基于改进Ritz法的耗能减震高层建筑结构地震响应分析

IMPROVED RITZ METHOD FOR SEISMIC RESPONSE ANALYSIS OF TALL BUILDING WITH DAMPERS

用改进Ritz法计算耗能减震高层建筑结构的地震响应。改进Ritz法采用基于外荷载空间分布的Ritz向量和基于外荷载频率的Ritz向量。其中,基于外荷载空间分布的Ritz向量用Lanczos法形成。基于外荷载频率的Ritz向量则用外荷载主频的平方进行特征值平移后再用Lanczos法形成。文中还给出上述两种Ritz向量的截断标准。之后用改进Ritz法的Ritz向量对结构动力方程进行线性变换。由于耗能减震高层建筑结构的阻尼是非比例阻尼,广义阻尼矩阵是非对角矩阵,所以文中采用拟力实模态法对线性变换后的耦联动力方程进行求解。最后的算例说明该方法用于耗能减震高层建筑结构的地震响应分析是有效可行的。

The improved Ritz method is introduced to analyze seismic response of tall building with passive energy dissipation devices, in which both load dependent Ritz vectors and frequency dependent Ritz vectors are put to use. The former vectors are generated by Lanczos algorithm, while the generation process of the later vectors is after eigenvalue shift according to the square of the predominant excitation frequency, though they are still formed by Lanczos algorithm. The cut-off criteria for Ritz vectors are also introduced. Then the Ritz vectors are employed to transform the dynamic equation from geometric coordinates to generalized Ritz coordinates. Since the damping of tall building with damper is non-proportional, dynamical equation transformed is in the coupling form. So pseudo-force method is employed to solve the coupled equation. Numerical example verifies the effectiveness of the proposed method for seismic analysis of tall building with damper.