Sub- and super-critical nonlinear dynamics of a harmonically excited axially moving beam
Sub- and super-critical nonlinear dynamics of a harmonically excited axially moving beam
复制标题
DOI：
10.1016/j.ijsolstr.2011.10.007
复制
发表时间：
2012
影响因子：
3.6
通讯作者：
M. Ghayesh;H. A. Kafiabad;T. Reid
中科院分区：
文献类型：
--
作者：
M. Ghayesh;H. A. Kafiabad;T. Reid
亚和超临界动力学的轴向移动梁受到横向谐波激振力检查的情况下，该系统被调谐到一个三比一的内部共振，以及为的情况下，它不是。该陀螺系统的运动方程采用伽辽金法离散，得到一组耦合的非线性微分方程。对于亚临界转速区，利用伪弧长延拓方法研究了系统的周期解，同时对系统的整体动力学进行了数值研究。在后一种情况下，通过直接时间积分得到了Poincaré映射的分支图。此外，对于一组选定的系统参数，系统的动力学的时间历程，相平面的肖像，和庞加莱地图的形式。最后，给出了不同系统参数对系统幅频响应的影响以及分岔图。
The sub- and super-critical dynamics of an axially moving beam subjected to a transverse harmonic excitation force is examined for the cases where the system is tuned to a three-to-one internal resonance as well as for the case where it is not. The governing equation of motion of this gyroscopic system is discretized by employing Galerkin’s technique which yields a set of coupled nonlinear differential equations. For the system in the sub-critical speed regime, the periodic solutions are studied using the pseudo-arclength continuation method, while the global dynamics is investigated numerically. In the latter case, bifurcation diagrams of Poincaré maps are obtained via direct time integration. Moreover, for a selected set of system parameters, the dynamics of the system is presented in the form of time histories, phase-plane portraits, and Poincaré maps. Finally, the effects of different system parameters on the amplitude-frequency responses as well as bifurcation diagrams are presented.