传统Spar平台垂荡主共振时非线性耦合响应的研究

Nonlinear coupled responses of a classic spar platform in the heave resonant waves

考虑瞬时波面影响,建立了Spar平台垂荡-纵摇运动的参数激励耦合运动方程,应用多尺度法导出了波浪频率接近垂荡固有频率时响应方程的一阶摄动解并做数值验证。计算结果显示:当波浪高度达到一定值时,纵摇运动中出现大量的亚谐频率成分;随着波浪高度进一步增大,纵摇运动将出现明显的幅值跳跃现象。研究结果表明,能量渗透现象是纵摇运动失稳的主要原因,波浪激励力矩对于纵摇本身的贡献很小。由于垂荡模态存在能量饱和现象,多余的垂荡能量将会向纵摇模态转移,导致出现大幅值的纵摇运动。

The parametric exciting coupled equations for heave and pitch of a Spar platform are established with considering the effect of time-varying incident wave elevation and the first order steady-state response of the equation is solved by the method of multiple scales and validated by the numerical method. The calculation result shows that many sub frequency components begin to appear in pitch mode when the wave height arrives at a certain value, as the wave height increases further, the jumping phenomenon occurs in pitch motion. It indicates that the energy penetration phenomenon is the main cause for the unstable pitch movement while the wave exciting moment plays very little roles on it. Because of the energy saturation in heave mode, the extra energy of heave mode will be transferred to the pitch mode and induces large-amplitude pitch response.