• Computational Structural Engineering : An International Journal
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• v.1 no.1
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• pp.31-38
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• 2001

In the case of the non-proportionally damped system such as the soil-structure interaction system, the structural control system and composite structures, the eigenproblem with the damping matrix should be necessarily performed to obtain the exact dynamic response. However, most of the eigenvalue analysis methods such as the subspace iteration method and the Lanczos method may miss some eigenvalues in the required ones. Therefore, the eigenvalue analysis method must include a technique to check the missed eigenvalues to become the practical tools. In the case of the undamped or proportionally damped system the missed eigenvalues can easily be checked by using the well-known Sturm sequence property, while in the case of the non-proportionally damped system a checking technique has not been developed yet. In this paper, a technique of checking the missed eigenvalues for the eigenproblem with the damping matrix is proposed by applying the argument principle. To verify the effectiveness of the proposed method, two numerical examples are considered.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.7
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• pp.1479-1486
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• 2011

In this paper, a simple and robust algorithm is proposed for detecting straight line segments in a steel plate image. Line detection from a steel plate image is a fundamental task for analyzing and understanding of the image. The proposed algorithm is based on small eigenvalue analysis. The proposed approach scans an input edge image from the top left comer to the bottom right comer with a moving mask. A covariance matrix of a set of edge pixels over a connected region within the mask is determined and then the statistical and geometrical properties of the small eigenvalue of the matrix are explored for the purpose of straight line detection. Before calculating the eigenvalue, each line segment is separated from the edge image where several line segments are overlapped to increase the accuracy of the line detection. Additionally, unnecessary line segments are eliminated by the number of pixels and the directional information of the detected line edges. The respects of the experiments emphasize that the proposed algorithm outperforms the existing algorithm which uses small eigenvalue analysis.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.854-859
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• 2001

An eigenvalue analysis of a tunable micro-mechanical actuator is presented. The actuator is modeled as a continuum structure. The eigenvalue modified by the tuning voltage is computed through the linearization of the relation between the electrostatic force and the displacement at the equilibrium. A staggered algorithm is employed to perform the coupled analysis of the electrostatic and elastic fields. The stiffness matrix of the actuator is modified at this equilibrium state. The displacement field is perturbed using an eigenmode profile of the actuator. The configuration change of the actuator due to perturbation modifies the electrostatic field and thus the electrostatic force. The equivalent stiffness matrix corresponding to the perturbation and the change in the electrostatic force is then added to stiffness matrix in order to explain natural frequency shifting. The numerical examples are presented and compared with the experiments in the literatures.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.37-49
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• 1999

In this paper we develop a general Homotopy method called the Group Homotopy method to solve the symmetric eigenproblem. The Group Homotopy method overcomes notable drawbacks of the existing Homotopy method, namely, (i) the possibility of breakdown or having a slow rate of convergence in the presence of clustering of the eigenvalues and (ii) the absence of any definite criterion to choose a step size that guarantees the convergence of the method. On the other hand, We also have a good approximations of the largest eigenvalue of a Symmetric matrix from Lanczos algorithm. We apply it for the largest eigenproblem of a very large symmetric matrix with a good initial points.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.1 s.118
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• pp.80-87
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• 2007

In this paper, a method for identifying the location and extent of a damage in a structure using residual forces was presented. Element stiffness matrix reduction parameters in a finite element model were used to describe the damaged structure mathematically. The element stiffness matrix reduction parameters were determined by minimizing a global error derived from dynamic residual vectors, which were obtained by introducing a simulated experimental data into the eigenvalue problem. Genetic algorithm was used to get the solution set of element stiffness reduction parameters. The proposed scheme was verified using Euler-Bernoulli beam. The results were presented in the form of tables and charts.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.5
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• pp.976-983
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• 1988

An efficient unbalance response analysis method for rotor-bearing systems with spin speed dependent parameters is developed by utilizing a generalized modal analysis scheme. The spin speed dependent eigenvalue problem of the original system is transformed into the spin speed independent eigenvalue problem by introducing a lambda matrix, assuming the bearing dynamic coefficients are well approximated by polynomial functions of spin speed. This method features that it requires far less computational effort in unbalance response calculations and that the influence coefficients are readily available. In addition, the critical speeds and the corresponding logarithmic decrements can be readily identified from the resulting eigenvalues.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.195-210
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• 2011

Bernoulli-Euler beam theory is used to develop an exact dynamic stiffness matrix for the flexural-torsional coupled motion of a three-dimensional, axially loaded, thin-walled beam of doubly asymmetric cross-section. This is achieved through solution of the differential equations governing the motion of the beam including warping stiffness. The uniform distribution of mass in the member is also accounted for exactly, thus necessitating the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, examples are given to confirm the accuracy of the theory presented, together with an assessment of the effects of axial load and loading eccentricity.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.4
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• pp.71-82
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• 2001

Using the computer simulation method, we invest19ate the probability distribution of maximum eigenvalue of pair-wise comparison matrix, which has been used as a parameter for measuring the consistency of responses in analytic hierarchy process (AHP). We show that the shape of the distribution of the maximum eigenvalue is different according to the dimension of the matrix. In addition, we cannot find any evidence that the distribution of the Consistency Index is a Normal distribution, which has been claimed in the Previous literature. Accordingly, we suggest using so called K-index calcu1ated based on the concept of cumulative distribution function lather than based on that of arithmetic mean because the probabilistic distribution cannot be assumed to be a Normal distribution. We interpret the simulation results by comparing them with the suggestion of Saaty[11]. Our results show that using Saaty＇s value could be too generous when the dimension of the matrix is 3 and strict over 4. Finally, we propose new criteria for measuring the response consistency in AHP.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.6A
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• pp.888-893
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• 1999

This paper introduces M-ary multitrack run-length (d.k) constrained codes for optical storage systems. We calculate capacities and densities of the codes. We have driven a general form of the state transition matrix for M-ary multitrack (d,k) codes. Using the largest eigenvalue of the transition matrix, we calculate the capacity and density. The capacity approaches to the limit with a small k constraint compared to single-track codes.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.79-92
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• 2000

We investigate numerical properties of Newton's algorithm for improving an eigenpair of a real matrix A using only fixed precision arithmetic. We show that under natural assumptions it produces an eigenpair of a componentwise small relative perturbation of the data matrix A.