【摘要】 船舶在纵浪中参数激励横摇运动的稳定性对船舶的航行安全性有着重要影响。文章研究了船舶在随机纵浪中的主共振响应及系统的稳定性问题。将随机参数激励项考虑为一窄带随机过程,建立了简化的船舶在随机纵浪中参数激励横摇线性模型,用多尺度法分离了系统的快速项,求出了系统的最大Lyapunov指数和稳态概率密度,由最大Lyapunov指数得到了系统零解稳定的条件。研究表明,船舶的阻尼、随机波浪的中心频率及带宽和随机参数激励幅值等对船舶在随机纵浪中参数激励横摇稳定性有影响。更多还原

【Abstract】 The stability of ship’s parametrical rolling in longitudinal waves is very important for ship’s safety.In this paper,the principal resonance of ship’s parametrical rolling in stochastic longitudinal waves is studied.Considering the stochastic parametrically excited term as bounded noise,the ship’s simplified linear rolling equation in stochastic longitudinal waves was set up,the method of multiple scales was used to determine the equations of modulation of amplitude and phase.The formula of system’s maximum Lyapunov exponents was obtained.The study indicates that the ship’s damping,the main frequencies of the stochastic wave and the bandwidth of the waves influence the ship’s safety region in longitudinal waves.更多还原