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本文讨论了平面有限厚弹性地基上结构的抗震分析,提出用振型分解法求解结构一地基系统的动力反应。该法基于地震时结构的高阶振型的反应一般较小,而考虑用少数几个较低的基本振型来描述系统的运动,将动力方程化为只含少数几个广义坐标的耦合的常微分方程组,然后用逐步数值积分的方法求解。与常用的逐步求解法相比,这一方法大大减少了问题的未知数,求解简便,并且能够应用于振型迭加法不适用的非比例阻尼情况。
This paper discusses the seismic analysis of the structure on a plane-thick finite elastic foundation, and proposes the vibration-type decomposition method to solve the dynamic response of the structural-foundation system. The method is generally based on the response of the high-order modes of the structure at the time of the earthquake. It is considered to describe the motion of the system using a few lower basic mode shapes and transform the dynamic equation into a coupled ordinary differential with only a few generalized coordinates. The equations are then solved using a stepwise numerical integration method. Compared with the commonly used stepwise solution method, this method greatly reduces the number of unknowns of the problem, and is easy to solve. It can also be applied to non-proportional damping cases where the mode superposition method is not suitable.