大型非比例阻尼线性系统的地震反应复振型分析方法

The applied method of dynamic analysis for large linear structures with non-classical damping

对于大型非比例阻尼线性系统,当采用基于复振型的振型叠加方法进行动力反应分析时,按照通用算法(例如雅克比法)求解结构全部振型向量的计算工作量很大,甚至是不现实的。本文将经典阻尼系统中行之有效的Lanczos法和子空间迭代法加以推广和改进,给出了一组可对原来的方程进行自由度缩减的实向量基,然后与Foss变换相结合,得到一组实用的复向量基,使之适用于求解复杂非比例阻尼线性系统的任意低阶复振型和相应的复特征值,适用于任意扰力作用下的动力反应分析。理论推导和实例计算表明,本文所给出的复向量基概念清晰,计算效率高,能够适应对具有非比例阻尼特性的大型复杂结构进行动力分析的实际需要,其中包括地震作用下的时程分析和反应谱振型叠加分析。

For large linear non-classically damped system, when mode superposition method based on complex vector is used to analyze seismic responses, the amount of calculating total mode vectors using Jacobi method is fairly large and unpractical indeed. In this paper, Lanczos algorithm and subspace iteration method, which are effective in computing modes of classical damped linear system, are extended and modified to find a set of real vector basis to reduce freedom of primary equation. Combined with Foss transform, a set of applied complex vector basis is derived to analyze the first order complex eigenpairs for dynamic analysis of large non-classically damped linear system under random excitation. From the theoretical analysis and numerical examination, it could be pointed out that the complex vector basis derived in this paper not only has clear physical significance and good computational efficiency, but also is adapted to analyze dynamic responses of large non-classically damped linear system, including seismic responses in time domain and mode superposition based on seismic design spectra in frequency domain.