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.