Sobre a existência e a estabilidade de movimentos periódicos em sistemas com vibro-impacto com folga simétrica

Abstract

In this work the mathematical modeling of a base harmonically excited vibro-impact system is presented. The system has been investigated by several researchers who have many aspects of the global dynamics. However, they have only admitted one pattern of periodic motions, that is, a motion with the same period as the excitation force. Hereby, it is shown that several patterns of periodic motions can occur and their existence and stability conditions must be accurately investigated. Periodicity conditions are applied on the state at the instants of impacts in order to obtain a map of the next impact based on the state of the previous one. This nonlinear map is used to obtain the conditions of existence of periodic motions with specific patterns. Applying the existence conditions, the stability of the motion can be carried out by analyzing the eigenvalues of the map while taking these conditions into account