Investigating the Effect of Viscous Friction Forces on Stability of Vibro-impact Systems

This chapter is devoted to the study of the influence of viscous friction forces on the stable operation of vibration-impact systems. In § 4.1, the dynamics of a single-mass vibrating impactor are considered taking into account viscous friction forces. The coordinates of fixed points corresponding to single-impact n-fold periodic motions are obtained, and their stability is investigated. The bifurcation parameters of the N- and C-surfaces are found and constructed in space. It is shown that taking into account, the forces of viscous friction lead to smoothing out the infinite discontinuities of individual parts of the stability regions. The magnitude of the impact velocity decreases. Some new properties of bifurcation C-surfaces are indicated, consisting in the fact that the usually existing superposition of single-impact periodic movements with different multiplicities (n = 1, 2, 3, …) is eliminated by these bifurcation surfaces. Recommendations are given for choosing optimal parameter values. In the case of resonance, a complete partition of the three-dimensional parameter space into stability regions of single-impact n-multiple periodic motions has been carried out. It is shown that in this case, multiple ( \(n \ge 2\) ) stable single-impact periodic movements do not exist. The second paragraph examines the stability of the operation of a two-mass vibration-impact mechanism taking into account viscous friction forces. Finding the coordinates of fixed points, drawing up a characteristic polynomial and studying stability is carried out using a developed special software product. The main conclusions are presented at the end of the chapter.