• Ocean Systems Engineering
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• 제10권1호
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• pp.67-86
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• 2020

The main goal of this study is to investigate the free vibration analysis of a large sag catenary with application to the jumper in hybrid riser system. The equation of motion is derived by using the variational method based on the virtual work principle. The finite element method is applied to evaluate the numerical solutions. The large sag catenary is utilized as an initial configuration for vibration analysis. The nonlinearity due to the large sag curvature of static configuration is taken into account in the element stiffness matrix. The natural frequencies of large sag catenary and their corresponding mode shapes are determined by solving the eigenvalue problem. The numerical examples of a large sag catenary jumpers are presented. The influences of bending rigidity and large sag shape on the free vibration behaviors of the catenary jumper are provided. The results indicate that the increase in sag reduces the jumper natural frequencies. The corresponding mode shapes of the jumper with large sag catenary shape are comprised of normal and tangential displacements. The large sag curvature including in the element stiffness matrix increases the natural frequency especially for a case of very large sag shape. Mostly, the mode shapes of jumper are dominated by the normal displacement, however, the tangential displacement significantly occurs around the lowest point of sag. The increase in degree of inclination of the catenary tends to increase the natural frequencies.

• Ocean Systems Engineering
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• 제11권1호
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• pp.59-81
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• 2021

The nonlinear formulation using the principle of virtual work-energy for free vibration of a large-sag extensible catenary riser in two dimensions is presented in this paper. A support at one end is hinged and the other is a free-sliding roller in the horizontal direction. The catenary riser has a large-sag configuration in the static equilibrium state and is assumed to displace with large amplitude to the motion state. The total virtual work of the catenary riser system involves the virtual strain energy due to bending, the virtual strain energy due to axial deformation, the virtual work done by the effective weight, and the inertia forces. The nonlinear equations of motion for two-dimensional free vibration in the Cartesian coordinate system is developed based on the difference between the Euler's equations in the static state and the displaced state. The linear and nonlinear stiffness matrices of the catenary riser are obtained and the eigenvalue problem is solved using the Galerkin finite element procedure. The natural frequencies and mode shapes are obtained. The results are validated with regard to the reference research addressing the accuracy and efficiency of the proposed nonlinear formulation. The numerical results for free vibration and the effect of the nonlinear behavior for catenary riser are presented.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2007년도 춘계학술대회 논문집
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• pp.227-235
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• 2007

The railway catenary is softer in the middle of a span than at the end. This stiffness variation induce the vertical motion of a moving pantograph, which results in the large variation of contact forces. To reduce the vertical motion of a pantograph, we can introduce a pre-sag of the contact wire. The pre-sag changes merely equilibrium position of the contact wire. Because the pantograph must follow the sag added to the motion of the contact wire, the sag gives downward forces to the pantograph. If the pre-sag is proper, the variation of the vertical motion of the pantograph is reduced. However, excessive sag worses the current collection performance because the pantograph receives too large downward forces by the contact wire. The objective of the paper is to establish the theoretical basis to understand how the pre-sag affect the contact force variation and to propose the proper sag for the railway catenary for the train speed up to 200 km/h.

• 대한토목학회논문집
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• 제34권3호
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• pp.711-721
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• 2014

현수교 주케이블은 다수의 PPWS로 구성되며 설계조건과의 차이를 고려하여 이들의 시공위치에 정확히 가설하는 작업이 필요하다. 이를 위하여 다수의 PPWS 중 수개의 PPWS는 절대 새그측량을 수행하며 이를 기준으로 나머지 PPWS를 몇 개의 그룹으로 나누어 상대 새그를 측량하여 목표로 하는 시공위치에 가설하기 위한 PPWS 길이 조정작업을 수행한다. 현장여건을 반영한 시공은 새그변화요인에 대하여 새그민감도를 산정하고 이에 해당하는 PPWS 길이 조정량을 계산하여 새그를 조정하는 순서로 진행된다. 본 연구에서는 PPWS 양단 지지점의 변위에 따른 새그민감도의 미분관계식을 도출하였다. 그리고, 일련의 연구수행으로 제안된 새그민감도 산정식의 현장 실증에 선행하여 모형 현수선 시스템을 구축하고 이에 대한 검증실험을 수행하였으며 실험결과로부터 도출된 새그민감도 산정식의 타당성을 확인하였다.