船舶非线性自由横摇运动的近似解析解

具有一定精度的近似解析解有助于方便分析船舶非线性横摇运动及其稳定性.针对以线性加立方项的阻尼力矩和回复力矩模型为基础的非线性自由横摇运动方程,运用奇异摄动理论中的多尺度法,经繁复推导给出了完整的精确至二阶的解析解,解决了消除二阶非线性项中久期项的处理问题.文中给出的解析解可以作为船舶非线性自由横摇运动的近似解析解.为此,以一船模的自由横摇为算例,计算了解析解的时间历程和平面相图,通过与Runge-Kutta法的数值解进行比对分析后表明,利用该解析解近似描述和研究船舶非线性自由横摇是可行的.

An approximate analytical solution for nonlinear free rolling of ships

An approximate analytical solution with comparative accuracy is helpful in investigating nonlinear rolling of ships and its stability.The equation,on the basis of the mixed linear-plus-cubic damping model and mixed linear-plus-cubic restoring model of nonlinear free rolling of ships,is solved with the multi-scale method of the perturbation theory,and then a complete analytical solution accurate to second-order is presented.Moreover,how to eliminate the secular term in the second-order terms of the solution is also introduced.By comparing the results of the time history and phasigram of the analytical solution with the Runge-Kutta numerical solutions for a ship model,the application of the analytical solution presented to nonlinear free rolling of ships is considered to be feasible.