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Computational Science, Engineering & Technology Series
ISSN 1759-3158
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

Full Bibliographic Reference for this chapter
P. Hager, N.E. Wiberg, "The Rational Krylov Algorithm for Nonlinear Eigenvalue Problems", in B.H.V. Topping, (Editor), "Computational Mechanics for the Twenty-First Century", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 19, pp 379-402, 2000. doi:10.4203/csets.3.19
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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