基于尖点突变的船舶横摇倾覆研究

Study on ship rolling and capsizing based on the cusp catastrophe

针对船舶在规则波中非线性横摇导致的倾覆现象,提出了采用突变理论进行分析的方法.在建模过程中,将船舶非线性横摇方程恢复力矩取到七次项,阻尼力矩取至三次项以便于推导.经数学变换,将船舶非线性横摇方程转化为尖点突变模型的形式.由理论分析,得出了当船舶倾覆时,其自然横摇频率与三次、五次、七次恢复力系数满足一定的函数关系.在忽略七次恢复力系数影响的情况下,得出了船舶自然横摇频率与三次、五次恢复力矩的关系式,并绘出了相应的曲面图.

Catastrophe theory is introduced to analyze the ship capsizing phenomenon in regular waves caused by nonlinear rolling. In the modeling process, damping moment and restoring moment are approximated to third power and restoring moment was approximated to seventh power separately for convenience. Through mathematical manipulation, the nonlinear rolling model of the ship is transformed into a cusp catastrophe model. By the theoretical analysis, it＇s found that the natural rolling frequency is m a certain relationship with the third, the fifth and the seventh power restoring force coefficient in case of capsizing. At last, ignoring the impact of the seventh power restoring force coefficient, the relational expression between natural rolling frequency and the third and the fifth power restoring force coefficients are deduced, then the corresponding relationship curved face are mapped.