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.