• Title/Summary/Keyword: Catenary Equation

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Dynamic response analysis of floating offshore wind turbine with different types of heave plates and mooring systems by using a fully nonlinear model

  • Waris, Muhammad Bilal;Ishihara, Takeshi
    • Coupled systems mechanics
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    • v.1 no.3
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    • pp.247-268
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    • 2012
  • A finite element model is developed for dynamic response prediction of floating offshore wind turbine systems considering coupling of wind turbine, floater and mooring system. The model employs Morison's equation with Srinivasan's model for hydrodynamic force and a non-hydrostatic model for restoring force. It is observed that for estimation of restoring force of a small floater, simple hydrostatic model underestimates the heave response after the resonance peak, while non-hydrostatic model shows good agreement with experiment. The developed model is used to discuss influence of heave plates and modeling of mooring system on floater response. Heave plates are found to influence heave response by shifting the resonance peak to longer period, while response after resonance is unaffected. The applicability of simplified linear modeling of mooring system is investigated using nonlinear model for Catenary and Tension Legged mooring. The linear model is found to provide good agreement with nonlinear model for Tension Leg mooring while it overestimates the surge response for Catenary mooring system. Floater response characteristics under different wave directions for the two types of mooring system are similar in all six modes but heave, pitch and roll amplitudes is negligible in tension leg due to high restraint. The reduced amplitude shall lead to reduction in wind turbine loads.

Form-finding analysis of suspension bridges using an explicit Iterative approach

  • Cao, Hongyou;Zhou, Yun-Lai;Chen, Zhijun;Wahab, Magd Abdel
    • Structural Engineering and Mechanics
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    • v.62 no.1
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    • pp.85-95
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    • 2017
  • This paper presents an explicit analytical iteration method for form-finding analysis of suspension bridges. By extending the conventional analytical form-finding method predicated on the elastic catenary theory, two nonlinear governing equations are derived for calculating the accurate unstrained lengths of the entire cable systems both the main cable and the hangers. And for the gradient-based iteration method, the derivation of explicit calculation for the Jacobian matrix while solving the nonlinear governing equation enhances the computational efficiency. The results from sensitivity analysis show well performance of the explicit Jacobian matrix compared with the traditional finite difference method. According to two numerical examples of long span suspension bridges studied, the proposed method is also compared with those reported approaches or the fundamental criterions in suspension bridge structural analysis, which eventually confirms the accuracy and efficiency of the proposed approach.

A study on the optimal value for the towers height of the ropeway (가공색도의 지주높이 최적치에 관한 연구)

  • 최선호;박용수
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.12 no.2
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    • pp.381-388
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    • 1988
  • The heights of the towers of a ropeway are theoretically derived and the result is experimentally verified. The accuracy in the equation of deflection angle obtained by applying the characteristics of catenary curve was confirmed through experiment. By applying these equations the optimal values of the tower heights could be obtained because the deflection angles trade off each other. The deflection angle was measured by using the curve fitting technique.

Analysis for Autotransformer-Fed AC Electric Railroad System Using Constant Current Mode (정전류 철도 부하를 이용한 교류 전기 철도 급전 시스템 해석)

  • 이승혁;정현수;김진오
    • Proceedings of the KSR Conference
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    • 2001.10a
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    • pp.329-334
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    • 2001
  • This paper presents exact autotransformer-fed AC electric railroad system modeling using constant current mode. The theory is based on the solution of algebraic. The proposed modeling is considered the line self-impedances and mutual-impedances. Besides, the load modeling improved results are obtained as application to the proposed constant current mode. In the analysis on AT-fed AC electric railroad system circuit, a generalized analysis method using the loop equation on a case by case. the simulation objectives are to calculate the catenary and rail voltages with respect to ground, as the train moves along a section of line between two adjacent ATs. The model contains assumptions regarding the representation of the autotransformer, the impedance of the track/catenary system, and the grounding arrangements, which all effect the accuracy of the result. The modeling results seem very reasonable. It is established that techniques for the AC electric railroad system modeling and analysis.

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Optimal Design of a High-Speed Linear Synchronous Motor in a Dynamic Tester for Catenary Current Collection (전차선로-집전계 주행시험기 추진용 고속 선형동기전동기의 최적설계)

  • Lee, Hyung-Woo;Kwon, Sam-Young;Lee, Byung-Song;Park, Hyun-June
    • Proceedings of the KSR Conference
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    • 2006.11b
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    • pp.665-674
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    • 2006
  • This paper presents the optimal design of a high-speed (200[km/h]) Linear Synchronous Motor which will be used as a propulsion system of a dynamic tester for catenary-current collection used in railways. Motor performance, especially detent force minimization on various design schemes has been investigated in detail by using FEM (Finite Element Method). Simulation-based DOE (Design of Experiments) method is also applied in order to reduce the large number of analysis according to each design variable and consider the effect among variables. The optimal design in all aspects is proposed by an optimization algorithm using a regression equation derived from the simulation-based DOE and the performance is verified by FEM.

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Comparison of simplified model and FEM model in coupled analysis of floating wind turbine

  • Kim, Byoung Wan;Hong, Sa Young;Sung, Hong Gun;Hong, Seok Won
    • Ocean Systems Engineering
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    • v.5 no.3
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    • pp.221-243
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    • 2015
  • This paper compares simplified and finite element method (FEM) models for tower and blade in dynamic coupled analysis of floating wind turbine. A SPAR type wind turbine with catenary mooring lines is considered in numerical analysis. Floating body equation is derived using boundary element method (BEM) and convolution. Equations for mooring line, tower and blade are formulated with theories of catenary, elastic beam and aerodynamic rotating beam, respectively and FEM is applied in the formulation. By combining the equations, coupled solutions are calculated. Tower or blade may be assumed rigid or lumped body for simplicity in modeling. By comparing floating body motions, mooring line tensions and tower stresses with the simple model and original FEM model, the effect of including or neglecting elastic, rotating and aerodynamic behavior of tower and blade is discussed.

Dynamic Analysis of Elastic Catenary Cable Subjected to Current (조류 하중을 받는 탄성 현수선 케이블의 동적 해석)

  • 백인열;장승필;윤종윤
    • Journal of the Earthquake Engineering Society of Korea
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    • v.2 no.2
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    • pp.95-104
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    • 1998
  • The dynamic behavior of the marine cable is essentially nonlinear and dominated by geometric nonlinearity. Furthermore, fluid drag force makes the problem more complex and difficult. Therefore, it has certain limitations to obtain the dynamic behavior of the marine cable by analytical method. The purpose of this paper is to apply the elastic catenary cable element to the problem of under water cable including the hydrodynamic effects of fluids. The static and dynamic formulations for the three-dimensional elastic catenary coble under water effects are derived and the finite element analysis procedures are presented. In the analysis, the hydrodynamic forces are modeled by modified Morison equation. A comparison of the results obtained using present method with previously published results showed the validity of present method. The dynamic behavior of the marine cable subjected to current is investigated using present method and it can be illustrated that the dynamic behavior of the marine cable subjected to current varies with the incident angle of the current and inclined angle of the cable.

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Free vibration of tapered arches made of axially functionally graded materials

  • Rajasekaran, S.
    • Structural Engineering and Mechanics
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    • v.45 no.4
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    • pp.569-594
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    • 2013
  • The free vibration of axially functionally graded tapered arches including shear deformation and rotatory inertia are studied through solving the governing differential equation of motion. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal arches with hinged-hinged, hinged-clamped and clamped-clamped end restraints. In this study Differential Quadrature element of lowest order (DQEL) or Lagrangian Interpolation technique is applied to solve the problems. Three general taper types for rectangular section are considered. The lowest four natural frequencies are calculated and compared with the published results.

Experimental Verification of Sag Sensitivities using Catenary Model for PPWS Configuration Control in a Suspension Bridge (모형 현수선을 이용한 현수교 PPWS 형상관리를 위한 새그민감도의 실험적 검증)

  • Jeong, Woon;Seo, Ju Won;Lee, Sung Hyung
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.34 no.3
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    • pp.711-721
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    • 2014
  • PPWS, a large number of which a main cable of a suspension bridge consists of, must be precisely erected at a target location under construction considering the differences among design conditions. The absolute sag is measured for several PPWSs, which are reference strands and the relative sag is surveyed from them to other PPWSs, which are divided into several groups. And the adjustment of PPWS length is performed to erect it at target configuration. When PPWS is being under erection in a real bridge site, the procedures are as follows; evaluate sag sensitivities according to sag variation factors, calculate an adjustment length of PPWS corresponding to them and adjust a sag of PPWS by controlling the calculated amount of PPWS length. In this study, the differential-related equations of sag sensitivity were proposed for support movement of PPWS. Before site demonstration study of a series of them, we established a catenary model system and accomplished verification tests of them. From test results, the validation of them was done.

The Analysis of 4-Conductors Catenary System of AC Railway Feeding System and Calculation of Induced Voltage near Rail Track using the FDTD Method (교류 전기철도 급전계통 4도체군 전차선로 분석 및 FDTD 방법을 이용한 선로 주변 유도전압 계산에 관한 연구)

  • Ryu, Kyu-Sang;Yeom, Hyoung-Sun;Cho, Gyu-Jung;Lee, Hun-Do;Kim, Cheol-Hwan
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.65 no.12
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    • pp.1958-1964
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    • 2016
  • AC railway feeding system use single phase to supply power to the railway vehicles. And the system use the rail track as a return current path, so that current flows in the rail. In this situation inductive interference on communication system and unsafe environment can appear on railway system. Therefore knowing the current distribution of catenary system and analysing the return current is required. In this study detail return current distribution was analyzed by modeling the catenary system as 4-conductors group. The distribution characteristics and trends of return current were studied by using the PSCAD/EMTDC and FDTD method that based on Maxwell equation was used to calculate the induced voltage. Simulation code was made by MATLAB. Using this study result data, we can suggest the proper installation location of digital device and these data can be used for additional studies related to return current or induced voltage as a base data.