IMPROVED FIRST-ORDER APPROXIMATION OF EIGENVALUES AND EIGENVECTORS

A method based on reduced basis approximation concepts is presented fo r improved first order approximation of eigenvalues and eigenvectors o f modified structural dynamic systems. The terms of a local approximat ion based on Taylor or matrix power series are used as basis vectors f or approximating the perturbed eigenparameters, For each eigenmode, a reduced eigensystem is generated by using the baseline eigenvector and the first-order approximation term as Ritz vectors, The solution of t he reduced eigensystem leads to two possible estimates of each perturb ed eigenvalue and eigenvector, Criteria for selection of the best appr oximation are presented. The zero- and first-order Rayleigh quotient a pproximation can be directly recovered as special cases of the present method. Results are presented for approximate dynamic reanalysis of a 25-bar planar truss structure. It is shown that high-quality approxim ation of the perturbed eigenparameters can be obtained for moderate pe rturbations in the stiffness and mass matrices. For very large local p erturbations of the structure, including deletion of some structural m embers, it is shown that the present method yields reasonable-quality approximations.