• Title/Summary/Keyword: Catenary equation

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Design of Mooring Lines of a Floating Offshore Wind Turbine in South Offshore Area of Jeju (제주 해양환경에 적합한 부유식 해상풍력발전기 계류선 설계)

  • Choung, Joonmo;Kim, Hyungjun;Jeon, Gi-Young
    • Journal of the Society of Naval Architects of Korea
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    • v.51 no.4
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    • pp.300-310
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    • 2014
  • This paper presents a mooring design procedure of a floating offshore wind turbine. The environment data of south offshore area of Jeju collected from Korea Hydrographic and Oceanographic Administration(KHOA) are used for hydrodynamic analyses as environmental conditions. We considered a semi-submersible type floating wind turbine based on Offshore Code Comparison Collaborative Continuation(OC4) DeepCWind platform and National Renewable Energy Laboratory(NREL) 5 MW class wind turbine. Catenary mooring with studless chain is chosen as the mooring system. Important design decisions such as how large the nomial sizes are, how long the mooring lines are, how far the anchor points are located, are demonstrated in detail. Considering ultimate limit state and fatigue limit state based on 100-year return period and 50-year design life, respectively, longterm predictions of breaking strength and fatigue are proposed.

A Study on Mechanical Analysis of Cable Logging Systems - with an Example of a Standing Skyline - (가선집재시스템 역학구조 해석에 관한 연구 - 고정식 가선집재시스템을 중심으로 -)

  • Chung, Joo Sang
    • Journal of Korean Society of Forest Science
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    • v.82 no.1
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    • pp.34-43
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    • 1993
  • In this paper, the characteristics of cable logging operations are discussed from a standpoint of mechanics. An example of standing skyline operations is used to illustrate the mechanical principles. Using force and moment boundary conditions, the maximum allowable payload was formulated as a function of slope profile, system geometry and operation options. This formulation includes fundamental equations for log drag and single segment mechanics. The catenary link model is the basic assumption in simulating cable segment stretches. In order to demonstrate the solution procedures of the formulation, a computer model was developed. The model uses Secant algorithm to determine the solution of the complex nonlinear equation set. Finally, the computer model was demonstrated using a hypothetical data set.

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Nonlinear Dynamic Analysis of a Large Deformable Beam Using Absolute Nodal Coordinates

  • Jong-Hwi;Il-Ho;Tae-Won
    • International Journal of Precision Engineering and Manufacturing
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    • v.5 no.4
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    • pp.50-60
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    • 2004
  • A very flexible beam can be used to model various types of continuous mechanical parts such as cables and wires. In this paper, the dynamic properties of a very flexible beam, included in a multibody system, are analyzed using absolute nodal coordinates formulation, which is based on finite element procedures, and the general continuum mechanics theory to represent the elastic forces. In order to consider the dynamic interaction between a continuous large deformable beam and a rigid multibody system, a combined system equations of motion is derived by adopting absolute nodal coordinates and rigid body coordinates. Using the derived system equation, a computation method for the dynamic stress during flexible multibody simulation is presented based on Euler-Bernoulli beam theory, and its reliability is verified by a commercial program NASTRAN. This method is significant in that the structural and multibody dynamics models can be unified into one numerical system. In addition, to analyze a multibody system including a very flexible beam, formulations for the sliding joint between a very deformable beam and a rigid body are derived using a non-generalized coordinate, which has no inertia or forces associated with it. In particular, a very flexible catenary cable on which a multibody system moves along its length is presented as a numerical example.

Study on Optimum Design of FPSO Spread Mooring System (FPSO 다점 계류 시스템의 최적 설계 연구)

  • Lim, Yu-Chang;Kim, Kyung-Su;Choung, Joon-Mo;Kim, Jae-Woo;Kim, Jin-Tae;Yeo, Seung-Hoon
    • Journal of Ocean Engineering and Technology
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    • v.23 no.6
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    • pp.61-66
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    • 2009
  • For a spread-moored FPSO (Floating Production, Storage, & Off-loading) subjected to environmental excitation from waves, current, and wind, a procedure to determine optimum length and stiffness of mooring lines is suggested using quasi-static frequency domain response analyses. Coupled relations between design parameters are closely examined. In consideration of this, optimized design parameters are proposed based on minimum weight condition. The initial design parameters for numerical analyses are calculated using the static catenary equation of mooring lines. It is demonstrated the line tension and vessel's offset are influenced by the mooring line length and stiffness. Accordingly it is suggested the optimum vessel's offset range should be determined considering line fatigue damage. The availability and limitation of the application of quasi-static analysis method for spread mooring system are explained by comparing the result of time domain analysis with one of frequency domain analysis.

Nonlinear Motion Analysis of FPSO with Turret Mooring System (터렛계류된 FPSO의 비선형 운동 해석)

  • 임춘규;이호영
    • Journal of the Society of Naval Architects of Korea
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    • v.40 no.1
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    • pp.20-27
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    • 2003
  • The FPSO is moored by mooring lines to keep the position of it. The nonlinear motion analysis of the moored FPSO must be carried out in the initial design stage because sea environments affect motion of it. In this paper, the mathematical model is based on the slow motion maneuvering equations in the horizontal plane considering wave, current and wind forces. The direct integration method is employed to estimate wave loads. The current forces are calculated by using mathematical model of MMG. The turret mooring forces are quasi-statically evaluated by using the catenary equation. The coefficients of a model for wind forces are calculated from Isherwood's experimental data and the variation of wind speed is estimated by wind spectrum according to the guidelines of API-RP2A. The nonlinear motions of FPSO are simulated under external forces due to wave, current, wind including mooring forces in time domain.

Dynamic Analysis of Current Collection System in High Speed Train (고속전철용 집전시스템의 동적해석)

  • 최연선;최진민;경진호
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1995.10a
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    • pp.142-147
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    • 1995
  • Dynamic characteristics of current collection system is one of the major factors which decide the performance of high speed train. To find good design parameters of the current collection system design guide is prepared through the engineering analysis in this study. The analysis starts from the statics of catenary system which results in the sinusoidal variation of stiffness, which is inherently nonlinear Mathieu equation. Simple physical models of rigid trolley wire and Mathieu equation are considered. To simulate the dynamic response of current collection system, numerical integration based on central difference method and modal analysis are presented. The calculated results of central difference method show superior to those of Euler based algorithm.

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Motion Analysis of Two Point Moored Oil Tanker (2점 계류된 선박에 대한 운동 해석)

  • Lee, Ho-Young;Lim, Choon-Gyu
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2003.10a
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    • pp.232-236
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    • 2003
  • The anchor is laid on seabed and the main engine is worked to against incident environmental loads in typoon. As the main engine is broken down in the storm, the anchor chain is cutted and the vessel is drifted. Although a ship is moored by two point mooring lines to keep the her position, a ship is crashed into a rock because of typoon and the accident of oil spilling may be occured. In this paper, we studied the position-keeping of a ship which is analyized based on the slow motion maneuvering equations considering wave, current and wind. The direct integration method is employed to estimate wave loads. The current forces are calculated by using mathematical of MMG. The two point mooring forces are quasisatatically evaluated by using the catenary equation. The coefficeints of wind forces are modeled from Isherwood’s emperical data and the variation of wind speed is estimated by wind spectrum. The nonlinear motions of a two point moored ship are simulated considering wave, current, wind load in time domain.

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Drift Motion Analysis on Horizontal Plane of a Two-Point Moored Oil Tanker (2점 계류된 선박에 대한 수평면상 표류운동 해석)

  • 이호영;임춘규
    • Journal of Ocean Engineering and Technology
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    • v.18 no.3
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    • pp.8-12
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    • 2004
  • The anchor is laid on the seabed, and the main engine is working against incident environmental loads in a typhoon. As the main engine is broken Mum in the storm, the anchor chain is cut and the vessel drifts. Although a ship is moored by two-point mooring lines to maintain her position, it has crashed into a rock because of a typhoon, resulting in a possible accidental oil spillage. In this paper, we studied maintenance of a ship's position, which is analyzed based on the slow motion maneuvering equations considering wave, current, and wind. To estimate wave loads, the direct integration method is employed. The current forces are calculated, using MMG (Mathematical Modeling Group). Th two-point mooring forces are quasi-statistically evaluated, using the catenary equation. Th coefficients of wind forces are modeled from Isherwood's empirical data, and the variation of wind speed is estimated by wind spectrum. The nonlinear motions of a two-point moored ship are simulated, considering wave, current, and wind load, in specific domain of time.

The Development of a Sliding Joint for Very Flexible Multibody Dynamics (탄성 대변형 다물체동역학을 위한 슬라이딩조인트 개발)

  • Seo Jong-Hwi;Jung Il-Ho;Sugiyama Hiroyuki;Shabana Ahmed A.;Park Tae-Won
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.29 no.8 s.239
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    • pp.1123-1131
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    • 2005
  • In this paper, a formulation for a spatial sliding joint, which a general multibody can move along a very flexible cable, is derived using absolute nodal coordinates and non-generalized coordinate. The large deformable motion of a spatial cable is presented using absolute nodal coordinate formulation, which is based on the finite element procedures and the general continuum mechanics theory to represent the elastic forces. And the non-generalized coordinate, which is neither related to the inertia forces nor external forces, is used to describe an arbitrary position along the centerline of a very flexible cable. In the constraint equation for the sliding joint, since three constraint equations are imposed and one non-generalized coordinate is introduced, one constraint equation is systematically eliminated. Therefore, there are two independent Lagrange multipliers in the final system equations of motion associated with the sliding joint. The development of this sliding joint is important to analyze many mechanical systems such as pulley systems and pantograph/catenary systems for high speed-trains.

Nonlinear Motion Analysis of FPSO with Turret Mooring System (터렛계류된 FPSO의 비선형 운동 해석)

  • Lim, Choon-Gyu;Lee, Ho-Young
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2002.10a
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    • pp.161-166
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    • 2002
  • As offshore oil fields move towards the deep ocean, the oil production systems such as FPSO are being built these days. Generally, the FPSO is moored by turret mooring lines to keep the position of FPSO. Thus nonlinear motion analysis of moored FPSO must be carried out in the initial design stage because sea environments affect motion of it. In this paper the mathematical model is based on the slow motion maneuvering equations in the horizontal plane considering wave, current and wind forces. The direct integration method is employed to estimate wave loads. The current forces are calculated by using mathematical model of MMG. The turret mooring forces are quasi-statically evaluated by using the catenary equation. The coefficients of a model for wind forces are calculated from Isherwood's experimental data and the variation of wind speed is estimated by wind spectrum according to the guidelines of API-RP2A. The nonlinear motions of FPSO are simulated under external forces due to wave, current, wind including mooring forces in time domain.

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