Multiple Non-Smooth Events in Multi-Degree-of-Freedom Vibro-Impact Systems

Abstract

Abstract.The behaviour of a multi-degree-of-freedom vibro-impact system is studied using a two degree-of-freedom impact oscillator as a motivating example. A multi-modal model is used to simulate the behaviour of the system, and examine the complex dynamics which occurs when both degrees of freedom are subjected to a motion limiting constraint. In particular the chattering and sticking behaviour which occurs for low forcing frequencies is discussed. In this region a variety of nonsmooth events can occur, including newly studied phenomena such as sliding bifurcations. In this paper the multiple nonsmooth events which can occur in the two degree-of-freedom system are categorised, and demonstrated using numerical simulations.

Nonsmooth Modal Analysis of Piecewise-Linear Impact Oscillators

“…A majority of such works consists either in i) regularizing the impact condition(s) with the addition of springs [4,7,15,19,27,28,36,41] or ii) investigating the dynamics of a forced vibro-impact oscillator [12,34,35,43,44]. Regularizing is known to introduce numerical stiffness [1,2] and is not considered in this work (the relationship between regularized and infinitely rigid impact was studied using a two-degree-of-freedom system with an elastic stop with one impact per period in ref.…”

Nonlinear dynamics and triboelectric energy harvesting from a three-degree-of-freedom vibro-impact oscillator

“…This is one way of displaying the dynamic behaviour of vibro-impact and the present bifurcation idea is similar to that in Ref. [56], which is quite different from the conventional bifurcation concept. Therefore, the countable dots at each value of R δ represent the number of impacts, rather than the order of periodicity, in one vibration period of periodic motions, while the uncountable dots indicate the impacts of non-periodic vibrations.…”

“…Chatter is characterized by many consecutive impacts and might therefore be exploited in triboelectric energy harvesting from vibro-impact systems. In the study of a multi-degree-of-freedom vibroimpact system, Wagg [56,61] discussed the chattering and sticking behaviour which appeared at low forcing frequencies, and showed that a variety of non-smooth events could possibly occur. Here, a numerical simulation is conducted to determine whether chatter can appear in the present system at low forcing frequencies.…”

Impulsive control of sticking motion in van der Pol one-sided constraint system

“…Sticking motions of a two degree of freedom system with multiple motion limiting constrains were considered in [22]. And Wagg also researched sticking motions of multiple degree of freedom vibro-impact system in [23]. Feng et al discussed the chattering bifurcations in a Duffing unilateral vibro-impact system in [24].…”