EIGENVALUE EMBEDDING IN FINITE ELEMENT MODEL UPDATING OF GYROSCOPIC SECOND-ORDER VIBRATING STRUCTURES 6th BRAZILIAN CONFERENCE ON DYNAMICS, CONTROL AND THEIR APPLICATIONS ñ DINCON 2007

The eigenvalue embedding problem addressed in this paper is the one of reassigning a few troublesome eigenvalues of a nite element model to some suitable chosen ones, in such a way that the updated model keeps its symme- try properties and the remaining large number of eigenval- ues and eigenvectors of the original model is to remain un- changed. This problem naturally arises in the process of sta- bilizing large-scale system where dangerous vibrations had been detected, and which can be responsible for undesired phenomena such as resonance. The model matrices are up- dated using low rank updates that keep their structure regard- ing symmetry. Algorithm and numerical examples are pro- vided. Numerical experimentation with real-life data, com- ing from a well-known matrix web repository, have been pre- sented.