基于状态空间理论分析圆柱形拱坝静动力响应

Analysis of Static and Dynamical Response of the Cylindrical Arch Dam Based on the State Space Theory

本文应用现代控制论中的状态空间理论,引入圆柱形拱坝内应力与位移作为状态变量,根据圆柱形拱坝的控制方程及其混合能量变分原理,推导出状态方程。对静力问题,将指数矩阵函数展成级数来求解;对动力问题,采用状态空间迭代法来求解。由于状态空间法同时可算出各种应力与位移量,因此应力与位移的精度均较高。文中给出圆柱形拱坝动力响应问题的数值算例,所得计算结果与其他方法进行了比较。

By applying the state space theories in the modem control theory, the displacement and the stress in cylindrical arch dam are taken as state variables. According to the control equation of cylindrical arch dam and mixed energy variation principle, the state equation is derived. The exponential matrix function exhibition series was applied to solve the static problem; adopt the state space iterative method was applied to solve dynamic problem. Since state space method can at the same time make various stress and displacement finally to measure, therefore, the precision of stress and displacement is higher. The numerical example of problem to dynamical response of the cylindrical arch dam is given, and results of other methods are compared.