• Title/Summary/Keyword: 라그랑지 방정식

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A Study on the Transport of Microplastics Contained in the Wastewater of the King Sejong Station according to the Wave Effect (파랑 효과에 따른 세종과학기지 방류수에 포함된 미세플라스틱 이송에 관한 연구)

  • Kim, Bo-Kyung;Hwang, Jin Hwan
    • Proceedings of the Korea Water Resources Association Conference
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    • 2021.06a
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    • pp.245-245
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    • 2021
  • 해양으로 유출된 5 mm 이하의 크기로 분해된 미세플라스틱이 해양 환경 오염의 주요 원인으로 자리잡았다. 최근에는 청정해역으로 알려진 남극해에서도 발견되고 있어 남극해에 잔류하는 미세플라스틱 오염 수준을 이해하기 위해 노력하고 있다. 하지만, 파랑의 효과를 고려한 남극해의 해수 순환 구조와 미세플라스틱의 고유 특성을 반영한 미세플라스틱의 거동 및 공간적 분포에 대한 복합적 이해는 상대적으로 부족하다. 남극해에서 발견된 미세플라스틱은 과학기지들의 방류수나, 조사선 등과 같은 인위적인 활동으로 인해 집적될 수 있으며, 특히 영구적으로 거주하는 과학기지에서 흘려보내는 방류수에 포함된 미세플라스틱은 과학기지 주변 해수 오염에 직접적인 영향을 줄 것으로 예상된다. 따라서, 본 연구에서는 파랑 효과에 따른 남극 킹조지 섬(King George Island)에 위치한 세종과학기지의 방류수에 포함된 미세플라스틱의 이송에 대해 모의하였다. 세종과학기지가 위치한 킹조지 섬과 넬슨 섬(Nelson Island) 사이의 멕스웰 만(Maxwell Bay)의 해수 흐름을 재현하기 위하여 해수 유동 모델(Delft3D-FLOW)이 사용되었다. 또한, 해수 유동 모델에 파랑 모델(Delft3D-WAVE)을 결합하여 파랑의 효과가 미세플라스틱의 이송에 미치는 영향을 확인하였다. 세종과학기지의 방류수가 흘러나가는 마리안 소만(Marian Cove)의 유속장을 바탕으로 이송, 확산, 입자의 침강 속도를 고려하여서, 세종과학기지에서 밀물 시 방출한 입자를 라그랑지안 입자 추적(Lagrangian Particle Tracking) 방법을 이용해 추적하였다. 해수의 밀도보다 가벼운 플라스틱의 경우 해수 표층의 흐름을 따라 소만 내부로 이송되어 해안선에 도달하고, 해수의 밀도보다 무거운 플라스틱의 경우 소만 내부로 이송되나 입자의 침강 속도로 인해 방출 위치 근처에서 집적된다. 파랑의 효과를 고려하게 되면, 고려하기 전보다 두 종류의 미세플라스틱 모두 소만 내부로 더 멀리 이송되는데, 이는 파랑으로 인한 힘(wave-induced force)이 해수 유동 모델의 운동방정식에 추가되며 파랑 에너지 분산으로 인해 해수 흐름에 변화를 준 것으로 보인다.

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Structural Modal Analysis Using Substructure Hybrid Interface Modes (혼합경계의 부분구조 모드를 이용한 구조물의 모드해석)

  • 김형근;박윤식
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.5
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    • pp.1138-1149
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    • 1993
  • A new mode synthesis method using Lagrange multipliers and substructure hybrid interface modes is presented. Substruture governing equations of motion are derived using Lagrange equations and the constraints of geometric compatibility between the substructures are treated with Lagrange multipliers. Fixed, free, and loaded interface modes can be employed for the modal bases of each substructure. In cases of the fixed and loaded interface modes, two successive modal transformation relations are used. Compared with the conventional mode synthesis methods, the suggested method does not construct the equations of motion of the coupled structure and the final characteristic equation becomes a polynomial. Only modal parameters of each substructure and geometric compatibility conditions are needed. The suggested method is applied to a simple lumped mass model and parametric study is performed.

Development of Multi-Purpose Satellite 2 with Deployable Solar Arrays: Part 1. Dynamic Modeling (다목적2호기 태양전지판의 전개시스템 개발: PART 1. 동적 모델링)

  • Gwak,Mun-Gyu;Heo,Seok
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.31 no.9
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    • pp.38-45
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    • 2003
  • This research is concerned with the dynamic modeling of the multi-purpose satellite with deployable solar arrays equipped with strain energy hinges(SEH). To this end, we proposed the use of the equivalent torsional spring for the SEH and derived the equations of motion assuming that the satellite and solar arrays are being rigid. We also considered the effect of the support string for the ground experiment model, which has been observed as a critical factor affecting the deployment in the ground experiments. From the numerical simulation results, it is found that solar arrays are deployed in a similar pattern but the hub motions are different because of the support strings. It was concluded that the non-gravity deployment of the solar arrays can be approximately simulated by the ground experimental facility. The effects of the support string are also investigated by varying the length of the string. It was found that the current length of the string is adequate for the ground experiment. Ground experimental results will follow.

Unknown-Parameter Identification for Accurate Control of 2-Link Manipulator using Dual Extended Kalman Filter (2링크 매니퓰레이터 제어를 위한 듀얼 확장 칼만 필터 기반의 미지 변수 추정 기법)

  • Seung, Ji Hoon;Park, Jung Kil;Yoo, Sung Goo
    • Journal of the Korea Convergence Society
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    • v.9 no.6
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    • pp.53-60
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    • 2018
  • In this paper, we described the unknown parameter identification using Dual Extended Kalman Filter for precise control of 2-link manipulator. 2-link manipulator has highly non-linear characteristic with changed parameter thought tasks. The parameter kinds of mass and inertia of system is important to handle with the manipulator robustly. To solve the control problem by estimating the state and unknown parameters of the system through the proposed method. In order to verify the performance of proposed method, we simulate the implementation using Matlab and compare with results of RLS algorithm. At the results, proposed method has a better performance than those of RLS and verify the estimation performance in the parameter estimation.

Model for Flow Analysis of Fresh Concrete Using Particle Method with Visco-Plastic Flow Formulation (점소성 유동 입자법에 의한 굳지 않은 콘크리트의 유동해석 모델)

  • Cho, Chang-Geun;Kim, Wha-Jung;Choi, Yeol
    • Journal of the Korea Concrete Institute
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    • v.20 no.3
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    • pp.317-323
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    • 2008
  • In the current study, A model for the flow analysis of fresh and highly flowable concrete has been developed using a particle method, the moving particle semi-implicit (MPS) method. The phenomena on the flow of concrete has been considered as a visco-plastic flow problem, and the basic governing equation of concrete particle dynamics has been based on the Navier-Stokes equation in Lagrangian form and the conservation of mass. In order to formulate a visco-plastic flow constitutive law of fresh concrete, concrete is modeled as a highly viscous material in the state of non-flow and as a visco-plastic material in the state of flow after reaching the yield stress of fresh concrete. A flow test of fresh concrete in the L-box was simulated and the predicted flow was well matched with the experimental result. The developed method was well showed the flow motion of concrete particles because it was formulated to be based on the motion of visco-plastic fluid dynamics.

Dynamic Interaction Analysis of Vehicle-Suspension Bridge Considering Flexural and Torsional Behaviors and Shear Deformation Effects (휨 및 비틀림 거동 및 전단변형 효과를 고려한 차량-현수교의 동적 상호작용 해석)

  • Kim Moon-Young;Lim Myoung-Hun;Kwon Soon-Duck;Kim Ho-Kyung;Kim Nam-Il
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.18 no.4 s.70
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    • pp.361-372
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    • 2005
  • In the previous study(Kim 등, 2004), the finite element method was used for the vortical vibration analysis of suspension bridge with the effects of the shear deformation and the rotary inertia under moving load considering the bridge-vehicle interaction. The purpose of this study is to investigate the effect of an eccentric vehicle and shear deformation. So we firstly performs the eigenvalue analysis for the free vortical and the torsional vibration of suspension bridges using FEM analysis. Next the equations of motion considering interaction between suspension bridges and vehicles/trains are derived using the mode superposition method. And then dynamic analysis was performed using the Newmark method. Finally through the numerical examples, the dynamic responses of bridges are investigated according to the proposed procedure.

A Study on the Coupled Shaft-Torsional and Blade-Bending Vibrations in the Flexible Rotor-Coupling-Blade System (유연체 로터-커플링-블레이드 시스템의 로터 축과 블레이드의 연성 진동에 관한 연구)

  • Lee, Sun-Sook;Oh, Byung-Young;Yoon, Hyung-Won;Cha, Seog-Ju;Na, Sung-Soo
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.05a
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    • pp.221-226
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    • 2005
  • In this paper, a dynamic model for the rotor shaft-coupling-blade system is developed. The blades are attached to a disk and driven by an electric motor shaft which is flexible in torsion. We assumed that the shaft torsional flexibility is lumped in the flexible coupling which is usually adopted in rotor systems. The Lagrangian approach with the small deformation theory for both blade-bending and shaft-torsional deformations is employed for developing the equation of the motion. The assumed modes method is used for estimating the blade transverse deflection. The numerical results highlight the effects of both structural damping of the system and the torsional stiffness of the flexible coupling to the dynamic response of the blade. The results showed strong coupling between the blade bending and shaft torsional vibrations in the form of inertial nonlinearif, stiffness hardening and softening.

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Out-of-plane Structural Intensity Analysis of Rectangular Thick Plate (직사각형 후판의 면외 진동인텐시티 해석)

  • Kim, Kook-Hyun;Cho, Dae-Seung
    • Journal of Ocean Engineering and Technology
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    • v.26 no.4
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    • pp.42-49
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    • 2012
  • A numerical method is presented for an out-of-plane structural intensity analysis of rectangular thick plates with arbitrary elastic edge constraints. The method adapts an assumed mode method based on Timoshenko beam functions to obtain the velocities and internal forces needed for a structural intensity analysis. To verify the presented method, the structural intensity of a square thick plate under harmonic force excitation, for which four edges are simply supported, is analyzed, and the result is compared with existing solutions using the assumed mode method based on trigonometric functions. In addition, numerical analyses are carried out for a rectangular-shaped thick plate under harmonic force excitations, of which three edges are simply supported and one edge utilizes an arbitrary elastic edge constraint. These numerical examples show the good accuracy and applicability of the presented method for rectangular thick plates with arbitrary edge constraints.

A Study on the Coupled Shaft-torsional and Blade-bending Vibrations in the Flexible Rotor-coupling-blade System (유연체 로터-커플링-블레이드 시스템의 로터 축과 블레이드의 연성 진동에 관한 연구)

  • Oh, Byung-Young;Lee, Sun-Sook;Yoon, Hyungwon;Cha, Seog-Ju;Na, Sungsoo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.9 s.102
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    • pp.1023-1029
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    • 2005
  • In this paper, a dynamic model for the rotor shaft-coupling-blade system was developed. The blades are attached to a disk and driven by an electric motor shaft which is flexible in torsion. We assumed that the shaft torsional flexibility was lumped in the flexible coupling which is usually adopted in rotor systems. The Lagrangian approach with the small deformation theory for both blade-bending and shaft-torsional deformations was employed for developing the equation of the motion. The Assumed Modes Method was used for estimating the blade transverse deflection. The numerical results highlight the effects of both structural damping of the system and the torsional stiffness of the flexible coupling to the dynamic response of the blade. The results showed strong coupling between the blade bending and shaft torsional vibrations in the form of inertial nonlinearity, stiffness hardening and softening.

Study of a Mixed Finite Element Model for the Analysis of a Geometrically Nonlinear Plate (기하학적 비선형 판재 해석을 위한 혼합형 FE Model 연구)

  • Kim, Woo-Ram;Choi, Youn-Dae
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.34 no.10
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    • pp.1427-1435
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    • 2010
  • A mixed finite element model was developed using the classical plate theory to analyze the nonlinear bending of a plate. The appropriate weight functions for the constraints integrated over the domain were determined by the Lagrange multiplier method by using the principle of minimum virtual energy; which provides the constitutive relations between force-like variables and strains. All of detail terms of element wise coefficient matrices and associate tangent matrices to be used in the Newton iterative method are presented. Then, the linear solutions of the current model and those of the traditional displacement model under the SS (simple support) boundary conditions were compared with the existing analytical solution. The post-processed images of the nonlinear results of the force-like variables are presented to show the continuity of the solutions at the joint of the element boundaries. Finally, the converged nonlinear finite element solutions of the current model are compared with those of existing traditional displacement model.