VIBRATION THEORY OF CONTINUOUS BEAM UNDER THE ACTION OF MOVING LOAD

This paper uses the small paramter method to investigate the dynamic calculation ofthe whole vibration process of trains passing through a continuous beam,considering theeffects of the mass and the damping as well as the masses of the moving loads.By solving aset of integral equation,we find out the general solution of continuous beam under theaction of arbitrary moving load PF(t) and calculate,the case of single moving load beingQ_i P_isin(α_it ε_i). By concluding our results,We establish the dynamic theory ofvibration of continuous beam acted by the moving load.Finally, as an example, we calculate the vibration question of two-span continuousbeam.The deflections of two midspan are shown in Fig.2 and Fig.3.     

EXACT FINITE ELEMENT METHOD

In this paper,a new method,exact element method for constructing finite element,ispresented.It can be applied to solve nonpositive definite or positive definite partialdifferential equation with arbitrary variable coefficient under arbitrary boundarycondition.Its convergence is proved and its united formula for solving partial differentialequation is given.By the present method,a noncompatible element can be obtained and thecompatibility conditions between elements can be treated very easily.Comparing the exactelement method with the general finite element method with the same degrees of freedom,the high convergence rate of the high order derivatives of solution can be obtained.Threenumerical examples are given at the end of this paper,which indicate all results canconverge to exact solution and have higher numerical precision.     

INCOMPATIBLE CURVED QUADRILATERAL PLATE BENDING ELEMENT WITH 12-DEGREES OF FREEDOM

This paper presents a new curved quadrilateral plate element with12-degree freedom by the exact element method.The method can be used to arbitrary non-positive and positive definite partial differential equations without variation principle.Using this method,the compatibility conditions between element can be treated very easily,if displacements and stress resultants are continuous at nodes between elements.The displacements and stress resultants obtained by the present method can converge to exact solution and have the second order convergence speed.Numerical examples are given at the end of this paper,which show the excellent precision and efficiency of the new element.     

复合载荷下圆底扁球壳非线性稳定性

本文采用半解析方法研究在中心分布载荷及中心集中力联合作用下,圆底扁球壳的非线性稳定性问题.避免了求近似解析解时繁重的人工计算,而p-W_m特征关系仍可由显式表达.     

GENERAL SITUATION OF THE PARTICIPATION OF EDITORIAL BOARD MEMBERS OF APPLIED MATHEMATICS AND MECHANICS IN THE 16th.INTERNATIONAL CONGRESS OF THEORETICAL AND APPLIED MECHANICS

The 16th.International Congress of Theoretical and Applied Mechanics(ICTAM),which isheld every four years under the auspices of International Union of Theoretical and AppliedMechanics(IUTAM),was held on Aug.19,1984 Aug.25,1984 in Lyngby Industrial University.Copenhagen.Denmark.35 representatives of the People’s Republic of China participated in this     

非均匀变厚度梁的动力响应的一般解

在本文中提出一个新方法——阶梯折算法来研究在任意载荷下任意非均匀和任意变厚度伯努利-欧拉梁的动力响应问题.研究了自由振动和强迫振动.新方法需要将区间离散为一定数目的元素,每个元素可看作是均匀和等厚度的.因此均匀、等厚度梁的一般解可在每个元素上应用.然后用初参数表示的整个梁的一般解使之满足相邻二元素间的物理和几何连续条件,这样就可以得到解析形式的自由振动的频率方程和解析形式的强迫振动的最终解,它化为求解二元线性代数方程,与离散元素的数目无关.现在的方法可推广应用至任意非均匀及任意变厚度有粘滞性和其他种类的梁以及其他结构元件问题上去.     

非均匀变截面梁动力响应的一般解

本文利用精确解析法￣［１］给出非均匀变截面梁在任意谐振荷载和边界条件下的动力响应的一般解。问题最后归结为求解一个非正定微分方程。对于这一问题用一般变分法求解失败，利用本文的方法，这个问题的一般解可以写成解析的形式。因此对优化特别方便。本文给出收敛性证明。文末给出的算例表明本文的方法可获得满意的结果。     

计及行动载荷质量及惯性力影响的列车过桥动力理论

本文研究了列车过桥的整个过程的动力计算,计及桥梁的阻尼效应和行动载荷质量。用小参数法求出了在任意单个行动载荷(=PF(t),其中P为常量,F(t)为时间的任意函数)作用下的铁路桥梁动力方程的一般解,建立了完整的列车过桥动力理论,并具体计算了单个行动载荷为PF(f)=Q+Psin(αt+ε)的情况下的解,其中α为折合回频率,Q为常量,ε为相角。最后文中计算了著名的Newark Dyke桥的实例,并讨论了所得结果。     

复合材料层合板的分析

在复合材料层合板静力和动力分析方面,本文提出了一个层合板理论.此理论从板的总挠度中分开了由弯曲所产生的挠度W_b与由剪切产生的挠度W_s,因而使得求控制方程的解变得容易了.而且便于讨论和分析横向剪切变形对层合板弯曲,振动和稳定性的影响.     

轴对称非均匀圆柱壳非线性屈曲的一般解

在文献[7]和[11]的基础上,本文提出了一个新的方法,用于计算轴对称非均匀圆柱壳在任意轴对称荷载和边界条件下的非线性屈曲的临界载荷,并导出这个问题的一般解,最后仅需求解一个非线性代数方程,该方程可用解析形式表达,本文提出的方法,具有计算速度快,容易处理各种边界条件和载荷,简便等优点。三个算例表明,利用本文的方法可获得满意的结果。