纵浪上船舶的动稳性研究

在纵浪上航行的船舶，当升沉（或纵摇）固有频率约为横摇固有频率的2倍时将发生参数激励主共振。本文考虑升沉对横摇的耦合作用，建立了非线性参数激励横摇运动方程。用多尺度方法对方程进行求解，用Floquet理论和分岔理论对定常解进行稳性分析，获得了参数激励主共振下的不稳定域和可以导致船舶倾覆的多数区域，为船舶的动稳性研究提供了一种新的方法。与数值结果的比较验证了本文的结论。

THE EFFECT OF PRINCIPAL PARAMETRIC EXCITATION ON THE STABILITY OF SHIPS IN LONGITUDINAL SEAS

To the ships in longitudinal waves, the principal parametric resonance will occurwhen the natural heave(or pitch)frequency is about twice the roll frequency. A nonlinearparametrical equation is obtained including the coupling effect of heave on roll. The multiple scale method is presented in solving the equation, and the Floquet theory and bifurcation theory are used to determine the stability of steady-state response. The results aresummarized in a bifurcation that display the instability boundaries and the region in whicha ship may capsize. The analysis presents a new method to the stability research of a ship,which is confirmed by numerical method.