A numerical method is presented for computation of eigenvector
derivatives used an iterative procedure with guaranteed convergence. An approach
for treating the singularity in calculating the eigenvector derivatives is
presented, in which a shift in each eigenvalue is introduced to avoid the
singularity. If the shift is selected properly, the proposed method can give very
satisfactory results after only one iteration. A criterion for choosing an adequate
shift, dependent on computer hardware is suggested: it is directly dependent on
the eigenvalue magnitudes and the number of bits per numeral of the computer.
Another merit of this method is that eigenvector derivatives with repeated
eigenvalues can be easily obtained if the new eigenvectors are calculated. These
new eigenvectors lie Uadjacent" to the m (number of repeated eigenvalues) distinct
eigenvectors, which appear when the design parameter varies. As an
example to demonstrate the efficiency of the proposed method in the case of distinct
eigenvalues, a cantilever plate is considered. The results are compared with
those of Nelsons method which can find the exact eigenvector derivatives. For
the case of repeated eigenvalues, a cantilever beam is considered. The results are
compared with those of Daileys method which also can find the exact
eigenvector derivatives. The design parameter of the cantilever plate is its
thickness, and that of the cantilever beam its height.