基于实用完备模态的动柔度式——特征向量导数

Dynamic Flexibility Formulae Based on Practical Complete Modal Space——Eigenvector Derivatives

首次提出了用于计算很多特征向量导数的一种精确动柔度法和一种简化动柔度法。精确动柔动式是依赖作者提出的实用完备模态空间建立的。与所有现成的“直接法”（即动刚度法）不同，本方法相当于只需要求解特征向量导数支配方程一次便可计算很多特征向量的导数，因此，待求导的特征向量个数越多，本文方法的计算效率越高。精确动柔度法可给出“导数”的精确值，简化动柔度法可引出良好的近似值。

A practical and simplified technique for computing a large number of eigenvector derivatives of a complex structural system has been developed. This technique uses the dynamic flexibility method and is based on the practical complete modal space approach. Unlike other published methods, this technique requires only to solve the system governing equation once, regardless the number of eigenvector derivatives needed to be computed. Using this method, the computer time required to obtain more than one eigenvector derivative can be dramatically reduced. This method gives the mathematical expressions of the solutions for eigenvector derivatives and is easier for engineers to perform theoretical formulation. This method can be applied to system with and without repeated eigenvalues. Both theoretical derivations and numerical results are presented. This method gives better numerical precision and can be a very good tool for engineers to compute many eigenvector derivatives.