陀螺系统与反对称矩阵辛本征解的计算

用状态向量法,引出陀螺线性系统的广义本征问题,证明了本征向量之间的加权共轭辛正交关系,以及用本征向量对任意状态向量的展开定理。运用反对称矩阵胞块组成的LDL~T分解,将本征方程导向辛本征问题的标准型。这套方法适用于陀螺系统K阵不正定的情形。对于辛本征问题用SH变换将矩阵化为半边三对角线胞块阵或三对角线胞块阵,然后再求解其全部本征解。为陀螺系统的模态分析打下了基础。     

单点子域积分与差分

通过稳定性分析、显式与隐式积分，表明了单点子域积分相对于差分法的优越性．     

矩阵黎卡提方程的精细积分法

选择恰当的参数，将２￣Ｎ类算法用于代数与微分黎卡提方程。证明了算得的解是如此精确，几乎是计算机上的精确解。数例验证了该结论。     

不对称实矩阵的本征对共轭子空间迭代算法

对于大型不对称实矩阵A的本征值问题Ax=λx本文提出了共轭子空间迭代算法,指出怎样计算模最大的前p个本征对的方法,同时还求出了转置阵A~T的前P个本征向量。这个迭代算法是收敛的。数值例题表明了方法的有效性。     

参数二次规划法在计算力学中的应用(一)

绪言 一系列论文发表了关于参数变分原理在弹性接触问题和弹塑性分析中的理论和应用。所提出的参数最小势能原理和参数最小余能原理的特点是构造的能量泛函中含有两类变量:一类是状态变量,它们和经典变分原理中的一样;另一类是控制变量,它们不参加变分,但控制着变分过程,使问题的非线性本构特性(或状态方程)得以满足。参数变分原理     

平面八节点四边形理性元

推导平面八节点四边形理性有限元列式，采用具有直到四次多项式的平面问题的微分方程的解作为插值函数，算例结果表明平面八节点四边形理性有限元的有效性。     

A STUDY ON SHIP VIBRATION USING FINITE ELEMENT METHOD

when the beam theory was used to calculate ship hull vibration,greater discrepancies were found between theoretical cal-culations and actual measurements especially at higher modes.Thusthe beam model cannot be considered as a practical one for higher-mode calculations.This paper presents the application of two-dimensional finite element model for the calculation of ship ver-tical vibration.Using the multi-element structural dynamic a-nalysis program DDJ(DL)developed by ourselves,the hull vibra-tion analysis of two ships(vessel A and vessel B)was carriedout on the Model-709 Computer made in the People’s Republic ofChina.The results of the calculation,when compared with actualmeasurements.show that the two-dimensional model is much moreefficient than the traditional beam model.The agreement be-tween the calculations and measurements has been improved greatly,and this discrepancy at the4th·and5th-modes has decreased towithin5%as compared to that of more than20%in the traditionalmodel.Furthermore.the mode     

THE HAMILTONIAN SYSTEM AND COMPLETENESS OF SYMPLECTIC ORTHOGONAL SYSTEM

I.IntroductionThemethodofseparationofvariablesisimportanttosolvethesoluti0n0fprobIem0fmathematicalphysics,butmanyproblen1sofmathematicalphysicscannotseparatet'ariab1es,thereforeitrestrictstheranget0appIicatemethodofseparationofvariable.Inthepaperlll,Zhong…     

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H∞ DECENTRALIZED CONTROL SYSTEMS (Ⅱ)

When using H ∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems, which are analysed using H∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H ∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H ∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H∞ control are presented in part (Ⅰ)of the paper. The modal synthesis method for computation of the optimal H ∞ norm of decentralized control systems and numerical examples are presented in part (Ⅱ).     

WKBJ近似保辛吗?

WKBJ短波近似是最常用的有效求解方法之一。保守体系的微分方程可用Hamilton体系的方法描述，其特点是保辛。保辛给出保守体系结构最重要的特性。但WKBJ短波近似却未曾考虑保辛的问题。本文给出验证近似解保辛的条件，并指出WKBJ近似难于保辛。然后给出正则变换的摄动保辛方法。数值例题展示了提出的保辛算法的有效性。