考虑平方阻尼及分段线性刚度铰接塔-油轮系统的分岔与混沌特性

BIFURCATION AND CHAOS OF ALT–TANKER WITH SQUARE DAMPING AND PIECEWISE LINEAR STIFFNESS

研究了铰接塔-油轮系统在规则激励下的分岔和混沌特性。将该系统简化为单自由度分段线性恢复刚度,含平方阻尼的动力学分析模型,建立了铰接装载塔的分段非线性运动方程。使用增量谐波平衡法(IHB)获得系统周期解,结合Floquet理论判断系统周期解的稳定性,使用增量弧长法进行路径跟踪,获得了系统响应曲线和通向混沌的道路,发现两种由倍周期分岔导致的混沌运动。并且,为了验证系统的混沌运动,计算得到了两种混沌运动从产生到消失过程的最大Lyapunov指数图。

The bifurcation and chaos of ALT （Articulated loading tower）-Tanker system under regular excitation are studied. The system is simplified into single degree of freedom dynamics model with piecewise linear restoring forces and square damping, then the piecewise nonlinear motion equation of ALT is established. The steady periodic solution of ALT is obtained by incremental harmonic balance （IHB） method. The stability analysis is performed by using Floquet theory. The path-following procedure using the incremental arc length method is used to trace response curves and the road of entering into chaos. The system exhibits two kinds of chaotic motion through a sequence of period doubling bifurcations. The max Lyapunov exponent diagrams of two kinds of chaotic motion from beginning to vanishing are obtained for validating chaotic motion of the system.