(西安交通大学，西安 710049)

［摘要］考虑层间结构分布质量及楼层处集中质量，在层局部坐标中建立运动微分方程。建立频域内的层间场传递矩阵，利用楼层集中质量动力平衡建立频域内的层间点传递矩阵。引入基础动力刚度并利用基础动力平衡，结合傅氏变换，得到结构地震反应与竖向地震作用输入之间的关系，并给出相关求解方法。将文中模型用于求解结构在竖向地震作用下的动力反应，并与常用的集中质量模型和均布质量模型的计算结果进行对比。算例表明，文中模型考虑了结构实际质量分布，用于多、高层建筑结构的土结构动力相互作用的分析中，结果合

理可靠，并能更好地适用于质量和刚度分布比较复杂的结构形式。

［关键词］土-结构动力相互作用；竖向地震反应；频域分析；传递矩阵

Frequency-domain approach for vertical dynamic soil-structure interaction

Zhu Wenwei, Zhang Shuoying

(Xi′an Jiaotong University，Xi′an 710049,China)

Abstract:In order to take into account the distributed mass along the stories of structure, equation of motion is given in the local coordinates of the story. The field transfer matrix is founded in the frequency domain and the point transfer matrixis founded by using the dynamic equilibrium of the lumped mass at the floor. The dynamic stiffness of base is introduced and the dynamic equilibrium of base isused. Structural response under vertical earthquake can be obtained through theFast Fourier Transform technique. For the sake of contrast, it gave the examples of the model and two other ordinarily used models, the lumped mass model and the uniformly distributed mass model. It showed that the method takes into account the real mass distribution, so that numerical results are more reasonable and more reliable than the other models. The model is capable of analyzing multi-stories and high-rise structures with soil-structure interaction being taken into account and could be well used in those structures with much more complicated mass and stiffness distributions.

Keywords:soil-structure interaction; vertical seismic response; frequency-domain analysis; transfer matrix