Local modifications of damped linear systems

A procedure is developed for determining the eigenvalues and eigenvectors of a discrete linear-vibration system resulting from the addition or removal of a discrete element. In this procedure the known characteristics of the original system are used to generate the modified characteristic equation directly without having to solve the modified eigenvalue problem explicitly. Because of the form of the modified characteristic equation, the problem is ideally suited to numerical solution by the Newton Raphson iteration procedure. If repeated eigenvalues exist, the system matrices may not be diagonalizable by classical modal methods. However, the system can be reduced to Jordan Canonical form and the procedure presented incorporates this possibility. © 1971, American Institute of Aeronautics and Astronautics, Inc., All rights reserved