基于状态空间理论的工程结构地震时程响应分析

Analysis of time history responses of engineering structures during earthquakes based on state space theory

基于状态空间理论分析与计算工程结构地震时程响应问题,根据结构动力学方程,引入结构系统的状态变量,建立结构地震时程响应分析的状态方程,并给出非齐次状态方程的解.为了求解矩阵指数函数,着重介绍了凯莱-哈密尔顿(Kaley-Hamilton)法、状态空间迭代法和精细积分法.对结构动力时程响应问题按这三种解法分别建立了计算格式,并编制相应计算程序.最后,给出若干数值算例,其计算结果表明,状态空间法分析计算结构动力时程响应,其精度好,效率高,是一种非常有效的方法.

The engineering structure time history response in earthquakes was analyzed by means of state space theory. The state equations of the engineering structure time history responses were established with the inhomogeneous solutions given on the basis of the structure dynamic equations and the state variables. The Kely-Hamilton method, the state space method and the fine integral method were applied with the corresponding computing format and programs to solve the matrix exponential function. Several numerical examples demonstrate that the state space method has better accuracy and higher efficiency for analyzing structures dynamic time history responses.