ON THE EXISTENCE AND STABILITY OF SOLUTION FOR SEMI－HOMOGENEOUS BOUNDARY VALUE PROBLEM

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＦＯＲＳＥＭＩ－ＨＯＭＯＧＥＮＥＯＵＳＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＤｏｎｇＱｉｎｘｉ（董勤喜）；ＨｕａｎｇＸｉａｎｋａｉ（黄先开）（ＲｅｃｅｉｖｅｄＪｕｌｙ．４．１９...     

NEW METHOD FOR THE CONSTRUCTION OF INTEGRABLE HAMILTONIAN SYSTEMS

ＡＮＥＷＭＥＴＨＯＤＦＯＲＴＨＥＣＯＮＳＴＲＵＣＴＩＯＮＯＦＩＮＴＥＧＲＡＢＬＥＨＡＭＩＬＴＯＮＩＡＮＳＹＳＴＥＭＳＧａｏＰｕｙｕｎ（高普云)（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｉｊｉｎｇ２１０?..     

The Analysis of Stability of Bingham Fluid Flowing Down an Inclined Plane

ＴＨＥＡＮＡＬＹＳＩＳＯＦＳＴＡＢＩＬＩＴＹＯＦＢＩＮＧＨＡＭＦＬＵＩＤＦＬＯＷＩＮＧＤＯＷＮＡＮＩＮＣＬＩＮＥＤＰＬＡＮＥＷａｎｇＰｅｉｇｕａｎｇ（王培光）；ＷａｎｇＺｈｅｎｄｏｎｇ（王振东）（ＲｅｃｅｉｖｅｄＤｅｃ．１．１９９４；Ｃｏｍｍｕｎｉｃ...     

THE MECHANICAL METHOD OF CONSTRUCTING THE DISPLACEMENT FUNCTIONS IN ELASTICITY

ＴＨＥＭＥＣＨＡＮＩＣＡＬＭＥＴＨＯＤＯＦＣＯＮＳＴＲＵＣＴＩＮＧＴＨＥＤＩＳＰＬＡＣＥＭＥＮＴＦＵＮＣＴＩＯＮＳＩＮＥＬＡＳＴＩＣＩＴＹ＊／／ＺｈａｎｇＨｏｎｇ－ｑｉｎｇ（张鸿庆）ＦｅｎｇＨｏｎｇ（冯红）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃ...     

THE THEORETICAL COST OF SEQUENTIAL AND PARALLEL ALGORITHMS FOR SOLVING LINEAR SYSTEMS OF EQUATIONS

ＴＨＥ　ＴＨＥＯＲＥＴＩＣＡＬ　ＣＯＳＴ　ＯＦ　ＳＥＱＵＥＮＴＩＡＬ　ＡＮＤ　ＰＡＲＡＬＬＥＬ　ＡＬＧＯＲＩＴＨＭＳ　ＦＯＲ　ＳＯＬＶＩＮＧ　ＬＩＮＥＡＲ　ＳＹＳＴＥＭＳ　ＯＦ　ＥＱＵＡＴＩＯＮＳＳａｌｍａｎＨ．Ａｂｂａｓ（ＲｅｃｅｉｖｅｄＭａｙ２４...     

INITIAL VALUE PROBLEM FOR HIGH DIMENSIONAL DYNAMIC SYSTEMS

ＩＮＩＴＩＡＬＶＡＬＵＥＰＲＯＢＬＥＭＦＯＲＨＩＧＨＤＩＭＥＮＳＩＯＮＡＬＤＹＮＡＭＩＣＳＹＳＴＥＭＳＺｈｕＣｈａｎｇ－ｊｉａｎｇ（朱长江）（Ｉｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉｓ．，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｗｕｈａｎ４３００７１）（Ｒｅｃｅｉｖｅｄ...     

THE ANALYSIS OF STABILITY OF BINGHAM FLUID FLOWIGN DOWN AN INCLINED PLANE

ＴＨＥＡＮＡＬＹＳＩＳＯＦＳＴＡＢＩＬＩＴＹＯＦＢＩＮＧＨＡＭＦＬＵＩＤＦＬＯＷＩＮＧＤＯＷＮＡＮＩＮＣＬＩＮＥＤＰＬＡＮＥＷａｎｇＰｅｉｇｕａｎｇ（王培光）ＷａｎｇＺｈｅｎｄｏｎｇ（王振东）（ＲｅｃｅｉｖｅｄＤｅｃ．１．１９９４．Ｃｏｍｍｕｎｉｃａ...     

NUMERICAL MODELING OF THE INITIAL STAGE OF THE GENERATION OF UNSTEADY VORTICES FROM SHARP CORNER IN PLANE COMPRESSIBLE FLOW

ＮＵＭＥＲＩＣＡＬＭＯＤＥＬＩＮＧＯＦＴＨＥＩＮＩＴＩＡＬＳＴＡＧＥＯＦＴＨＥＧＥＮＥＲＡＴＩＯＮＯＦＵＮＳＴＥＡＤＹＶＯＲＴＩＣＥＳＦＲＯＭＳＨＡＲＰＣＯＲＮＥＲＩＮＰＬＡＮＥＣＯＭＰＲＥＳＳＩＢＬＥＦＬＯＷＨｕａｎｇＤｕｎ（黄敦）（Ｄｅｐａｒｔ．...     

A GENERAL FREQUENCY DEPENDENT DIGITAL OPTIMAL PREVIEW SERVO SYSTEM

ＡＧＥＮＥＲＡＬＦＲＥＱＵＥＮＣＹＤＥＰＥＮＤＥＮＴＤＩＧＩＴＡＬＯＰＴＩＭＡＬＰＲＥＶＩＥＷＳＥＲＶＯＳＹＳＴＥＭＡＧＥＮＥＲＡＬＦＲＥＱＵＥＮＣＹＤＥＰＥＮＤＥＮＴＤＩＧＩＴＡＬＯＰＴＩＭＡＬＰＲＥＶＩＥＷＳＥＲＶＯＳＹＳＴＥＭ￥ＬｉａｏＦｕｃｈ...     

A－HIGH－ORDER ACCURACY EXPLICIT DIFFERENCE SCHEME FOR SOLVING THE EQUATION OF TWO－DIMENSIONAL PARABOLIC TYPE

Ａ－ＨＩＧＨ－ＯＲＤＥＲＡＣＣＵＲＡＣＹＥＸＰＬＩＣＩＴＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＦＯＲＳＯＬＶＩＮＧＴＨＥＥＱＵＡＴＩＯＮＯＦＴＷＯ－ＤＩＭＥＮＳＩＯＮＡＬＰＡＲＡＢＯＬＩＣＴＹＰＥＭａＭｉｎｇｓｈｕ（马明书）（ＲｅｃｅｉｖｅｄＪｕｎｅ２,１...     

Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model

The steady state solution of the system of equations consisting of the full Navier-Stokes equations and two turbulence equations has been obtained using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time-stepping scheme with a stability-bound local time step, while the turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positivity. Low-Reynolds-number modifications to the original two-equation model are incorporated in a manner which results in well-behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.     

Another form of equations of motion for constrained multibody systems

This paper presents a new and simplified set of explicit equations of motion for constrained mechanical systems. The equations are applicable with both holonomic and nonholonomic systems and the constraints may, or may not, be ideal. It is shown that this set of equations is equivalent to governing equations developed earlier by others. The connection of these equations with Kane's equations is discussed. It is shown that the developed equations are directly applicable with controlled systems where the controlling forces and moments may be subject to constraints. Finally, a procedure is presented for determining which control force systems are equivalent. Examples are presented to demonstrate the advantages, features, and range of application of the equations.     

多体系统指标2运动方程HHT方法违约校正1）

采用Cartesian绝对坐标建模方法，完整约束多体系统运动方程是指标3的微分--代数方程（differentialalgebraic equations，DAEs），数值求解指标3的DAEs属于高指标问题，通过对位置约束方程求导，可使运动方程的指标降为2.位置约束方程求导得到的是速度约束方程.直接求解指标3的运动方程，速度约束方程得不到满足，而且高指标DAEs的数值求解存在一些问题.论文首先采用HHT（Hilber--Hughes--Taylor）直接积分方法求解降指标得到的指标2运动方程，此时速度约束方程参与离散计算，从机器精度上讲速度约束自然得到满足，而位置约束方程没有参与计算，存在“违约”.针对违约问题，采用基于Moore--Penrose广义逆理论的违约校正方法，消除位置约束方程的违约.指标2运动方程HHT方法违约校正，将HHT方法和违约校正方法很好地结合，在数值求解指标2运动方程的过程中，位置约束方程和速度约束方程都不存在违约问题，而且新方法没有引入新的未知数向量，离散得到的非线性方程组的方程数量与原指标2运动方程的方程数量相同，求解规模没有扩大.新方法的实用和有效性通过算例的数值实验得到验证，数值实验也说明新方法保持了HHT方法本身具有的数值阻尼可以控制和二阶精度的特性.最后从非线性方程组的求解规模和计算速度上与其他方法进行了比较分析，说明新方法的优势所在.     

考虑质量耦合效应的流体饱和孔隙介质波动方程

利用混合物理论和连续介质力学的基本原理，推导了考虑质量耦合效应的流体饱和弹性孔隙介质的波动方程，并与经典的Biot波动方程进行了对比．结果表明：该文得到的方程包含了Biot波动方程的所有要素，且形式与后者基本相同．比较而言，该文推导过程具有更明确的物理意义，概念也更完整．     

多体系统动力学方程违约修正的数值计算方法

多体系统动力学方程为微分代数方程,一般将其转化成常微分方程组进行数值计算,在数值积分的过程中约束方程的违约会逐渐增大.本文对具有完整、定常约束的多体系统,在修改的带乘子Lagrange正则形式的方程的基础上,根据Baumgarte提出的违约修正的方法,给出了一种多体系统微分代数方程违约修正法和系统的动力学方程的矩阵表达式.通过对曲柄-滑块机构的数值仿真,计算结果表明本文给出的方法在计算精度和计算效率上好于Baumgarte提出的两种违约修正的方法.     

压电复合材料层合梁的分岔、混沌动力学与控制

研究了简支压电复合材料层合梁在轴向、横向载荷共同作用下的非线性动力学、分岔和 混沌动力学响应. 基于von Karman理论和Reddy高阶剪切变形理论，推导出了压电复合层合梁的动力学方程. 利用 Galerkin法离散偏微分方程，得到两个自由度非线性控制方程，并且利用多尺度法得到了平 均方程. 基于平均方程，研究了压电层合梁系统的动态分岔，分析了系统各种参数对倍周期 分岔的影响及变化规律. 结果表明，压电复合材料层合梁周期运动的稳定性和混沌运动对外 激励的变化非常敏感，通过控制压电激励，可以控制压电复合材料层合梁的振动，保持系统 的稳定性，即控制系统产生倍周期分岔解，从而阻止系统通过倍周期分岔进入混沌运动，并 给出了控制分岔图.     

带约束非线性多体系统动力学方程数值分析方法

Lagrange方法是建立带约束多体系统动力学方程的普遍方法之一 ,其方程的形式为微分 代数方程组 ,数值计算与数值分析是研究多体系统动力学特性的重要方法。本文利用缩并法给出了带约束多体系统动力学方程的隐式数值计算方法和Lyapunov指数的计算方法。将数值仿真、Lya punov指数计算和Poincare映射有机结合 ,分析非线性多体系统动力学行为。通过一个算例 ,说明该方法的有效性     

多体动力学超定运动方程广义-α求解新算法

完整约束多体系统第一类Lagrange方程建模得到的运动方程是指标-3形式的微分-代数方程(differental-algebraic equations,DAEs).如果同时考虑速度约束,将得到超定运动方程,该方程是指标-2的超定微分-代数方程(over-determined differential-algebraic equations,ODAEs).基于结构动力学中常用的广义-α方法,将其拓展,求解包含速度约束的超定运动方程,相对于其他求解指标-2 ODAEs的算法,新的算法没有增加离散得到的非线性方程组方程的数目.通过数值实验验证算法,并说明其求解ODAEs不存在精度降阶的现象,仍然具有二阶精度,同时算法的数值耗散也是可以控制的.最后新方法与其他求解多体系统ODAEs形式运动方程算法的CPU时间进行了比较分析.     

Nonlinear vibration of corrugated shallow shells under uniform load

Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution, the nonlinear forced vibration of a corrugated shallow shell under uniform load is investigated. The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green's function. To solve the integral-differential equations, expansion method is used to obtain Green's function. Then the integral-differential equations are reduced to the form with degenerate core by expanding Green's function as series of characteristic function. Therefore, the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic force is obtained by considering single mode vibration. As a numerical example, forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied. The obtained solutions are available for reference to design of corrugated shells     

The equations of motion of a system under the action of the impulsive constraints

In order to solve the problem of motion for the system with n degrees of freedom under the action of p impulsive constraints, we must solve the simultaneous equations consisting of n+p equations. In this paper, it has been shown that the undetermined multipliers in the equations of impact can be cancelled for the cases of both the generalized coordinates and the quasi-coordinates. Thus there are only n-p equations of impact. Combining these equations with p impulsive constraint equations, we have simultaneous equations consisting of n equations. Therefore, only n equations are necessary to solve the problem of impact for the system subjected to impulsive constraints. The method proposed in this paper is simpler than ordinary methods.