Vibration of the Translation and the Inclination Motions Coupled System Under the Periodic Base Motion (Auto-parametric Resonance and Influences of Height of Center of Mass, Unbalance of Mass and Difference between Support Stiffness)

Abstract

This is a study on the vibration characteristics of the translation and the inclination motions-coupled systems, which is the dynamical model of a train, a vehicle, and so on. It mainly investigates the nonlinear vibration of such a system which is subject to the base periodic displacement. The study observes the occurrence of the auto-parametric resonance at the resonance point of the translational motion, when the ratio between the natural frequencies of the inclinational motion and the translational motion is close to one-to-two. Moreover, the occurrence of an almost periodic motion is observed when this ratio is slightly different from one-to-two. The main discussion is based on the occurrence regions of the auto-parametric resonance and the almost periodic motion. This paper clarifies that the occurrence region of the auto-parametric resonance widely exists from about the ratio two-to-three to about the ratio one-to-three. It also notes on the influence of unbalance of the center of mass which produces slight linear coupling terms between the translational motion and the inclinational motion. The results of this paper indicate that the auto-parametric resonance is not the special phenomenon and it easily occurs. These theoretical results are confirmed by the experiments.