Switching Mechanism of Periodic and Chaotic Motions in an Extended Fermi-acceleration Oscillator

Albert Luo and Yu Guo, Mechanical and Industrial Engineering, University of Southern Illinois

An extended Fermi acceleration oscillator consisting of a particle moving vertically between a fixed wall and the excited piston is investigated. The motion switching bifurcation of a particle in such a generalized Fermi oscillator is presented through the theory of discontinuous dynamical systems. Periodic motions in the Fermi-acceleration oscillator are determined analytically and the corresponding local stability and bifurcation are obtained. From switching bifurcation and period-doubling bifurcation, parameter maps of periodic and chaotic motions will be developed for a global view of motions in the Fermi acceleration oscillator. To illustrate switching phenomena, the acceleration responses of the particle and base in the Fermi oscillator are presented. Poincare mapping sections are also used to illustrate chaos, and energy dissipation in chaotic motions can be evaluated.