Author
Man-Gi Ko
Bio: Man-Gi Ko is an academic researcher from Kongju National University. The author has contributed to research in topics: Eigenvalues and eigenvectors & Sturm's theorem. The author has an hindex of 3, co-authored 4 publications receiving 67 citations.
Papers
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TL;DR: In this article, a simplified method for the computation of first-, second-and higher-order derivatives of eigenvalues and eigenvectors associated with repeated eigen values is presented.
35 citations
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TL;DR: In this article, the modified modal methods for computing the sensitivities of the eigenpairs of asymmetric damped system using a few lowest sets of modes are proposed, and the proposed methods achieve better calculating efficiency than the previous modal method.
Abstract: Many real systems such as moving vehicles on roads, missiles following trajectories and ships in sea water have asymmetric mass, damping and stiffness matrices. Eigen-sensitivity analysis methods for the symmetric damped system cannot be used in the asymmetric damped case. Therefore, a method for calculating eigenpair sensitivity of the asymmetric damped system is needed. To do this, a modal method employing a modal superposition idea was recently developed. Since the accuracy of the modal method is dependent on the number of modes used in calculation, the modal method needs higher eigenvectors to guarantee the accuracy. In large-scale systems, however, only a few lower modes are generally considered for the dynamic analysis. Hence, if the modal method is used to obtain the eigen-sensitivity of the large-scale system, the significant errors could not be avoided due to the lack of the information of higher modes. In this paper, the modified modal methods for computing the sensitivities of the eigenpairs of asymmetric damped system using a few lowest sets of modes are proposed. Numerical example shows that the proposed methods achieve better calculating efficiency than the previous modal method. Copyright © 2004 John Wiley Sons, Ltd.
26 citations
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TL;DR: In this paper, the authors present numerical methods of counting the number of eigenvalues for non-proportionally damped systems in some interested regions on the complex plane, such as the soil-structure interaction system, the structural control system and composite structures.
7 citations
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TL;DR: In this article, a Schur-Cohn matrix is constructed from the coeffi-cients of the characteristic polynomial for the damped system, and LDL T factorized using some standard numerical algorithms.
Abstract: This technical note presents a method of checking the number of complex eigenvalues in some interested regions or the multiplicity of some complex eigenvalues for nonproportionally damped system. A Schur-Cohn matrix is constructed from the coeffi- cients of the characteristic polynomial for the damped system, and LDL T factorized using some standard numerical algorithms. By observing signs of the diagonal elements of the above diagonal matrix D, we can determine the number of complex eigenvalues in some interested regions or the multiplicity of some complex eigenvalues, which is very similar to the well-known Sturm sequence property for undamped systems. To verify the applicability of the proposed method, two numerical examples are considered.
2 citations
Cited by
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TL;DR: In this paper, the authors provide an overview along with a critical appraisal of available methods for uncertainty propagation of linear systems subjected to dynamic loading, where uncertain structural properties are treated as random quantities by employing a stochastic approach.
93 citations
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TL;DR: In this paper, the authors proposed a new approach based on auxiliary mass spatial probing using spectral centre correction method (SCCM), to provide a simple solution for damage detection by just using the response time history of beam-like structures.
71 citations
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TL;DR: The aim of this paper is to show how to compute the left and right eigenvector derivatives separately and independently such that those can be computed in a parallel way and the calculation of eigenvalue sensitivity of N damped asymmetric systems with repeated eigenvalues is derived.
48 citations
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TL;DR: In this article, a generalized eigenproblem is formed and its normalizations are presented and discussed, and a unified consideration of the computation of the sensitivity and Hessian matrix is studied for both the self-adjoint and non-selfadjoint cases.
47 citations
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TL;DR: In this paper, an algebraic method is presented for simultaneous computation of the derivatives of eigenvalues and those of their associated right and left eigenvectors, for asymmetric damped systems.
38 citations