非线性横摇导致船舶倾覆的突变研究

针对规则波中船舶非线性横摇而产生的倾覆现象,提出了采用了突变理论进行分析的方法.在船舶横摇运动方程的建模过程中,将阻尼力矩取至三次项,恢复力矩取至七次项. 在此基础之上,经数学变换,将船舶非线性横摇模型转换成了尖点突变模型的形式,并对模型进行了求解,得到了系统突变时的临界函数关系式与关系曲线.分析结果表明,倾覆现象与船舶自然横摇频率和恢复力系数有关,其倾覆的临界条件是自然横摇频率和恢复力系数的函数.当自然横摇频率与恢复力系数满足突变临界函数的关系式与关系曲线时,会导致系统的突变,即船舶的倾覆.

Ship capsizal caused by catastrophic nonlinear rolling

Catastrophe theory was put forward to analyze the phenomenon of ship capsizal caused by nonlinear rolling in regular waves. When establishing an equation for nonlinear rolling of a ship, damping moment was approximated to third power and restoring moment was approximated to seventh power. On the basis of this, by mathematical manipulation, the ships nonlinear rolling model was transformed into a cusp catastrophe model, and the catastrophe model was then solved. The critical functional relationship and its curve at system catastrophe were derived.Analysis showed that capsizal is due to two factors: the natural rolling frequency of the ship and the coefficient of restoring force. The critical capsizal condition is a function of these two factors. When these two factors satisfy the critical functional relationship and its curve, catastrophe is inevitable, and the ship capsizes.