Eigenvibrations of a plate with elastically attached loads

Abstract

In this contribution we consider the rational eigenvalue problem governing free vibrations of a plate with elastically attached masses. We discuss the numerical solution of the problem by an iterative projection method generalizing the Arnoldi method for linear eigenproblems. Taking advantage of a minmax characterization of the eigenvalues for nonoverdamped problems the projected eigenproblems are solved by safeguarded iteration. Special care is taken to determine all eigenvalues between two consecutive poles, and to inhibit the method from converging to the same eigenvalues repeatedly.