基于增量谐波平衡方法的Spar平台垂荡纵摇耦合内共振响应研究

针对经典的Spar平台垂荡纵摇耦合运动问题,为解决传统小参数摄动方法和时间步进分析方法的不足,提出将增量谐波平衡方法(Incremental Harmonic Balance Method,IHBM)应用于研究其内共振响应特性。根据Floquet稳定性分析理论,对周期解的稳定性和分叉特性进行分析;在此基础上,通过将该方法与增量弧长法相结合,实现了快速、连续获得Spar平台垂荡纵摇耦合周期运动响应的目的;将IHBM计算结果与时域模拟和多尺度法计算结果进行对比,验证了该方法的准确性和高效性,该方法能够准确预测当波浪激励力频率满足一定条件,系统发生内共振时引起的纵摇不稳定运动现象。对于垂荡纵摇耦合产生的概周期运动,该方法结合Floquet理论能准确预测其发生的参数区间,从而为该周期运动的分析提供良好的基础。

Swing-pitch coupled internal resonance responses of Spar platform based on IHBM

To overcome shortcomings of the classical perturbation method and the time integration method in analyzing swing-pitch coupled response motion of a Spar platform,the incremental harmonic balance method(IHBM)was proposed to study characteristics of the coupled responses.Floquet stability analysis theory was used to analyze the stability and bifurcation behavior of a periodic solution.Then,IHBM combined with the arc-length method was adopted to realize rapidly and continuously solving the Spar platform’s swing-pitch coupled periodic motion responses.The results using IHBM were compared with those using the time domain simulation and the multi-scale method to verify the correctness and high efficiency of IHBM.It was shown that IHBM can be used to predict pitch unstable phenomena induced by the system internal resonance;it can be combined with Floquet theory to predict parametric intervals of quasi-periodic motion induced by swing-pitch coupled motion to provide a good foundation for quasi-periodic motion analysis.