Computation of Eigenvector Derivatives Using HPDF Expression

The computation of many eigenvector derivatives is required in the fields of structural optimal design, and update and localization of model error. Existing methods, except for the incomplete truncated modal methods and a dynamic flexibility method proposed by the writers, are not efficient for the calculation of many eigenvector derivatives. The precision of the incomplete truncated modal methods sometimes is poor. For this reason, a higher-precision dynamic flexibility (HPDF) expression is first proposed. Then on the basis of this HPDF expression, both a higher-precision truncated modal method and an HPDF method have been analyzed. The HPDF method is a different form of the early dynamic flexibility method. The HPDF expression is based on a geometrical series expansion. That is, the first several terms of the series can allow the solution to converge to an exact value of the dynamic flexibility expression when the difference between each eigenvalue at the frequency axis is large. Once the concentrated eigenroots exist, the convergence speed slows. This limitation can be overcome using a shifting frequency technique.