NUMERICAL-METHOD FOR SENSITIVITY ANALYSIS OF EIGENSYSTEMS WITH NONREPEATED AND REPEATED EIGENVALUES

A numerical method is presented for computation of eigenvector derivat ives used an iterative procedure with guaranteed convergence. An appro ach for treating the singularity in calculating the eigenvector deriva tives is presented, in which a shift in each eigenvalue is introduced to avoid the singularity. If the shift is selected properly, the propo sed method can give very satisfactory results after only one iteration . A criterion for choosing an adequate shift, dependent on computer ha rdware is suggested; it is directly dependent on the eigenvalue magnit udes and the number of bits per numeral of the computer. Another merit of this method is that eigenvector derivatives with repeated eigenval ues can be easily obtained if the new eigenvectors are calculated. The se new eigenvectors lie ''adjacent'' to the m (number of repeated eige nvalues) distinct eigenvectors, which appear when the design parameter varies. As an example to demonstrate the efficiency of the proposed m ethod in the case of distinct eigenvalues, a cantilever plate is consi dered. The results are compared with those of Nelson's method which ca n find the exact eigenvector derivatives. For the case of repeated eig envalues, a cantilever beam is considered. The results are compared wi th those of Dailey's method, which also can find the exact eigenvector derivatives. The design parameter of the cantilever plate is its thic kness, and that of the cantilever beam its height. (C) 1996 Academic P ress Limited