• Title/Summary/Keyword: 라그랑지 식

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An Efficient Response Analysis Method for a Structural System Using Substructure Modes (부분구조의 모드를 이용한 구조계의 효율적 응답해석)

  • 김형근;박윤식
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.5
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    • pp.1084-1094
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    • 1993
  • An efficient method for determining forced responses of a general linear structural system in time domain using subtructure modes and Lagrange multipliers is presented. Compared with the conventional mode synthesis methods, the suggested method does not construct the equations of motion of the combined whole structure and thus the modal parameters of the whole structure are not required. Only modal parameters of each substructure and geometric compatibility conditions are needed. Both the loaded interface free-free modes and free interface modes can be employed as the modal bases of each substructure. Recurrence discrete-time state equations based upon state transition matrix are formulated for the transient analysis of a parameter-changing system. It is shown form numerical examples that the suggested method is very accurate and efficient to calculate transient responses compares with the direct numerical integration method.

Vibration Suppression Using Eddy Current Damper (와전류 감쇠기를 이용한 진동 억제)

  • Kwak, Moon-Kyu;Lee, Myeong-Il;Heo, Seok
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.13 no.10
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    • pp.760-766
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    • 2003
  • This paper is concerned with the eddy current damper which can be used to enhance the damping of the host structure. The operating principle of the eddy current damper is first explained in detail. The dynamic interaction between the magnets and the copper plate produces eddy current thus resulting in the damping force. By attaching the eddy current damper to the host structure, the damping of the total structure can be increased so that vibrations can be suppressed. The advantage of the eddy current damper is that it doesn't require any electronic devices and power supply The effect of the eddy current damper on the global dynamic characteristics of the structure is investigated by considering the cantilever with the eddy current damper. Experimental results show that the eddy current damper is an effective device for vibration suppression.

A Three-Dimensional Rigid-Viscoplastic Finite Element Analysis of isothermal Square Die Extrusion of a Square Section Based on ALE Description (강-점소성 ALE 유한요소 수식화에 근거한 사각형 형재의 평금형 등온 압출에 대한 3차원 해석)

  • 강연식;양동열
    • Transactions of Materials Processing
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    • v.5 no.1
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    • pp.55-60
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    • 1996
  • In the finite element analysis of metal forming processes the updated Lagrangian approach has been widely and effectively used to simulate the non-steady state problems. however some difficulties have arisen from abrupt flow change as in extrusion through square dies. In the present work an ALE(arbitrary Lagrangian-Euleria) finite element formulation for deforma-tion analysis are presented fro rigid-viscoplastic materials. The developed finite element program is applied to the isothermal analysis of square die extrusion of a square section. The computational results are compared with those by the updated Lagrangian finite element analysis.

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섭동을 고려한 위성편대비행 연료 최적 재배치 문제에 대한 근사 해석해 연구

  • Lee, Sang-Jin;Park, Sang-Yeong
    • Bulletin of the Korean Space Science Society
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    • 2010.04a
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    • pp.28.1-28.1
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    • 2010
  • 이 연구에서는 기존 선형 상대운동방정식에 차등중력, 주위성의 이심율, J2 섭동 등의 비선형항을 추가하여 보다 정확한 상대운동방정식을 만든 후 섭동이론을 적용하여 위성편대 연료최적화 재배치 문제에 대한 근사 해석해를 구하고자 한다. 먼저, 비선형 섭동항을 테일러 급수를 이용하여 2차항까지 전개한 후, 이를 기존 선형상대운동방정식에 추가하여 새로운 비선형 상대운동방정식을 만든다. 이 때 사용된 선형상대운동방정식은 힐스 방정식으로 주위성의 궤도가 일반적인 타원이고 위성 간 상대거리가 충분히 가깝다고 가정한다. 최적화 조건으로부터 상태벡터와 라그랑지 곱수로 이루어진 연립 미분방정식이 만들어 지는데, 이 식은 힐스 방정식에 기인한 선형부분과 2차 비선형항에 기인한 섭동부분으로 나뉜다. 이 때, 이 연립미분방정식의 해는 선형부분의 해와 섭동으로 인한 변화량의 합으로 근사할 수 있으며 그 변화량은 섭동이론을 적용하여 얻을 수 있다. 이와 같이 얻어진 해는 여러 섭동의 비선형항을 2차까지 포함한 상대운동방정식을 사용했기 때문에, 기존 선형상대운동방정식을 사용하여 구한 최적해 보다 더 정확한 결과를 얻을 것이라 예상한다.

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Efficient Algorithms for Multicommodity Network Flow Problems Applied to Communications Networks (다품종 네트워크의 효율적인 알고리즘 개발 - 정보통신 네트워크에의 적용 -)

  • 윤석진;장경수
    • The Journal of Information Technology
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    • v.3 no.2
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    • pp.73-85
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    • 2000
  • The efficient algorithms are suggested in this study for solving the multicommodity network flow problems applied to Communications Systems. These problems are typical NP-complete optimization problems that require integer solution and in which the computational complexity increases numerically in appropriate with the problem size. Although the suggested algorithms are not absolutely optimal, they are developed for computationally efficient and produce near-optimal and primal integral solutions. We supplement the traditional Lagrangian method with a price-directive decomposition. It proceeded as follows. First, A primal heuristic from which good initial feasible solutions can be obtained is developed. Second, the dual is initialized using marginal values from the primal heuristic. Generally, the Lagrangian optimization is conducted from a naive dual solution which is set as ${\lambda}=0$. The dual optimization converged very slowly because these values have sort of gaps from the optimum. Better dual solutions improve the primal solution, and better primal bounds improve the step size used by the dual optimization. Third, a limitation that the Lagrangian decomposition approach has Is dealt with. Because this method is dual based, the solution need not converge to the optimal solution in the multicommodity network problem. So as to adjust relaxed solution to a feasible one, we made efficient re-allocation heuristic. In addition, the computational performances of various versions of the developed algorithms are compared and evaluated. First, commercial LP software, LINGO 4.0 extended version for LINDO system is utilized for the purpose of implementation that is robust and efficient. Tested problem sets are generated randomly Numerical results on randomly generated examples demonstrate that our algorithm is near-optimal (< 2% from the optimum) and has a quite computational efficiency.

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Design of FIR Halfband Filters using Generalized Lagrange Polynomial (일반화된 라그랑지 다항식을 사용하는 FIR 하프밴드 필터 설계)

  • Bong, Jeongsik;Jeon, Joonhyeon
    • Journal of the Institute of Electronics and Information Engineers
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    • v.50 no.10
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    • pp.188-198
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    • 2013
  • Maximally flat (MAXFLAT) half-band filters usually have wider transition band than other filters. This is due to the fact that the maximum possible number of zeros at $z={\pm}1$ is imposed, which leaves no degree of freedom, and thus no independent parameters for direct control of the frequency response. This paper describes a novel method for the design of FIR halfband filters with an explicit control of the transition-band width. The proposed method is based on a generalized Lagrange halfband polynomial (g-LHBP) with coefficients parametizing a 0-th coefficient $h_0$, and allows the frequency response of this filter type to be controllable by adjusting $h_0$. Then, $h_0$ is modeled as a steepness parameter of the transition band and this is accomplished through theoretically analyzing a polynomial recurrence relation of the g-LHBP. This method also provides explicit formulas for direct computation of design parameters related to choosing a desired filter characteristic (by trade-off between the transition-band sharpness and passband & stopband flatness). The examples are shown to provide a complete and accurate solution for the design of such filters with relatively sharper transition-band steepness than MAXFLAT half-band filters.

A Study on Prediction Model Conformity of Line Source in Urban Area (도시지역에서의 선오염원 예측모델 적합성에 관한 연구)

  • Kim, Jin Hong;Park, Sun hwan;Chang, Yoon young
    • Journal of the Korean Society of Urban Environment
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    • v.18 no.4
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    • pp.511-521
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    • 2018
  • Despite the limitations and difficulty in the application of CALINE3 model for air dispersion prediction of roads and tunnels construction businesses in South Korea, the model is being used in all roads construction projects. This study compared the predicted values of CALINE3 and AERMOD model that is suggested by the US EPA, to the values of GRAL model, a Lagrangian particle tracking model developed in Europe, by applying the models to the existing roads of the urban areas. The result showed low relevance to the actual measurement value in the case of CALINE3 model, thus displaying a low trusted value when applying to the urban areas. In the case of using AERMOD model, the predicted values were overly expressed compared to the actual measurement value, thus leading to the need of adding a No2 conversion method to the model in the future. In the case of GRAL model, a Lagrangian particle tracking model, the relevance between the actual and predicted values were high as the model considers the surrounding topography and the buildings all together, thus confirming that the model can be used for air dispersion prediction of the roads in the urban areas. Lastly, the result of this study testing the air prediction models in Jeongneung Measuring Station points that it is necessary for the future studies to expand the testing areas and test the validity of the models continuously.

LES on breakup and atomization of a liquid jet into cross turbulent flow in a rectangular duct (사각 덕트내 난류 횡단류 유동장에 분사되는 액체 제트의 분열과 미립화에 관한 LES 해석)

  • Yoo, Young-Lin;Han, Doo-Hee;Sung, Hong-Gye;Jeon, Hyuk-Soo;Park, Chul-Hyun
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.44 no.4
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    • pp.290-297
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    • 2016
  • A two-phase Large Eddy Simulation(LES) has been conducted to investigate breakup and atomization of a liquid jet in a cross turbulent flow in a rectangular duct. Gas-droplet two-phase flow was solved by a coupled Eulerian-Lagrangian method which tracks every individual particles. Effects of liquid breakup models, sub-grid scale models, and a order of spatial discretization was investigated. The penetration depth in cross flow was comparable with experimental data by varying breakup model and LES scheme. SMD(Sauter Mean Diameter) distribution downstream of jet was analyzed.

Numerical Analysis of Dynamic Response of Floating Offshore Wind Turbine to the Underwater Explosion using the PML Non-reflecting Technique (PML 무반사 기법을 이용한 부유식 해상풍력발전기의 수중폭발에 따른 동응답 수치해석)

  • Cho, Jin-Rae;Jeon, Soo-Hong;Jeong, Weui-Bong
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.29 no.6
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    • pp.521-527
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    • 2016
  • This paper is concerned with the numerical analysis of dynamic response of floating offshore wind turbine subject to underwater explosion using an effective non-reflecting technique. An infinite sea water domain was truncated into a finite domain, and the non-reflecting technique called the perfectly matched layer(PML) was applied to the boundary of truncated finite domain to absorb the inherent reflection of out-going impact wave at the boundary. The generalized transport equations that govern the inviscid compressible water flow was split into three PML equations by introducing the direction-wise absorption coefficients and state variables. The fluid-structure interaction problem that is composed of the wind turbine and the sea water flow was solved by the iterative coupled Eulerian FVM and Largangian FEM. And, the explosion-induced hydrodynamic pressure was calculated by JWL(Jones-Wilkins-Lee) equation of state. Through the numerical experiment, the hydrodynamic pressure and the structural dynamic response were investigated. It has been confirmed that the case using PML technique provides more reliable numerical results than the case without using PML technique.

A Study on Dynamic Analysis Model and Stability of Stone Cultural Properties of Inverted Pendulum Type with 5 Joints (5개의 연결부를 가지는 역진자형 석조문화재의 동적 해석모델 및 안정성 연구)

  • Choi, Jae-Sung
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.25 no.3
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    • pp.21-30
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    • 2021
  • Architectural cultural properties suffer a lot of damage due to various environmental factors. In order to preserve damaged cultural properties, preventive preservation and long-term preservation management are becoming more important. Therefore, research on a scientific non-destructive testing method applicable to regular inspection is required. For related research, DangGan with a high flag-pole shape was selected as the subject of study among various cultural properties. Among the preserved DangGans, a basic study was conducted on the analysis technique to evaluate the structural stability by selecting Treasure No. 49 Naju SeokDangGan. An idealized model was presented and a multi-degree of freedom equation of motion was derived. In addition, an equation for estimating the critical stiffness value for each joint position is presented.