两栖车辆非线性横摇运动的Lyapunov特性指数分析

Lyapunov Characteristic Exponents for Analyzing the Nonlinear Rolling Motion of Amphibious Vehicle

为了确定两栖车辆在规则波浪激励下的非线性横摇运动形式,根据Lyapunov特性指数(LCE)的定义,采用QR分解法计算两栖车辆横摇运动的LCE,再根据计算出的LCE判断两栖车辆的运动形式.以两栖车辆为例,计算了当波浪频率与横摇固有频率的频率比为1时横摇运动为周期性的运动,当频率比为1.25时横摇运动为混沌运动,并通过数值仿真进行了验证.以频率比为控制变量,计算了当波浪扰动力矩一定时,两栖车辆在不同频率波浪激励下进入混沌运动的阈值.计算结果表明:利用LCE方法可以简单、准确地判断非线性横摇运动类型.

In order to determine the nonlinear rolling motion types of amphibious vehicle in regular waves,QR factorization method was applied to calculate Lyapunov characteristics exponents（LCE） according to the definition of LCE,and then the rolling motion types of amphibious vehicle could be judged by the obtained LCE.As an example,the LCE of the nonlinear rolling motion in regular wave of an amphibious vehicle were calculated in different frequency ratio between wave frequency and the nature frequency of rolling motion,respectively. When the frequency ratio R=1,the rolling motion is a period motion,and when the frequency ratio R=1.25,the rolling motion is a chaos motion.The obtained results are verified by numerical simulation results.Taking frequency as control variables,the LCE can be used to find the chaotic threshold of the amphibious vehicle nonlinear rolling motion in wave of different frequency at a constant disturbing moment of wave.The obtained result show the LCE is direct,concise and effective for judge the amphibious vehicle nonlinear rolling motion types.