Abstract
The dynamic model of a vibroimpact system subjected to harmonic excitation with symmetric elastic constraints is investigated with analytical and numerical methods. The codimension-one bifurcation diagrams with respect to frequency of the excitation are obtained by means of the continuation technique, and the different types of bifurcations are detected, such as grazing bifurcation, saddle-node bifurcation, and period-doubling bifurcation, which predicts the complexity of the system considered. Based on the grazing phenomenon obtained, the zero-time-discontinuity mapping is extended from the single constraint system presented in the literature to the two-sided elastic constraint system discussed in this paper. The Poincare mapping of double grazing periodic motion is derived, and this compound mapping is applied to obtain the existence conditions of codimension-two grazing bifurcation point of the system. According to the deduced theoretical result, the grazing curve and the codimension-two grazing bifurcation points are validated by numerical simulation. Finally, various types of periodic-impact motions near the codimension-two grazing bifurcation point are illustrated through the unfolding diagram and phase diagrams.
Highlights
In mechanical engineering, there exist the vibroimpact phenomena widely, and systems interacting via impact have been extensively studied in recent years
A lot of work has gone into investigating nonsmooth bifurcations [1,2,3,4,5,6,7,8] of dynamical systems. e focus of investigations has gradually begun to change from a unilateral constraint system [9,10,11] to a multiconstraint system [12,13,14,15,16,17]. e impact oscillators can be divided into rigid or elastic impact oscillators according to the hardness of constraint
Jiang and Wiercigroch [19] developed the concept of discontinuity geometry of rigid impact oscillators into the elastic impact oscillators, and the geometry analysis methods are applied to study the mechanisms of grazing bifurcations of system with unilateral soft constraint
Summary
There exist the vibroimpact phenomena widely, and systems interacting via impact have been extensively studied in recent years. Jiang and Wiercigroch [19] developed the concept of discontinuity geometry of rigid impact oscillators into the elastic impact oscillators, and the geometry analysis methods are applied to study the mechanisms of grazing bifurcations of system with unilateral soft constraint. E codimension-two grazing bifurcations in single-degree-of-freedom impact oscillators are studied and the dynamic response near the bifurcation points is presented in [45]. Xu et al [46] investigated the codimension-two grazing bifurcation in n-degree-of-freedom impact oscillator with bilateral constraints by using a classical approach of discontinuity mappings.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
