拟合楼层反应谱的三向地震动时程生成方法研究

Generation of tri-directional seismic time histories compatible with floor response spectra

为获得满足规范要求的拟合楼层反应谱的三向地震动时程,采用六阶常微分方程的本征函数为基函数,分解并重构天然地震动时程;通过构建影响矩阵,迭代计算逐步调整本征函数的幅值系数,最终实现预设拟合精度;引入正交化方法保证三向地震动时程两两之间的统计独立性,并通过两组算例提供验证。研究结果表明,迭代所得时程反应谱与目标楼层反应谱的拟合精度较高,迭代过程中时程反应谱均匀一致地向目标谱逼近,迭代过程收敛,所得三向地震动时程均无零飘现象,满足规范要求。

In order to obtain the tri-dimensional seismic ground motion time histories which are compatible with the corresponding floor response spectra,the eigenfunctions of the sixth order ordinary differential equation are used as the basis functions to decompose and reconstruct the real recorded earthquake ground motion.By constructing the influence matrix,the amplitude coefficient of the eigenfunction is gradually adjusted through iterative calculation,and the preset fitting accuracy threshold is finally achieved.The orthogonalization procedure is introduced to ensure the statistical independence between the tri-directional time histories,and two sets of numerical examples are provided.The examples show that it is capable of achieving high matching accuracy between the response spectra of generated time histories and the target spectra.During the iteration,the time history response spectrum uniformly approaches the target spectra.The iterative process converges;the generated seismic time histories are drift-free and satisfy the code requirements.