Vibro-impact system with non-ideal excitation: analytical investigations

This paper is concerned with an oscillator attached to a crank-slider mechanism, where the driving torque is not assumed as constant, but as dependent on its angular velocity. Moreover, it is affected by the motion of the oscillator, i.e. it represents the so-called non-ideal excitation. The displacement of the oscillator is limited by a barrier, and the impact can occur. Consequently, the system response can be both impact and non-impact, which makes the influence on the driving torque unknown, and important to predict for practical applications in hand-held percussion machines, pile driving machines, cutting and grinding machines, etc. This work provides the analytical analyses of the regular behaviour of such vibro-impact system with non-ideal excitation system for the first time. New insight into its dynamics is gained, in terms of the appearance of impact and non-impact solutions, values of the impact velocity and their dependence on other system parameters. Amplitude-frequency diagrams are also obtained, showing the regions of non-impact, impact behaviour, non-existence of period-one steady-state response, stable and unstable solutions and oblique jumps in the amplitude and frequency. The stability issue is also investigated, and novel results are obtained with respect to the impact velocity and the associated steady-state response. The analytical solutions are verified numerically, confirming their validity and accuracy.

Automated summary

This paper provides the first analytical analyses of the regular behavior of a vibro-impact system with a non-ideal excitation system, gaining new insights into its dynamics. The study explores the appearance of impact and non-impact solutions, values of impact velocity, and their dependence on other system parameters. The stability issue is investigated, resulting in novel findings regarding impact velocity and associated steady-state response.