特征向量导数计算的简单动柔度法

Simple Dynamic Flexibility Method for Calculation of Eigenvector Derivatives

在计算很多特征向量导教时，以Nelson法为代表的直接法都显出效率低下，第二作者为此发展了直接法的一个分支──动柔度法。本文虽是动柔度法的继续，但就非重特征值情况而言，它是一种最好的动柔度法，因为它像Fox法一样，“一步求解”便可获得通解，然而它又不存在Fox法的缺点──支配方程的系数阵为满阵，所以说，在计算很多非重特征值的特征向量导数时，简单动柔度法不仅在计算步骤上比Nelson法简单，而且在计算时间上成倍地减少。

When rnany eigenvector derivatives heed to be computed, the computational efficiency ofNelson's method,that is a deputy to the direct method,is lower. For this reason,the second author devel-oped a category of dynamic flexibility method,for example,the perturbation dynamic flexibility method andintermediate dynamic flexibility method,which can be considered as a branch of direct method. In order tosimplify the process of calculation for above -stated dynamic flexibility methods,a simple dynamic flexibili-ty (SDF)method is proposed in this paper. The SDF method is a continuation of early dynamic flexibilitytechnique,but it is best dynamic flexibility procedure for the computation of many eigenvector derivativeswith non-repeated eigenvalues,since it not only possesses the merits of early dynamic flexibility methods,but also overcomes the shortcomes of them. As with Fox's method the SDF method can obtain the generalsolution through'one -step solving'process,but the SDF method has not the shortcome of Fox's method,that is,the coefficient matirx of governing equation for Fox's method is a full matrix,and that for the SDFmethod is a band-state matrix. So in the calculation of many eigenvector derivatives with non-repeatedroots,adopting SDF method can save obviously the computer time in comparison with Nelson's method.