• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.243-248
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• 1997

A full multigrid scheme was used in computing some eigenvalues of the Laplace eigenvalues problem with the Dirichlet bound-ary condition. We get a system of algebraic equations with an aid of finite difference method and apply subspace iteration method to the system to compute first some eigenvalues. The result shows that this is very effective in calculating some eigenvalues of this problem.

• Structural Engineering and Mechanics
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• v.16 no.3
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• pp.341-360
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• 2003

The goal of this paper is to determine the eigenvalues of a uniform rectangular plate carrying any number of spring-damper-mass systems using an analytical-and-numerical-combined method (ANCM). To this end, a technique was presented to replace each "spring-damper-mass" system by a massless equivalent "spring-damper" system with the specified effective spring constant and effective damping coefficient. Then, the mode superposition approach was used to transform the partial differential equation of motion into the matrix equation, and the eigenvalues of the complete system were determined from the associated characteristic equation. To verify the reliability of the presented theory, all numerical results obtained from the ANCM were compared with those obtained from the conventional finite element method (FEM) and good agreement was achieved. Since the order of the property matrices for the equation of motion obtained from the ANCM is much lower than that obtained from the FEM, the CPU time required by the ANCM is much less than that by the FEM.

• Smart Structures and Systems
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• v.20 no.3
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• pp.263-272
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• 2017

This paper presents the time response of a mixed vibration system with the viscous damping and the hysteretic damping. There are two ways to derive the time response of such a vibration system. One is an analytical method, using the contour integral of complex functions to compute the inverse Fourier transforms. The other is an approximate method in which the analytic functions derived by Hilbert transform are expressed in the state space representation, and only the effective eigenvalues are used to efficiently compute the transient response. The unit impulse responses of the two methods are compared and the change in the damping properties which depend on the viscous and hysteretic damping values is investigated. The results showed that the damping properties of a mixed damping vibration system do not present themselves as a linear combination of damping properties.

• Structural Engineering and Mechanics
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• v.18 no.3
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• pp.331-342
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• 2004

The vibration control problem of structures with random parameters is discussed, which is approximated by a deterministic one. A method for calculating the standard deviations of eigenvalues of the closed-loop systems is presented by using the random perturbation. The method presented in this paper will not require the distribution function of the random parameters of the systems other than their means and variances. Similarly, the distribution function of the random eigenvalues will not be computed other than their means and variances. The standard deviations of eigenvalues of the uncertain closed-loop systems can be used to estimate the stability robustness. The present method is applied to a vibration control system to illustrate the application. The numerical results show that the present method is effective.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.162-167
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• 1994

An effective and disturbance suppressible controller can be obtained by assigning the left eigenstructure (eigenvalues/left eigenvectors) of a system. However, the disturbance decouplability is governed by the right eigenstructure(eigenvalues/right eigenvectors) of the system. In this paper, in order to obtain a disturbance decouplable as well as effective and disturbance suppressible controller, the concurrent assignment scheme of the left and right eigenstructure is proposed. The biorthogonality property between the left and right modal matrices of a system well as the relations between the achievable right modal matrix and states selection matrices are used to develop the scheme. The proposed concurrent eigenstructure assignment scheme guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible(achievable) sets of eigenvectors in the least square sense, respectively. A numerical example is presented to illustrate the usefulness of the proposed scheme.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.10a
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• pp.124-129
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• 2011

An improved NDIF method is introduced to efficiently extract eigenvalues of two-dimensional, arbitrarily shaped acoustic cavities. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped acoustic cavities, membranes, and plates, has the feature that it yields highly accurate eigenvalues compared with other analytical methods or numerical methods (FEM and BEM). However, the NDIF method has the weak point that the system matrix of the NDIF method depends on the frequency parameter and, as a result, a final system equation doesn't take the form of an algebra eigenvalue problem. The system matrix of the improved NDIF method developed in the paper is independent of the frequency parameter and eigenvalues can be efficiently obtained by solving a typical algebraic eigenvalue problem. Finally, the validity and accuracy of the proposed method is verified in two case studies, which indicate that eigenvalues and mode shapes obtained by the proposed method are very accurate compared to the exact method, the NDIF method or FEM(ANSYS).

• Journal of information and communication convergence engineering
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• v.13 no.4
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• pp.241-247
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• 2015

Cognitive radio has been attracting increased attention as an effective approach to improving spectrum efficiency. One component of cognitive radio, spectrum sensing, has an important relationship with the performance of cognitive radio. In this paper, after a summary and analysis of the existing spectrum-sensing algorithms, we report that the existing eigenvalue-based semi-blind detection algorithm and blind detection algorithm have not made full use of the eigenvalues of the received signals. Applying multi-antenna systems to cognitive users, we design a variety of spectrum-sensing algorithms based on the joint distribution of the eigenvalues of the received signal. Simulation results validate that the proposed algorithms in this paper are able to detect whether the signal of the primary user exists or not with high probability of detection in an environment with a low signal-to-noise ratio. Compared with traditional algorithms, the new algorithms have the advantages of high detection performance and strong robustness

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.230-235
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• 1996

Eigenstructure (eigenvalues/eigenvectors) assignment has been shown to be a useful tool for flight control system design. In the sense of the eigenstructure assignment, the effectiveness and disturbance suppressibility of a controller depend mainly on the left eigenstructure (eigenvalues/left eigenvectors) of a system. On the other hand, the disturbance decouplability is governed by the right eigenstructure (eigenvalues/right eigenvectors) of the system. In this paper, in order to obtain a disturbance decouplable as well as effective and disturbance suppressible controller, a concurrent assignment methodology of the left and right eigenstructures is proposed. The biorthogonality condition between the left and right modal matrices of a system as well as the relations between the achievable right modal matrix and state selection matrices are used to develop the methodology. The proposed concurrent eigenstructure assignment methodology guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible(achievable) sets of eigenvectors in the least square sense, respectively. The proposed design methodology is applied to designing a lateral flight control system for an L-1011 aircraft with disturbances.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.1415-1416
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• 2011

• Transactions of the Korean Society of Machine Tool Engineers
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• v.15 no.3
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• pp.8-16
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• 2006

This paper discusses design sensitivity analysis and its application to a structural dynamics modification. Eigenvalue derivatives are determined with respect to the element parameters, which include intrinsic property parameters such as Young's modulus, density of the material, diameter of a beam element, thickness of a plate element, and shape parameters. Derivatives of stiffness and mass matrices are directly calculated by derivatives of element matrices. The first and the second order derivatives of the eigenvalues are then mathematically derived from a dynamic equation of motion of FEM model. The calculation of the second order eigenvalue derivative requires the sensitivity of its corresponding eigenvector, which are developed by Nelson's direct approach. The modified eigenvalue of the structure is then evaluated by the Taylor series expansion with the first and the second derivatives of eigenvalue. Numerical examples for simple beam and plate are presented. First, eigenvalues of the structural system are numerically calculated. Second, the sensitivities of eigenvalues are then evaluated with respect to the element intrinsic parameters. The most effective parameter is determined by comparing sensitivities. Finally, we predict the modified eigenvalue by Taylor series expansion with the derivatives of eigenvalue for single parameter or multi parameters. The examples illustrate the effectiveness of the eigenvalue sensitivity analysis for the optimization of the structures.