AN EFFICIENT ALGEBRAIC-METHOD FOR THE COMPUTATION OF NATURAL FREQUENCY AND MODE SHAPE SENSITIVITIES .2. MULTIPLE NATURAL FREQUENCIES

In this paper an efficient algorithm whose stability is proved is deri ved for the computation of eigenpair derivatives for the real symmetri c eigenvalue problem with multiple eigenvalues. The eigenpair derivati ves can be obtained by solving algebraic equations with side condition s in the case of multiple eigenvalues, as well as distinct ones. For t he eigenvalue problem with multiple natural frequencies, the adjacent eigenvectors are used in the algebraic equation as side conditions, th ey lie adjacent to the m (multiplicity of multiple eigenvalue) distinc t eigenvalues, which appear when a design parameter varies. As an exam ple to demonstrate the efficiency of the proposed method in the case o f multiple eigenvalues, a cantilever beam is considered. The results o f the proposed method for calculating the eigenpair derivatives are co mpared with those of Dailey's method which finds the exact eigenvector derivatives. The design parameter of the cantilever beam is its heigh t. Copyright (C) 1996 Elsevier Science Ltd.