sonic points are then given in detail. Numerical results obtained with the described method are presented. Finally, conclusions are given.     

热超弹性材料中空穴增长的分岔问题

研究了受外加均布拉伸死载荷作用的不可压热超弹性材料中空穴突然快速增长的分岔问题.不同于外载荷较小的情况,不可压热超弹性材料球体中的预存微空在外载荷足够大时可以发生突然的快速增长,可视为一类分岔问题.给出了不同温度场下,不同初始半径的微空的增长曲线.预存微空的增长曲线相应于初始半径的极限是实心球体中空穴突然生成的分岔曲线.讨论了均匀和非均匀,升高或降低的温度场对空穴增长问题的影响;给出了预存微空能够发生突然的快速增长的临界载荷,得到了临界载荷与实心球体中空穴突然生成时的临界载荷之间的关系及临界载荷与温度变化之间的关系.     

TE modes of a layered nonlinear optical waveguide

The general theory is given of the propagation of electromagnetic TE modes in a layered structure consisting of a homogeneous dielectric layer between two homogeneous optically nonlinear semi-infinite dielectrics. Allowance is made for the nonlinear coefficients of the nonlinear media to be different and a detailed analysis is given, together with the appropriate formulae for the power flow down the guide, as a function of guide wave number, and layer thickness. Detailed consideration is given to the existence conditions for surface waves.     

Oscillation theorems of higher order nonlinear delay differential equations

ＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＯＦＨＩＧＨＥＲＯＲＤＥＲＮＯＮＬＩＮＥＡＲＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＪｉｎＭｉｎｇ－ｚｈｏｎｇ（靳明忠）（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉｃＣｏｕｒｓｅｓ,ＹｕｎｎａｎＩｎｓｔｉｔｕｔ...