Modelling of vibro-impact system driven by beat frequency

Abstract

A mathematical model of vibro-impact system accounting for oscillatory and progressive motion, and capable of transferring a high-frequency low-amplitude excitation into low-frequency high-amplitude response is developed. A special beat frequency kinematic excitation was used, which has two distinctive features: (i) the low-frequency modulated excitation is tuned to the natural frequency of the oscillating system, and (ii) the excitation is asymmetric. The model considers also visco-elastic properties of the media. It is demonstrated that this mechanism allows to overcome the resistance force of the media and to move forward. Several different ways to achieve a steady progression without supplying additional energy are explored, however, in all these cases progression rates are relatively low. A significant increase of progression rates is only possible by controlling the motion of the system. A simple control strategy enhancing progression rates substantially is proposed and implemented.