Sensitivity analysis of non-conservative eigensystems

Abstract

An expression for the derivatives of eigenvalues and eigenvectors of non-conservative systems is presented. Contrary to previous methods that use state space form (2 N-space) to consider damping, proposed method solves the eigenpair derivatives of damped system explicitly. The computation size of N-order is maintained and the eigenpair derivatives are obtained simultaneously from one equation so that it is efficient in CPU time and storage capacity. Moreover, this method can be extended to asymmetric non-conservative damped systems. Although additional problems are generated contrary to the eigenpair sensitivity methods of symmetric systems, in asymmetric case, an algebraic method for the eigenpair derivatives can be obtained through similar procedure. The proposed expression is derived by combining the differentiations of the eigenvalue problem and normalization condition into one linear algebraic equation. The numerical stability is proved by showing non-singularity of the proposed equation, and the efficiency of the derived expression is illustrated by considering a cantilever beam with lumped dampers and a whirling beam.