Existência e estabilidade de movimentos periódicos em sistemas com vibro-impacto com dois graus de liberdade

Abstract

In this work the mathematical modeling of a harmonically excited vibro-impact with 2DOF system is presented. Vibroimpact systems have been investigated by several researchers in the last decades, however, specific patterns of motion and stability still need to be more studied. Hereby, it is shown that several patterns of periodic motions can occur on vibro-impact systems, and the comprehension of their motion begins by accurately investigating their conditions of existence and stability. In this work, periodicity conditions have been 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 of a specific 1-2 symmetric topology pattern. Applying the existence conditions, the stability of the motion can be carried out by analyzing the eigenvalues of the map while taking these precincts into account.