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Pure Mathematics 2025
刚性立管顺流向与横向涡激振动的数值模拟分析
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Abstract:
涡激振动是深海立管在复杂海洋环境中常见的动力响应之一，常导致立管结构疲劳损坏。本研究针对刚性立管的涡激振动问题展开分析，重点讨论顺流向与横向振动特性。在数值模拟过程中，构建耦合常微分方程组来描述结构与尾流振子之间的相互作用，并采用四阶龙格–库塔法和有限差分法对其进行求解。模拟结果显示，两种数值方法所得结果高度一致，验证了所用方法的准确性与有效性。进一步地，基于该方法研究了一系列质量比与结构阻尼比条件下，位移振幅随折合速度的变化规律。
Vortex-induced vibration (VIV) is one of the common dynamic responses of deep-sea risers in complex ocean environments, often leading to fatigue damage of the riser structure. This study analyzes the VIV of rigid risers, with a focus on the in-line and cross-flow vibration characteristics. In the numerical simulation process, a coupled system of ordinary differential equations is constructed to describe the interaction between the structure and the wake oscillator. The fourth-order Runge-Kutta method and the finite difference method are employed to solve the system. The simulation results show a high degree of consistency between the two numerical methods, verifying the accuracy and effectiveness of the proposed approach. Furthermore, based on this method, the variation of displacement amplitude with reduced velocity is investigated under a series of mass ratio and structural damping ratio conditions.
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