• Journal of Institute of Control, Robotics and Systems
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• v.1 no.2
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• pp.78-82
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• 1995

In this paper, we consider the robustness analysis problem in state space models with linear time invariant perturbations. Based upon the discrete-time Lyapunov approach, sufficient conditions are derived for the eigenvalues of perturbed matrix to be located in a circle, and robustness bounds on perturbations are obtained. Spaecially, for the case of a diagonalizable hermitian matrix the bound is given in terms of the nominal matrix without the solution of Lyapunov equation. This robustness analysis takes account not only of stability robustness but also of certain types of performance robustness. For two perturbation classes resulting bounds are shown to be improved over the existing ones. Examples given include comparison of the proposed analysis method with existing one.

• Computational Structural Engineering
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• v.1 no.2
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• pp.83-90
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• 1988

The present work is concerned with the improvement of finite element for the analysis of plate bending structures. The element formulation is based upon Mindlin plate concept. The displacement field of this element is formed by adding nonconforming modes to two rotational displacement components of a 'heterosis plate element. The element has the requisite numbers of zero eigenvalues associated with rigid body modes to avoid the spurious zero energy mode. It is shown that the results obtained by the element converged to the exact solutions very rapidly as the mesh is refined and exhibited reliable solutions through numerical studies for standard benchmark problems. This element is shown to overcome the shear locking problem completely in very thin plate situation even for irregular meshes.

• Proceedings of the KSR Conference
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• 2005.05a
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• pp.536-543
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• 2005

Derivation procedures of exact dynamic stiffness matrices of thin-walled curved beams subjected to axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. Firstly this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using element force-displacement relationships. The natural frequencies of the nonsymmetric thin-walled curved beam are evaluated and compared with analytical solutions or results by ABAQUS's shell elements in order to demonstrate the validity of this study.

• Proceedings of the KSR Conference
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• 2000.11a
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• pp.358-365
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• 2000

For the general case of loading conditions and boundary conditions, it is very difficult to obtain closed form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. In consequence, most of previous finite element formulations are introduce approximate displacement fields to use shape functions as Hermitian polynomials, and so on. The Purpose of this study is to presents a consistent derivation of exact dynamic stiffness matrices of thin-walled straight beams, to be used ill tile free vibration analysis, in which almost types of boundary conditions are exist An exact dynamic element stiffness matrix is established from governing equations for a uniform beam element of nonsymmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequency is evaluated for the thin-walled straight beam structure, and the results are compared with analytic solutions in order to verify the accuracy of this study.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.258-262
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• 2004

An analytical method for the free vibration of two circular plates coupled with a fluid was developed by the Rayleigh-Ritz method. The two plates with unequal thickness and diameter are clamped along the cylindrical vessel wall. It is assumed that the fluid bounded by a rigid cylindrical vessel is incompressible and non-viscous. The wet mode shape of the circular plates is assumed as a combination of the dry mode shapes of the plates. The fluid motion is described by using the fluid displacement potential and determined by using the compatibility conditions along the fluid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives a eigenvalue problem. It is found that the theoretical results can predict well the fluid-coupled natural frequencies with excellent accuracy comparing with the finite element analysis result.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.492-498
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• 2000

As the disk rotation speed increases in information storage devices, aerodynamically excited disk vibration is induced by airflow around the disk. This paper investigates theoretical and experimental studies on the disk flutter instability in CD-ROM drives. The effect of airflow on the disk vibration is modeled as the distributed damping and lift forces. By analyzing the eigenvalue problem of the aero-elastic coupling model, we introduces a novel technique to predict the flutter speed by comparing experimental natural frequencies with analytical ones of a disk rotating in vacuum. The new method predicts that the vibration mode with two nodal diameters in a CD disk experiences the first flutter instability at 12,000 rpm.

• Proceedings of the KIEE Conference
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• 1997.11a
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• pp.146-148
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• 1997

An LMI-based parameterization of all $\gamma$-suboptimal reduced-order unbiased $H_{\infty}$ filters is provided in terms of a free matrix, using the unbiasedness condition, bounded real lemma and the general solution of the basic LMI. Also, by sequentially solving the generalized eigenvalue minimization and basic LMI problem, the optimal filter coefficient matrix can be obtained with the best achievable performance.

• 한국전산유체공학회:학술대회논문집
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• 1999.11a
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• pp.48-58
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• 1999

The Characteristic Flux Difference Splitting (CFDS) scheme designed to adapt the characteristic boundary conditions at the wall and inflow/outflow boundary planes satisfies Roe's property U, although the CFDS Jacobian matrix is decomposed by a product of elaborate transformation matrices and explicit eigenvalue matrix. When the CFDS algorithm, thus a variant of Roe's scheme, is applied straightforwardly to hypersonic flows over a blunt body, the strong bow shock gradually breaks down near the stagnation point. This numerical instability is widely observed by many researchers employing flux-difference method, known in the literature as the carbuncle phenomenon. Many remedies have been proposed and resulted in partial cures. When the idea of Sanders et al. which identifies the minimum eigenvalues near the discontinuity present is applied to CFDS method, it is shown that the instability problem can be controlled successfully. A few flux splitting methods have also been tested and results are compared against the Nakamori's Mach 8 blunt body flow.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.619-624
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• 2000

Longitudinal vibration of an axially moving material is investigated by using the assumed modes method. to circumvent a difficulty in choosing the comparison functions which satisfy the boundary conditions the assumed modes method is adopted by which equations of motion are discretized. Based on the discretized equations, the complex eigenvalue problem is solved and then the effects of the translating velocity on the natural frequencies and modes are analyzed.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.369-374
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• 2000

The buckling of two elastic layers bonded to a semi-infinite substrate under a transverse compressive plane strain is investigated. Incremental deformation theory is employed to describe the buckling behavior of both two isotropic layers and the semi-infinite substrate. The problem is converted to an eigenvalue-eigenvector case, from which the critical buckling strain and the wavelength of the buckled shape are obtained. The results are presented on the effects of the layer geometries and material properties on the buckling behavior.