受迫振动的随机响应在重力坝抗震中的应用

Application of random response of forced vibration in seismic resistance of gravity dam

文中为解决地震过程中重力坝的安全性问题,将随机微分方程理论引入到线性单自由度系统受迫振动的随机响应计算当中,提取质体初始位移和外界激励为随机变量,建立了基于受迫振动微分方程的随机微分方程模型,证明了其解过程为马尔可夫过程,并根据Fokker-Planck方程求解过程一阶联合概率密度。最后用实例验证了其方法在重力坝抗震中的有效性及可行性。

In order to solve the safety problem of gravity dam during the process of earthquake, the stochastic differential equation theory is introduced into the stochastic response calculation of the forced vibration of the linear single degree of freedom system. Extracting the initial displacement of the plastids and the external excitation as the random variables, based on the differential equation of forced vibration the stochastic differential equation model is built. It is proved that the process is the Markov process. The first order joint probability density is solved according to the Fokker-Planck equation. At last, these examples are given to demonstrate the effectiveness and feasibility of the method in seismic resistance of gravity dam.