An efficient technique for the computation of eigenvalue and eigenvector derivatives of cyclic structures

Abstract

Computing the derivatives of repeated eigenvalues and associated eigenvectors is computationally expensive. Since the eigenvectors are not unique, the second order derivatives of mass and stiffness matrices are required (Mills-Curran, Dailey). This paper concerns the use of symmetry properties of cyclic structures in order to reduce the computational efforts. By employing the approach, the solution of eigenvector derivatives can be attained independently and it is therefore attractive for parallel computation. It will be shown that the proposed technique is more efficient than previous methods.