A new technique for the global property of the vibro-impact system at the impact instant

In this paper, a new technique is proposed to study the global properties of the vibro-impact system at the impact instant. A special Poincaré section on the impact surface is chosen, which is composed of the co-dimensional time and the velocity. And a smooth impact-to-impact mapping is constructed as the Poincaré mapping. Consequently, we design a new technique for analyzing the dynamics of the system impact. The new technique specializes in analyzing the global property of the vibro-impact system at the impact instant. It cleverly utilizes the characteristics of the vibro-impact system and avoids the difficulties of non-smooth characteristics caused by impacts. Therefore, the dynamics of the vibro-impact system can be well retained. It is found that our method is valid and widely applicable to vibro-impact systems. A linear vibro-impact system and a nonlinear vibro-impact system are chosen as examples to verify the effectiveness of the new technique. The results show that the vibro-impact system exhibits some interesting dynamical phenomena at the impact instant, such as, the periodic cyclic characteristic and dramatic change of the impact behaviors.