基于多尺度法的船舶非线性横摇动力学研究

Study of Nonlinear Ship-Roll Dynamics Based on the Multi-Scale Method

摘要: 随着我国海洋强国战略的深入推进，海上运输和海洋资源开发规模持续扩大，船舶作为海洋经济活动的重要载体，其航行安全性日益受到关注。船舶横摇运动是影响航行安全的关键因素，特别是在恶劣海况下，非线性横摇可能引发大幅振荡甚至倾覆事故。本文针对船舶非线性横摇运动特性开展深入研究，旨在为提升船舶稳性提供理论支撑。研究首先建立包含非线性恢复力矩和阻尼力矩的横摇运动方程，然后通过多尺度法求得方程的近似解析解，揭示系统在不同参数条件下的动力学特性。在此基础上，采用数值模拟方法，系统分析横摇角随时间的变化规律；并通过对比不同阻尼条件下的运动特性，研究评估了阻尼对船舶稳定性的影响。该研究为船舶减摇装置的设计和航行控制策略的制定提供了重要参考，对保障海上作业安全、提高航运效率具有实际应用价值。

Abstract: With the further implementation of China’s maritime power strategy, the scale of maritime transportation and marine resource exploitation keeps expanding. As a vital carrier of marine economic activities, ships have drawn growing attention to their navigation safety. Ship rolling motion is a critical factor affecting navigational safety. In particular, under severe sea conditions, nonlinear rolling can induce large-amplitude oscillations and even lead to ship capsizing. This paper conducts an in-depth investigation into the characteristics of nonlinear ship rolling motion, aiming to provide theoretical support for the improvement of ship stability. In this study, a rolling motion equation involving a nonlinear restoring moment and a damping moment is firstly established. The multi-scale method is then employed to derive the approximate analytical solutions of the governing equation, so as to reveal the dynamic characteristics of the system under various parameter conditions. On this basis, numerical simulation is adopted to systematically analyze the time-varying law of the roll angle. By comparing the motion responses under different damping levels, the influence of damping on ship dynamic stability is comprehensively evaluated. The research findings offer an important reference for the design of ship anti-rolling devices and the formulation of navigation control strategies, and possess practical engineering value in ensuring maritime operation safety and enhancing shipping efficiency.