• 전산구조공학
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• 제9권4호
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• pp.209-217
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• 1996

구조물의 손상전후에 나타나는 고유진동수와 모드 형상으로 부터 Inverse Modal Perturbation기법을 이용하여 잔교식 부두나 돌핀과 같은 대규모 항만구조물의 손상도 추정을 위한 모드 기여도 계수를 근사적으로 직접 구하는 방법을 제시하였다. 잔교식 항만구조물의 고유치 해석을 통해 구조물의 강성 변화량과 구조물의 고유진동수와 모드 형상의 변화량과 요소 손상도 계수를 도입하여 Inverse Modal Perturbation의 2차항을 고려한 관계식을 유도하고 손상전후에 구조물의 강성 감소로 나타나는 구조물의 손상도를 추정하여 수렴정도를 고찰하였다.

• Journal of applied mathematics & informatics
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• 제3권2호
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• pp.193-204
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• 1996

Overflow queuing models are ofter analyzed by explicitly solving a large sparse singular linear systems arising from Kolmogorov balance equation. The system is often converted into an eigenvalue problem the dominant eigenvector of which is the desired null vector. In this paper we convert an overflow queuing problem the dominant eigenvector of which is the desired null vector. In this paper we convert an overflow queuing problem into an overflow queuing problem into an eigen-value problem into an eigen-value problem of size 1/2 of the original. Then we devise an orthogonal projector that enhances its convergence by removing unsanted eigen-components effectively. Numerical result with some suggestion is given at the end.

• 대한수학회지
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• 제57권6호
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• pp.1435-1449
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• 2020

In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

• Steel and Composite Structures
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• 제28권4호
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• pp.403-414
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• 2018

In this paper, the lateral-torsional buckling of axially-transversally functionally graded tapered beam is investigated. The structure cross-section is assumed to be symmetric I-section, and it is continuously laterally supported by torsional springs through the length. In addition, the height of cross-section varies linearly throughout the length of structure. The proposed formulation is obtained for the case that the elastic and shear modulus change as a power function along the beam length and section height. This structure carries two concentrated moments at the ends. In this study, the lateral displacement and twisting angle relation of the beam are defined by sinusoidal series. After establishing the eigenvalue equation of unknown constants, the beam critical bending moment is found. To validate the accuracy and correctness of results, several numerical examples are solved.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.355-362
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• 2008

We prove the existence of a unique positive solution for a class of systems of the following nonlinear suspension bridge equation with Dirichlet boundary conditions and periodic conditions $$\{{u_{tt}+u_{xxxx}+\frac{1}{4}u_{ttxx}+av^+={\phi}_{00}+{\epsilon}_1h_1(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\{v_{tt}+v_{xxxx}+\frac{1}{4}u_{ttxx}+bu^+={\phi}_{00}+{\epsilon}_2h_2(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small number and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel} h_1{\parallel}={\parallel} h_2{\parallel}=1$. We first show that the system has a positive solution, and then prove the uniqueness by the contraction mapping principle on a Banach space

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 하계학술대회 논문집 A
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• pp.342-344
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• 2004

In conventional small signal stability analysis, system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of state matrix. However, when a system contains switching elements such as FACTS devices, it becomes non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is by means of eigenvalue analysis of the system periodic transition matrix based on discrete system analysis method. In this research, RCF(Resistive Companion Form) method is used to analyse small signal stability of a non-continuous system including switching elements'. Applying the RCF method to the differential and integral equations of power system, generator, controllers and FACTS devices including switching elements should be modeled in the form of state transition matrix. From this state transition matrix eigenvalues which are mapped to unit circle can be calculated.

• 전자공학회논문지A
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• 제33A권5호
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• pp.75-84
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• 1996

planar circulator swith arbitrarily shaped ferrite resonators are analyzed in this paper. First, resonant frequencies and field distributions for the magnetized ferrite resonator are obtained using finite element method (FEM). Then the RF voltage distributions and other circuit parameters of the circulator which is formed by connecting three suitable transmission lines ot the ferrite resonator are derived from the green function . To remove the spurious solutions in analyzing the ferrite resonator, the results of eigenvalue analysis by node based FEM are comapred with the edge based fEM. The green function is expanded in terms of normalized eigenfunctions of th ecorresponding wave equation. Circulator parameters for circular disk resonator are clculated and compared with the analytical results. The experimental data for the designed circulator using hexagonal reosnator in the 850 MHz frequency range agree well iwth the simulated data.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.27-47
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• 2012

It has become apparent from the recent work by Choi et al. [3] on the nonlinear beam deflection problem, that analysis of the integral operator $\mathcal{K}$ arising from the beam deflection equation on linear elastic foundation is important. Motivated by this observation, we perform investigations on the eigenstructure of the linear integral operator $\mathcal{K}_l$ which is a restriction of $\mathcal{K}$ on the finite interval [$-l,l$]. We derive a linear fourth-order boundary value problem which is a necessary and sufficient condition for being an eigenfunction of $\mathcal{K}_l$. Using this equivalent condition, we show that all the nontrivial eigenvalues of $\mathcal{K}l$ are in the interval (0, 1/$k$), where $k$ is the spring constant of the given elastic foundation. This implies that, as a linear operator from $L^2[-l,l]$ to $L^2[-l,l]$, $\mathcal{K}_l$ is positive and contractive in dimension-free context.

• 대한기계학회논문집
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• 제5권4호
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• pp.293-302
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• 1981

In this paper, the stability of a flexible missle, idealized as a free-free beam, is evaluated by using the finite element method. For the study, heavy machinery part is modeled as a concentrated mass and the thrust, which is controlled by a feedback sensor located at a predetermined position, is considered as a constant follower force. The aerodynamic forces, the structural damping, the cross sectional variation servo lag effect are neglected in this study. With unconstrained variational principle, the finite element method is applied to the nondimensionalized beam eqution. The matrix eigenvalue equation is obtained and the eigenvalues are calculated by a computer for the stability analysis. The stability is evaluated by the inspection of the eigenvalues are calculated by a computer for the stabilith analysis. The stabilith is evaluated by the inspection of the eigenvalues of the problem. For the study, the behaviors of the eigenvalues at various thrusts and the effects of the magnitudes and positions of the concentrated mass and directional control constant are analyzed.

• 한국소음진동공학회논문집
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• 제17권11호
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• pp.1086-1092
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• 2007

This paper is concerned with the vibration analysis of a rectangular plate with multiple circular holes. On the contrary to the case of rectangular plate with multiple rectangular holes, it is very difficult to perform qualitative analysis on natural vibration characteristics because of geometrical inconsistency. In this paper, we applied the Independent Coordinate Coupling Method(ICCM) to the addressed problem, which was developed to compute natural vibration characteristics of the rectangular plate with a circular hole and proven to be computationally effective. The ICCM is based on Rayleigh-Ritz method but utilizes independent coordinates for each hole domain. By matching the deflection conditions for each hole imposed on the expressions, we can easily derive the reduced mass and stiffness matrices. The resulting equation is then used for the calculation of the eigenvalue problem. The numerical results show the efficacy of the Independent Coordinate Coupling Method.