水平地震时斜面水坝受到的非线性动水压力的全过程的解析解

本文给出在非线性Ｒａｙｌｅｉｇｈ阻尼作用下，由水平地震激发的水库内动水压力变化全过程的解析解：在激发初期其幅值较小，可用小参数法使控制方程线性化，从而求得各阶渐近控制方程的解析解；当动水压力的幅值增大到小参数展开不适用时，用ｖａｎ ｄｅｒｐｏｌ法求得非线性控制方程的渐近解，从而显示了动水压力的幅值从有序变化到发生突然跳跃的多值性的非线性本质。

Analytical Solutions in the Whole Procese of NonlinearHydrodynamic Pressure on an Inclined Dam Excited byHorizontal Seismic Force

In this study, we obtain the analytical solutions in the whoe process of a strong earthquake whichinduces the horizontal hydrodynamic pressure on an inclined dam by the horizontal ground motion atthe bottom of a reservoir. In the initial stage while the pressure is small, one may apply the small pa-rameter methed in the perturbation theory to deduce the nonlinear governing equation into a system oflinear asymptotic governing equations, and obtains the unique solution for each. As the pressure in- creases beyond the limit for the small parameter application, we use the van der Pol method to get theasymptotic solution for the nonlinear governing equation, then the pressure by no means varies contin-uously, rather, it's amplitude has sudden finite jump at a sudden instant.