• 충청수학회지
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• 제25권1호
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• pp.19-25
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• 2012

The purpose of this paper is to derive powers $A^{n}$ using a system of recursive sequences for a given $2{\times}2$ matrix A. Introducing a recursive sequence we have a quadratic equation. Solutions to this quadratic equation are related with eigenvalues of A. By solving this quadratic equation we can easily obtain an explicit form of $A^{n}$. Our method holds when A is defined not only on the real field but also on the complex field.

• 한국연소학회지
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• 제18권2호
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• pp.42-50
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• 2013

Linear stability analysis of radiating counterflow diffusion flames is numerically conducted to examine the instability characteristics of cellular patterns. Lewis number is assumed to be 0.5 to consider diffusional-thermal instability. Near kinetic limit extinction regime, growth rates of disturbances always have real eigen-values and neutral stability condition of planar disturbances perfectly falls into quasi-steady extinction. Cellular instability of disturbance with transverse direction occurs just before steady extinction. However, near radiative limit extinction regime, the eigenvalues are complex and pulsating instability of planar disturbances appears prior to steady extinction. Cellular instability occurs before the onset of planar pulsating instability, which means the extension of flammability.

• Structural Engineering and Mechanics
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• 제63권6호
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• pp.743-750
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• 2017

Modal parameter identification plays a key role in the structural health monitoring (SHM) for civil engineering. Eigensystem realization algorithm (ERA) is one of the most popular identification methods. However, the complex environment around civil structures can introduce the noises into the measurement from SHM system. The spurious modes would be generated due to the noises during ERA process, which are usually ignored and be recognized as physical modes. This paper proposes an improved stabilization diagram method in ERA to distinguish the spurious modes. First, it is proved that the ERA can be performed by any two Hankel matrices with one time step shift. The effect of noises on the eigenvalues of structure is illustrated when the choice of two Hankel matrices with one time step shift is different. Then, a moving data diagram is proposed to combine the traditional stabilization diagram to form the improved stabilization diagram method. The moving data diagram shows the mode variation along the different choice of Hankel matrices, which indicates whether the mode is spurious or not. The traditional stabilization diagram helps to determine the concerned truncated order before moving data diagram is implemented. Finally, the proposed method is proved through a numerical example. The results show that the proposed method can distinguish the spurious modes.

• 소음진동
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• 제7권4호
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• pp.645-653
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• 1997

For high performance rotating machinery, unstable vibrations may occur caused by hydrodynamic forces such as oil film forces, clearance excitation forces generated by the working fluid, and etc. In order to improve the availability one has to take into account the vibrations very accurately. When designing a rotating machinery, the stability behavior and the resonance response can be obtained by calculation of the complex eigenvalues. A suitable modifications of seal and/or bearing design may effectively improve the stability and the response of a rotor system. This paper deals with the optimum length and clearance of seals and bearings to minimize the resonance response(Q factor) and to maximize the logarithmic decrement in the operating speed under the constraints of design variables. Also, for an avoidance of resonance region from the operating speed, an optimization technique has been used to yield the critical speeds as far from the operating speed as possible. The optimization method is used by the genetic algorithm, which is a search algorithm based on the mechanics of natural selection and natural genetics. The results show that the optimum design of seals and bearings can significantly improve the resonance and the stability of the pump rotor system.

• Journal of Mechanical Science and Technology
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• 제18권4호
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• pp.630-639
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• 2004

The Stewart platform manipulator is a closed-kinematics chain robot manipulator that is capable of providing high structural rigidity and positional accuracy. However, this is a complex and nonlinear system, so the control performance of the system is not so good. In this paper, a new robust motion control algorithm is proposed. The algorithm uses partial state feedback for a class of nonlinear systems with modeling uncertainties and external disturbances. The major contribution is the design of a robust observer for the state and the perturbation of the Stewart platform, which is combined with a variable structure controller (VSC). The combination of controller and observer provides the robust routine called sliding mode control with sliding perturbation observe. (SMCSPO). The optimal gains of SMCSPO, which is determined by nominal eigenvalues, are easily obtained by genetic algorithm. The proposed fitness function that evaluates the gain optimization is to put sliding function. The control performance of the proposed algorithm is evaluated by the simulation and experiment to apply to the Stewart platform. The results showed high accuracy and good performance.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2011년도 춘계학술대회 논문집
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• pp.443-444
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• 2011

This paper discusses a model order reduction for large order rotor dynamics systems results from the finite element discretization. Typical rotor systems consist of a rotor, built-on parts, and a support system, and require prudent consideration in their dynamic analysis models because they include unsymmetric stiffness, localized nonproportional damping and frequency dependent gyroscopic effects. When the finite element model has a very large number of degrees of freedom because of complex geometry, repeated dynamic analyses to investigate the critical speeds, stability, and unbalanced response are computationally very expensive to finish within a practical design cycle. In this paper, the Krylov-based model order reduction via moment matching significantly speeds up the dynamic analyses necessary to check eigenvalues and critical speeds of a Nelson-Vaugh rotor system. With this approach the dynamic simulation is efficiently repeated via a reduced system by changing a running rotational speed because it can be preserved as a parameter in the process of model reduction. The Campbell diagram by the reduced system shows very good agreement with that of the original system. A 3-D finite element model of the Nelson-Vaugh rotor system is taken as a numerical example to demonstrate the advantages of this model reduction for rotor dynamic simulation.

• 대한기계학회논문집A
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• 제27권1호
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• pp.66-76
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• 2003

The arbitrary V-notched crack problem is considered. The general expressions for the stress components on this problem are obtained as explicit series forms composed of independent unknown coefficients which are denoted by coefficients of eigenvector. For this results eigenvalue equation is performed first through introducing complex stress functions and applying the traction free boundary conditions. Next solving this equation, eigenvalues and corresponding eigenvectors are obtained respectively, and finally inserting these results into stress components, the general equations are obtained. These results are also shown to be applicable to the symmetric V-notched crack or straight crack. It can be shown that this solutions are composed of the linear combination of Mode I and Mode II solutions which are obtained from different characteristic equations, respectively. Through performing asymptotic analysis for stresses, the stress intensity factor is given as a closed form equipped with the unknown coefficients of eigenvector. In order to calculate the unknown coefficients. based on these general explicit equations, numerical programming using the overdetermined boundary collocation method which is algorithmed originally by Carpenter is also worked out. As this programming requires the input data, the commercial FE analysis for stresses is performed. From this study, for some V-notched problems, unknown coefficients can be calculated numerically and also fracture parameters are determined.

• 대한전기학회논문지:전력기술부문A
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• 제49권4호
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• pp.168-176
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• 2000

This paper presents the Hessenberg method, a new sparsity-based small signal stability analysis program for large interconnected power systems. The Hessenberg method as well as the Arnoldi method computes the partial eigen-solution of large systems. However, the Hessenberg method with pivoting is numerically very stable comparable to the Householder method and thus re-orthogonalization of the krylov vectors is not required. The fractional transformation with a complex shift is used to compute the modes around the shift point. If only the dominant electromechanical oscillation modes are of concern, the modes can be computed fast with the shift point determined by Fourier transforming the time simulation results for transient stability analysis, if available. The program has been successfully tested on the New England 10-machine 39-bus system and Korea Electric Power Co. (KEPCO) system in the year of 2000, which is comprised of 791-bus, 1575-branch, and 215-machines. The method is so efficient that CPU time for computing five eigenvalues of the KEPCO system is 3.4 sec by a PC with 400 MHz Pentium IIprocessor.

• 전산구조공학
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• 제4권1호
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• pp.73-82
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• 1991

판의 탄소성 좌굴문제는 판 구조의 해석과 설계시의 중요성으로 인하여 상당한 관심이 모아져 온 분야이다. 본 연구에서는 유한요소법에 의한 효율적인 탄소성 좌굴해석 프로그램을 개발하였다. 탄소성 강성행렬을 구성하기 위한 소성이론으로는 실험결과와 잘 일치하는 Stowell의 변형이론을 사용하였으며, 좌굴하중을 해석하기 위해서는 고유치해석에 의한 반복기법을 사용하였다. 고유치해석에서는 불필요한 고유치의 계산을 피할 수 있는 subspace반복기법을 사용하였다. 해석결과를 Stowell이 제시한 이론해와 Pride에 의한 실험결과와 비교하여 프로그램의 타당성을 보이고, 이를 이용하여 단순지지, 또는 고정된 경계조건에 대하여 일축 또는 이축응력이 작용되는 여러 경우에 대하여 좌굴하중을 구하였다. 또한, 탄소성 좌굴에 미치는 형상비의 영향을 검토하였다.

• Nuclear Engineering and Technology
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• 제55권9호
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• pp.3388-3400
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• 2023

Detailed analysis of the neutron pathway through matter inside the nuclear reactor core is exceedingly needed for safety and economic considerations. Due to the constant development of high-performance computing technologies, neutronics analysis using computer codes became more effective and efficient to perform sophisticated neutronics calculations. In this work, a commercial pressurized water reactor (PWR) presented by Virtual Environment for Reactor Applications (VERA) Core Physics Benchmark are modeled and simulated using a high-fidelity simulation of OpenMC code in terms of criticality and fuel pin power distribution. Various problems have been selected from VERA benchmark ranging from a simple two-dimension (2D) pin cell problem to a complex three dimension (3D) full core problem. The development of the code capabilities for reactor physics methods has been implemented to investigate the accuracy and performance of the OpenMC code against VERA SCALE codes. The results of OpenMC code exhibit excellent agreement with VERA results with maximum Root Mean Square Error (RMSE) values of less than 0.04% and 1.3% for the criticality eigenvalues and pin power distributions, respectively. This demonstrates the successful utilization of the OpenMC code as a simulation tool for a whole core analysis. Further works are undergoing on the accuracy of OpenMC simulations for the impact of different fuel types and burnup levels and the analysis of the transient behavior and coupled thermal hydraulic feedback.