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I.W. Lee, M.-C. Kim and H.J. Jung

Department of Civil Engineering, Korea Advanced Institute of Science and Technology, Taejon, Korea

doi:10.4203/ccp.55.4.1

I.W. Lee, M.-C. Kim, H.J. Jung, "Solution of Eigen Problems for Non-Proportional Damping Systems by Lanczos Method", in B.H.V. Topping, (Editor), "Advances in Computational Structural Mechanics", Civil-Comp Press, Edinburgh, UK, pp 69-75, 1998. doi:10.4203/ccp.55.4.1

Abstract

A solution method is presented to solve the eigenproblem arising in the dynamic analysis of non-proportional damping systems with symmetric matrices. The method is based on the use of Lanczos method to generate one pair of Krylov subspaces of trial vectors, which is then used to reduce a large eigenvalue problem to a much smaller one. The method retains the n order quadratic eigenproblem, without the need to use the method of matrix augmentation traditionally used to cast the problem as a linear eigenproblem of order 2n. In the process, the method preserves the sparseness and symmetry of the system matrices and does not invoke complex arithmetic, therefore, making it very economical for use in solving large problems. Numerical results are presented to demonstrate the good efficiency and accuracy of the method.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 55 ADVANCES IN COMPUTATIONAL STRUCTURAL MECHANICS Edited by: B.H.V. Topping Paper IV.1 Solution of Eigen Problems for Non-Proportional Damping Systems by Lanczos Method I.W. Lee, M.-C. Kim and H.J. Jung Department of Civil Engineering, Korea Advanced Institute of Science and Technology, Taejon, Korea doi:10.4203/ccp.55.4.1 purchase the full-text of this paper Full Bibliographic Reference for this paper I.W. Lee, M.-C. Kim, H.J. Jung, "Solution of Eigen Problems for Non-Proportional Damping Systems by Lanczos Method", in B.H.V. Topping, (Editor), "Advances in Computational Structural Mechanics", Civil-Comp Press, Edinburgh, UK, pp 69-75, 1998. doi:10.4203/ccp.55.4.1 Abstract A solution method is presented to solve the eigenproblem arising in the dynamic analysis of non-proportional damping systems with symmetric matrices. The method is based on the use of Lanczos method to generate one pair of Krylov subspaces of trial vectors, which is then used to reduce a large eigenvalue problem to a much smaller one. The method retains the n order quadratic eigenproblem, without the need to use the method of matrix augmentation traditionally used to cast the problem as a linear eigenproblem of order 2n. In the process, the method preserves the sparseness and symmetry of the system matrices and does not invoke complex arithmetic, therefore, making it very economical for use in solving large problems. Numerical results are presented to demonstrate the good efficiency and accuracy of the method. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £95 +P&P)
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