Computational Mechanics for the Twenty-First Century
Edited by: B.H.V. Topping

Chapter 19

THE RATIONAL KRYLOV ALGORITHM FOR NONLINEAR EIGENVALUE PROBLEMS

P. Hager and N.E. Wiberg
Department of Structural Mechanics, Chalmers University of Technology, Gothenburg, Sweden

This paper deals with free vibration analysis of damped mechanical systems, where the damping effects are modelled by a viscoelastic constitutive relation. The equations of motion are solved approximately by the displacement based Finite Element Method, FEM. The resulting FE equations is put as a nonlinear eigenproblem involving matrices of large order. We study a method to solve the nonlinear eigenproblem by means of rational Krylov, formulated in the RKS ALGORITHM. Numerical examples show that the proposed technique is effective and yields accurate solutions.

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