A new method for calculating derivatives of eigenvalues and eigenvectors for discrete structural systems

A new method is presented for calculating the derivatives of eigenvalues and eigenvectors for discrete structural systems. In the cases of distinctive eigenvalues, proportional damping is assumed and the exact eigen-pair derivatives of arbitrary order are calculated. For a repeated eigenvalue, its first-order derivatives are calculated by solving a reduced eigenvalue problem of order equal to the eigenvalue's geometric multiplicity. The new method is computationally efficient and numerically robust. Examples are presented to illustrate the use and effectiveness of the new method.