Improving Condensation Methods for Eigenvalue Problems via Rayleigh Functional

The dynamic analysis of structures using the nite element method leads to very large eigenvalue problems. Condensation is often required to reduce the number of degrees of freedom of these problems to manageable size. The (statically or dynamically) condensed problem can be considered as linearization of a matrix eigenvalue problem which is nonlinear with respect to the eigenparameter. As a consequence only a few natural frequencies can be obtained with su cient accuracy. We use the Rayleigh functional of the nonlinear problem to improve the eigenvalue approximations considerably. Two examples are presented to demonstrate the e ciency of the method.