结构动力响应分析的李雅普诺夫法  

LYAPUNOV METHOD FOR THE ANALYSIS OF STRUCTURAL DYNAMIC RESPONSES

作　　者：李秀梅[1] 吴锋[1] 苏金凌[1] 

机构地区：[1]广西大学土木建筑工程学院,南宁530004

出　　处：《工程力学》2010年第11期16-21,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(19872001);广西科学研究与技术开发计划项目(桂科攻0861001-12)

摘　　要：将结构的位移及速度响应作为状态变量,采用Lyapunov(李雅普诺夫)人工小参数法求解状态方程,导出状态方程一种新的离散形式的级数解。将秦九韶算法引入级数解的计算,提高了计算的效率和稳定性,同时给出了该文算法的计算格式和步骤。该算法无需对转换矩阵H求逆,也无须做指数矩阵eH运算,仅做矩阵向量相乘及向量求和运算,计算稳定而且效率高,精度仅由级数项数有关的几个参数控制,很容易达到任意精度要求,适合并行计算及压缩存储,可应用于工程结构抗震计算。最后通过典型算例进一步证实了该文算法的精度和效率。In this paper, the displacement and velocity response of a structure are taken as the state variable. In order to solve the state equation, the Lyapunov’s artificial small parameter method is used, and a new series solution for the time-discrete form of the equation is presented. Hornor’s scheme is applied to the calculation of the series solution, and the computational efficiency and stability are therefore greatly improved. The corresponding computation scheme and procedure for the proposed algorithm are also presented. The algorithm is only composed of repetitious matrix-vector multiplication and vector summation and the calculations of the inverse matrix H^ -1 and exponential matrix e^H are excluded, which results in high computational efficiency and stability. The accuracy of the algorithm is only controlled by the parameters related to the series, thusly the algorithm can easily achieve arbitrary-order accuracy in theory, and is suitable for parallel computing and compression storage. The proposed method can be used for seismic calculations of engineering structures. Two numerical examples are given to demonstrate the validity and efficiency of the method.

关 键 词：动力响应 状态方程 李雅普诺夫法 级数解 秦九韶算法 

分 类 号：TU311.3[建筑科学—结构工程]