Sub- and super-critical nonlinear dynamics of a harmonically excited axially moving beam |
| |
Authors: | Mergen H Ghayesh Hossein A Kafiabad Tyler Reid |
| |
Institution: | 1. Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada H3A 2K6;2. Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA |
| |
Abstract: | 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. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|