Ｖ形河谷中土石坝垂直振动的近似解析

假设坝体的剪切模量随深度呈指数变化，运用三维剪切楔理论，导出了土石坝垂直振动的控制微分方程，采用分离变量和伽辽金逼近法求得了计算土石坝垂直振动前三阶振型自频率的代数公式；然后应用反应谱技术，获得了相应的估计土石坝垂直地震反应的最大位移、最大速度、最大加速度以及最大应力的计算公式。

Approximate Solution to Vertical Vibration of Earth-Rock Dams in Triangular Canyons

In this paper, an approximate theoretical method is proposed for evaluation of vertical earthquake responses of inhomogeneous earth rock dams in triangular canyons. Under the assumption that the shear modulus of dam material varies with depth as an exponent function, and based on the three dimensional shear wedge theory, a governing differential equation of vertical vibration is derived for earth rock dams. Then, by use of the variable separation and Bubnov Galerkin method, some algebraic formulas are derived for calculation of the natural frequencies of the first, second, and third vibration modes of dams, and by use of the technique of response spectrum, some corresponding formulas are obtained for calculation of some maximum values reflecting earthquake responses of dams, such as the maximum dynamic displacement, velocity, acceleration, stress, and so on.