A global analysis of a non-linear system under parametric excitation

Abstract

A strongly non-linear mechanical system consisting of a rigid damped bar subjected to a periodic parametric excitation is treated here in an exact manner. The emphasis is on the global behavior of this system which is carried out by using the point mapping and the cell-to-cell mapping methods. Even though the mechanical system is a simple one, yet it has a very complex global behavior. It is shown here that the newly developed theory of cell-to-cell mappings offers a tremendous advantage in obtaining the global domains of attraction of strongly non-linear dynamical systems.