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P. Hager and N.E. Wiberg

Department of Structural Mechanics, Chalmers University of Technology, Gothenburg, Sweden

doi:10.4203/csets.3.19

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

Abstract

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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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Computational Science, Engineering & Technology Series ISSN 1759-3158 CSETS: 3 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 doi:10.4203/csets.3.19 purchase the full-text of this chapter 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 Abstract 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. purchase the full-text of this chapter (price £20) go to the previous chapter go to the next chapter return to the table of contents return to the book description purchase this book (price £138 +P&P)
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