Modeling of Dynamic Systems With Vibro-Impact Interaction and Discontinuity Mapping

Abstract

This paper presents an overview of selected modeling techniques of vibro-impact dynamics. Vibro-impact dynamics has occupied a wide spectrum of studies by dynamicists, physicists, and mathematicians. These studies may be classified into three main categories: modeling, mapping and applications. The main techniques used in modeling of vibro-impact systems include phenomenological modeling, Hertzian models, and non-smooth coordinate transformations developed by Zhuravlev and Ivanov. One of the most critical situations impeded in vibro-impact systems is the grazing bifurcation. Grazing bifurcation is usually studied through discontinuity mapping techniques, which are useful to uncover the rich dynamics in the process of impact interaction. Complex dynamic phenomena of vibro-impact systems such as sub-harmonic oscillations, chaotic motion, and coexistence of different attractors for the same excitation and system parameters but under different initial conditions will be discussed.