Three-dimensional map for a piecewise-linear capsule system with bidirectional drifts

Abstract

A three-dimensional map is studied in this paper to provide a fundamenta lunderstanding for the vibro-impact capsule system, which is a non-autonomous two degrees-of-freedom non-smooth dynamical system consisting of soft impact and dry friction with forward and backward drifts. By using the map, one can investigate the global and local dynamics of the system and construct all possible local mappings for a wide range of parameter variation. An example study by varying the amplitude of external excitation of the system is presented. Our results show that the proposed map can effectively explain the occurrence of the boundary-intersection crossing and the sliding bifurcations observed inthe system.