弹性系统动力学总势能不变值原理及其在振动和动力稳定性分析中的应用

讨论了拉格朗日方程和哈密顿原理的不足 ,介绍了由曾庆元 2 2年前首次提出的弹性系统动力总势能不变值原理及形成系统矩阵的“对号入座”法则 ,阐明了不论系统如何复杂 ,其空间振动方程均可利用此原理和此法则简便建立 .它们独特的优点体现在解决了列车 桥梁 (或列车 轨道 )时变系统横向振动的问题 ,而这两个复杂动力系统的空间振动方程不能由动静法、拉格朗日方程或哈密顿原理等方法建立 .曾庆元和他的研究生们将列车 桥梁 (或列车 轨道 )视为一个整体系统 ,利用前述原理和法则建立了此系统的空间振动方程 ,在国内外首次求得了桥梁和轨枕的振动波形图 ,与相应的实测波形图良好接近 .文末提出了弹性动力系统总势能的概念 ,基于此概念 ,又提出了判别系统运动稳定性的能量准则 ,两个例题说明了此能量准则的应用 .

The Principle of Total Potential Energy With Stationary Value in Elastic System Dynamics and Its Application to the Analysis of Vibration and Dynamic Stability

This paper discusses the inadequacies in Lagrange's equations and in Hamilton's principle and introduces the principle of total potential energy with stationary value in elastic system dynamics and the "Set in right position" rule for formulating matrixes, both were first presented by Zeng Qing yuan 22 years ago. It is shown that however complicated an elastic dynamic system may be, its spatial vibration equations can be methodically and easily ormulated by the principle and the rule introduced above. Their peculiar advantages are well embodied in solving the problems in the lateral vibration analysis of train bridge(or train track) time varying system, which are two complex typical dynamic systems whose spatial vibration equations could not be established by using the method of direct equilibrations, Lagrange's equations or Hamilton principle etc.. Zeng Qing yuan and postgraduates regarded the train and the bridge(or track) as one whole system, established the spatial vibration equations of this system by the aforementioned principle and rule, and obtained, for the first time at home and abroad, some vibration wave figures of the bridge and of the tie, which are very close to those experimental wave figures. At the end of the paper, the concept of the total potential energy in an elastic dynamic system is put forward and based on which, the energy criterion distinguishing the stability of motion of a system is also presented. Two examples using the energy criterion to calculate the stability of motion are illustrated.