摘要
由于船舶阻尼系数和恢复力矩的的非线性 ,船舶大幅运动时横摇和纵摇耦合。各类船舶的纵摇固有频率接近横摇固有频率的两倍 ,存在基于动力学理论的 2∶ 1的内共振关系。本文考虑大幅波浪激励 ,建立了船舶横摇与纵摇耦合的非线性运动方程 ,针对纵摇和横摇频率存在 2∶ 1内共振关系以及波浪遭遇频率Ω等于 1 /4倍纵摇固有频率 ,采用多尺度方法 ,求出了运动方程的摄动解 ,得到了横摇与纵摇超谐运动的时间历程响应 ,分析了产生超谐共振的条件。研究表明 ,在大幅波浪激励下 ,船舶将出现超谐共振响应 ,其运动特征是 :横摇运动和纵摇运动均为两个不同频率谐波的迭加。横摇响应包括波浪遭遇频率谐波和横摇固有频率谐波 ;纵摇包括波浪遭遇频率谐波和纵摇固有频率谐波。两个谐波响应的迭加 ,使横摇和纵摇运动响应显著增加 ,并且横摇运动不再左右对称。针对算例进行了超谐运动响应计算 ,计算结果与本文的理论分析结论完全吻合。
The damping coefficients and restoring moments of a ship are nonlinear, which result in coupled rolling and pitch when the ship is in large amplitude motion. Generally, the ratio of a ships natural frequency of pitch to the natural frequency of roll is nearly 2 to 1, that meets the relation of internal resonance based on nonlinear dynamics. The nonlinear motion equations of coupled rolling and pitch of a ship are set up under the condition of rough sea exciting. Based on the 2∶1 relation of internal resonance of a ship and the wave encountering frequency Ω is close to the 1/4 natural frequency of pitch, the perturbation solutions of motion equations are solved and the time history response for rolling and pitch in super harmonic resonance are given by multiply scale method. It is shown that the super harmonic resonance motion will occur when a ship is in large waves. The characteristics of the resonance are that the rolling motion and pitch motion both are the superposition of two harmonic responses with different frequencies respectively. The rolling motion includes two harmonic components, one is in the wave encountering frequency, and another is in the rolling natural frequency. For pitch motion, one component is in the wave encountering frequency, and another is in the pitch natural frequency. Due to the superposition of two responses with different frequencies, the ship motion is increased and the rolling motion is not symmetrical. The calculated results are identical with the theoretical analysis.
出处
《中国造船》
EI
CSCD
北大核心
2002年第4期19-24,共6页
Shipbuilding of China
基金
国家自然科学基金资助项目 (5 96790 0 2 )
