用IHB法分析双谐波激励下铰接塔-油轮系统的非线性动力学特性

Nonlinear Dynamical Behavior of ALT-Tanker Under Two Harmonic Excitations with Incremental Harmonic Balance Method

研究了考虑平方阻尼情况下,铰接塔-油轮系统在双谐波激励下的非线性动力学特性。将该系统简化为单自由度分段线性恢复力,含平方阻尼的运动学分析模型,建立了铰接装载塔系统的分段非线性动力学方程。采用增量谐波平衡法获得系统周期解,使用Floquet理论判断系统的运动稳定性,结合路径跟踪法跟踪系统响应曲线,获得了系统所有可能的亚谐、谐波、组合谐波共振运动。分析了不对称恢复刚度比值对系统亚谐、组合谐波共振和对系统运动倍周期分岔点的影响,比较了考虑平方阻尼和不考虑平方阻尼情况下系统非线性动力学特性,得到了系统的一些重要的非线性动力学特点。

The nonlinear dynamical behaviors of ALT(articulated loading tower)-Tanker system under two harmonic excitations are investigated. The system is simplified into a single degree of freedom model with piecewise linear restoring force and square damping, the piecewise nonlinear motion equation is established. The steady periodic motions of the ALT-Tanker system are obtained with incremental harmonic balance(IHB) method. The stability analysis is performed via Floquet theory. The path-following procedure is used to trace response curves. And all of possible sub-harmonic, harmonic and combination-harmonic resonances are found out. The influence of the ratio of the non symmetric restoring rigidity on sub-harmonic, combination-harmonic resonances and the period doubling bifurcation is analyzed, the nonlinear dynamical behaviors considering square damping or not are compared. So some important nonlinear dynamical behaviors of ALT-Tanker system are acquired.