Nonlinear formulation and free vibration of a large-sag extensible catenary riser

IF 0.7 Q4 ENGINEERING, OCEAN Ocean Systems Engineering-An International Journal Pub Date : 2021-03-01 DOI:10.12989/OSE.2021.11.1.059
O. Punjarat, S. Chucheepsakul
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Abstract

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.
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大垂度伸缩悬链线立管的非线性公式及自由振动
本文利用虚功能原理,给出了大弧垂可伸展悬链线立管二维自由振动的非线性公式。一端的支架是铰接的,另一端是在水平方向上自由滑动的滚轮。悬链线立管在静态平衡状态下具有大的弧垂配置,并且假设其以大幅度位移到运动状态。悬链线立管系统的总虚功包括弯曲引起的虚应变能、轴向变形引起的虚应变速能、有效重量所做的虚功和惯性力。基于欧拉方程在静态和位移状态下的差异,建立了笛卡尔坐标系中二维自由振动的非线性运动方程。得到了悬链线立管的线性刚度矩阵和非线性刚度矩阵,并用Galerkin有限元程序求解了特征值问题。得到了固有频率和振型。该结果在参考研究中得到了验证,该研究涉及所提出的非线性公式的准确性和效率。给出了悬链线立管自由振动的数值结果和非线性行为的影响。
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期刊介绍: The OCEAN SYSTEMS ENGINEERING focuses on the new research and development efforts to advance the understanding of sciences and technologies in ocean systems engineering. The main subject of the journal is the multi-disciplinary engineering of ocean systems. Areas covered by the journal include; * Undersea technologies: AUVs, submersible robot, manned/unmanned submersibles, remotely operated underwater vehicle, sensors, instrumentation, measurement, and ocean observing systems; * Ocean systems technologies: ocean structures and structural systems, design and production, ocean process and plant, fatigue, fracture, reliability and risk analysis, dynamics of ocean structure system, probabilistic dynamics analysis, fluid-structure interaction, ship motion and mooring system, and port engineering; * Ocean hydrodynamics and ocean renewable energy, wave mechanics, buoyancy and stability, sloshing, slamming, and seakeeping; * Multi-physics based engineering analysis, design and testing: underwater explosions and their effects on ocean vehicle systems, equipments, and surface ships, survivability and vulnerability, shock, impact and vibration; * Modeling and simulations; * Underwater acoustics technologies.
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