计算重根特征向量一阶导数的完备模态法的一种改进

在重根特征向量导数计算的完备模态法的基础上，利用原特征值问题的二阶导数，推导了一种特征向量一阶导数的计算方法。该法不仅适用于重特征值问题，对于非重特征值问题，也具有明显的优越性。

Improved Complete Modal Method for Computing Eigenvector Derivatives at Repeated Eigenvalues

In modal analysis of symmetrical structures such as aircraft and buildings, repeated(especially double) eigenvalues occur.Zhang et al gave a complete modal method for determining first derivatives of eigenvectors at repeated eigenvalues[3].We find that this method needs to be improved if real success in such determination is to be attained.Utilizing eqs.(1)through(18),we show that the method of Ref[3]cannot in general really succeed in determining first derivatives of eigenvectors at repeated eigenvalues.The trouble with method of Ref.[3] is that in eq.(11)is not unique. In eq.(19),we replace with Z.which is unique. With this improvement of Zhang's complete modal method,after derivation,we obtain eqs.(32) and (35),which can be used really successfully to compute first derivatives of eigenvectors at repeated eigenvalues.