复杂链式结构动力分析中的直接迁移子结构方法

本文将频响函数和迁移矩阵引入子结构方法中，提出简单高效的直接迁移子结构方法。当子结构中内部自由度很大时，用这种方法进行链武结构的动力特性分析和求解谐和激励响应时依然能保持很高的计算效率和精度。而且有限元分析或试验得到的各子结构数据相互独立，因此对结构的不同组合进行分析只需改变相应连接条件；当结构有局部修改时也只需修正相应子结构的数据。这些特性对复杂链武结构动力优化和抗震设计问题十分有利。最后的数值算例说明了所提出方法的优越性及其在工程中的实用性。     

相同子结构串的本征对问题及展开解法

本文讲述了串连式子结构的分析计算方法,它相当于结构分析中按横截面展开的方法。文中讲述了移位不变法以及初参数与传递矩阵法两个方面,并指明了两种方法的联合运用及相互关系,截面上本征值问题的计算以及按本征向量展开等问题。     

A new appraoch of the dynamic substructure method

Researches show that there exists a modal transformation matrix which is similar to that of the fixed interface method in form but slightly different from that in content. Using the constrained modes and normal modes or Lanczos vectors, a new modal transformation developed from hybrid method is given, in which the interface forces are replaced by interface displacements. The first synthesis equations are assembled easily as with the fixed interface method, yet the interface coordinates can be further eliminated as with the free-interface method. The new method unifies the fixed- and free-interface methods as well as hybrid method,permitting easy implementation of the Lanczos vectors to replace normal modes so that only static modes are calculated. The dynamic substructure method thus becomes more flexible and efficient. This reveals the interrelations of various dynamic substructure methods. New formula for modal analysis and modal synthesis are developed and three examples are given for illustration.Supported by Doctoral Training Foundation of State Education Commission and NNSF of China.     

研究柔性体撞击问题的子结构离散方法

本文用子结构方法研究刚性小球和均质柔性杆的纵向撞击以及和均质柔性梁的横向撞击问题,导出了用模态坐标表示的动力学方程,通过对刚性小球和柔性杆的纵向撞击的仿真教育处发现,在总单元数相同的情况下,取8个子结构比较合理,在此基础上对刚性小球和均质柔性梁的横向撞击的特性进行研究,发现撞击力在变化过程中会产生上下波动,当梁的弹性模量增加时,撞击力增大,撞击时间缩短。     

结构动力重分析的子结构有理逼近

在基于子结构灵敏度综合的结构动力重分析方法的基础上,应用向量值函数有理逼近,提出了一种新的结构动力重分析方法。子结构方法的应用,有效减少了结构自由度数目,达到了减少计算量的目的。将向量值函数有理逼近应用于截断的Taylor级数,提高了计算精度,扩大了收敛范围,适用于结构作大修改的情形。数值算例表明,所提出的方法对结构参数发生大修改能够有效降低Taylor级数截断的误差,给出高精度的逼近结果。     

基于界面主从位移控制的频响子结构方法

在复杂工程结构频响子结构分析中,各个子结构的频响函数往往是由不同的部门获得,各个子结构的频响函数可能是在不同的坐标系下得到,亦或有些子结构具有某种对称性,这需要对相应的子结构频响函数进行旋转和镜像变换后才能进行整体拼接。此外,子结构拼接时交界面的连接点有时可能存在不一致,为了满足位移协调和力平衡条件,本文基于界面主从位移控制原理,提出一种改进的频响子结构方法,该方法既能考虑子结构的旋转和镜像变换,也能考虑子结构界面间的柔性连接,并可大幅提高计算效率。当界面位移控制阵为单位阵时,改进的方法退化为传统的频响子结构方法。数值算例验证了所提方法的正确性和有效性。     

轨道系统高频振动分析的动态子结构法

提出了包含钢轨断面弹性变形、轨下不连续支承、横垂向交叉导的轨道高频振动分析模型。根据轮轨特点,提出适合轮轨高频振动分析的阻抗聚缩法。预测结果与试验结果吻合较好。分析表明约８００Ｈｚ以下,钢轨振动表现为整体振动,再高频率钢轨发生断面弹性变形的振动。我国轨道系统第一、第二、阶二振频率分别为１５０Ｈｚ和３２０Ｈｚ,ｐｉｎｎｅｄ－ｐｉｎｎｅｄ共振频率的１２８０Ｈｚ。     

土-结构动力相互作用分析中基于人工边界子结构的地震波动输入方法

数值模拟是解决土-结构动力相互作用问题的重要手段,而合理地实现地震波动输入直接影响地震作用下土-结构动力相互作用问题数值模拟的精度。波动法是目前常用的地震动输入方法之一,该方法将输入地震动转化为人工边界上的等效荷载,相较于其他地震动输入方法,波动法模拟精度高,但实施上相对复杂。从有限元模型入手,推导了采用波动法确定等效输入地震荷载的另一种形式,以此为基础,提出了一种在人工边界上实现地震动输入的新方法。新方法通过对土-结构有限元模型中由包含人工边界节点的单元组成的子结构施加自由场位移时程并进行动力分析,直接获得可实现地震波动有效输入的等效荷载,然后将等效输入地震荷载施加在土-结构模型的人工边界节点上,从而完成土-结构动力相互作用问题分析中地震动输入和地震反应计算。与原有波动法相比,新方法避免了需分别计算人工边界上自由场应力和由引入人工边界条件带来的附加力,以及需要根据不同人工边界面确定荷载的作用方向等较为复杂的处理过程,具有等效地震荷载计算简便、地震动输入过程更易于实施的特点。采用竖直入射和斜入射地震波动作用下的弹性半空间和成层半空间地震反应算例验证了新方法的有效性。      

Perturbation solution for thermal expansion buckling of no expansion joint slope pavement plate

In this paper,the mechanical mechanism of thermal expansion buckling of no expansion joint slope pavement undergoing the action of a temperature field is analysed.By using regular perturbation method,the formula of perturbation solution for this problem is derived,the relationship between critical laying temperature difference of slope pavement and of level straight pavement is studied,and the unified solution and its.numerical results are also obtained.In terms of this research,rational laying temperature of no expansion joint slope pavement is given.     

大型辛矩阵本征问题的逆迭代法

基于共轭辛子空间迭代法,求解了大型辛矩阵的主要本征解。随着迭代的进行,可以无限地逼近其精确解。     

No-tension solids in the presence of thermal expansion: An explicit solution

In this paper the constitutive equation of no-tension materials is generalized in order to account for thermal dilatation. Subsequently, the explicit solution to the equilibrium problem of a circular ring subjected to two uniform radial pressures, p ₁ and p ₂, acting respectively on the inner and outer boundary and a temperature distribution depending linearly on the radius, is calculated. It is proven that if pressures p ₁ and p ₂ and the temperatures V ₁ and V ₂ of the inner and outer boundary, respectively, satisfy certain inequalities, then the well-known stress field corresponding to a linear elastic material is the solution for the non-linear elastic material under consideration. On the contrary, if these inequalities are not satisfied, the equilibrated stress field, negative semi-definite, is explicitly calculated and the corresponding displacement and fractures determined. In particular the dependence of the cracked regions on the temperatures V ₁ and V ₂ is analysed.

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Sommario In questo lavoro si generalizza l'equazione costitutiva dei materiali non resistenti a trazione, per tenere conto delle dilatazioni termiche. Successivamente si calcola la soluzione esplicita del problema di equilibrio di una corona circolare costituita da un materiale non resistente a trazione, soggetta a due pressioni radiali uniformi, p ₁ e p ₂, agenti rispettivamente sul bordo interno e sul bordo esterno e a una distribuzione di temperatura variabile linearmente col raggio. Si dimostra che se le pressini p ₁ e p ₂ e le temperature V ₁ e V ₂ rispettivamente del bordo interno ed esterno soddisfano alcune diseguaglianze, allora il noto campo di sforzo corrispondente ad un materiale elastico lineare è anche la soluzione per il materiale elastico non lineare qui considerato. Al contrario, se queste diseguaglianze non sono soddisfatte, lo stato di sforzo equilibrato e semidefinito negativo è calcolato esplicitamente e sono determinati i corrispondenti spostamenti e fratture. In particolare, viene analizzata la dipendenza della regione fratturata dalle temperature V ₁ e V ₂.

     

Eigenfunction expansion method to the solution of simultaneous equations and its application in mechanics

The solution of a homogeneous vector-matrix differential equation, when the operator is of linear second order, has been established by the method of eigenfunction approach. The uniqueness of the solution has been established for both the cases when the roots of the characteristic equations are distinct and when they are repeated. Finally, the theory has been applied on two problems of mechanics and the results are compared with the existing literature.     

马尔可夫链在冗余系统可靠度求解中的应用

求解了单支光纤陀螺失效率取不同值时系统可靠度随时间的变化曲线,并分析了冗余系统可靠度曲线的意义,为光纤陀螺惯性测量冗余系统的可靠性研究提供了重要的信息,并为冗余系统的费效比计算提供了可信的依据。对组成系统的器件进行冗余是提高系统可靠性的一种常用方法,定量研究复杂冗余系统的冗余关系和求解系统的可靠度是极其困难的,马尔可夫模型是一种有效的方法。分析和确定了一个复杂的光纤陀螺惯性测量冗余系统的冗余关系,介绍了马尔可夫模型的基本原理,讨论了冗余系统应用马尔可夫模型的条件,应用马尔可夫模型建立了冗余系统的状态转移图和状态转移矩阵,最后给出了冗余系统可靠度的解析表达式,定量求解了冗余系统的可靠度。     

Experimental examination of bicycle chain forces

This paper presents the results of an investigation evaluating the forces present in a statically loaded bicycle chain prior to and beyond sprocket engagement. Comparisons are made with previous investigations that have been limited to industrial chains and sprockets. The chain drive system for a bicycle differs from the industrial standard types not only in its size but in its operation. A high degree of lateral flexibility is required in the bicycle chain for it to operate with noncoplanar sprockets having an effective misalignment of 3 deg or more. The experimental analysis in this paper considers chain loads for a range of sprocket sizes and angles of misalignment. Results indicate that localized bending arising from misalignment between chain and sprocket can increase or decrease the strain on the side plates by a substantial fraction of the direct strain due to chain tension. The work presented here is part of a more general study of bicycle chain efficiency for competition applications.     

Molecular origin of viscoelasticity and chain orientation of glassy polymers

Dynamic birefringence and dynamic viscoelasticity of poly(4-methyl styrene) and poly(4-t-butyl styrene) were measured to investigate the molecular origin of viscoelasticity around the glass transition zone. The data were analyzed with a modified stress-optical rule: The birefringence and the stress were separated into two component functions of different molecular origins. One component is related to the orientation of the main chain axis and the other one to the rotation of the repeating units about the main chain axis. The strain dependence of the two characteristic orientation functions in the glassy zone was estimated and the orientation mechanism of repeating units was discussed.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

Mikusinski’s operators solution of three-order linear difference equation with variable coefficients

This paper proceeds the papers [3] [4], we make use of the idea of the variable number operators and some concepts and conclusions of the shifting operators series with variable coefficients in the operational field of Mikusinski, it is devoted to the solution of the general three-order linear difference equation with variable coefficients, and it is also devoted to the better solution formula for the some special three-order linear difference equations with variable coefficients: in addition, we try to provide the idea and method for realizing solution of the more than three-order linear difference equation with variable coefficients. Project Supported by the Science Foundation of Anhui Province     

大型结构特征值问题的Lanczos子结构并行算法

本文利用子结构和Lanczos方法,提出了大型结构固有频率与模态的并行解法。该方法在Lanczos方法的求解过程中,仅利用子结构刚度阵和质量阵并行进行凝聚,进而求得新的迭代矢量,最终求得三对角阵对应的特征值和特征向量。该算法在西安交通大学ELXSI-6400并行计算机上程序实现,计算结果表明能有效地节省计算时间和计算机的内存,为一种有效的大型工程结构动力问题的求解方法。     

On the uniformly valid asymptotic solution of non-linear Dirichlet problem

In this paper, Dirichlet problem for second order quasilinear elliptic equation with a small parameter at highest derivatives is studied. In case degenerate equation has no singular point and parameter is sufficiently small, the existence and uniqueness of solution are proved, and the uniformly valid asymptotic solution is derived on the entire domain.