Acceleration behaviors of Fermi accelerator model excited by Van der Pol oscillator
School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, P.R. China
Received in final form: 22 January 2019
Published online: 30 July 2019
In this paper, we investigate on dynamics of a generalized Fermi accelerator model with a moving wall described by a nonlinear Van der Pol oscillator. Different acceleration behaviors appear due to the discontinuity brought by impact and the stationary periodic excitation of the moving wall. Utilizing the theory of discontinuous dynamical systems, acceleration mechanism of the particle is studied and the analytical conditions for stick motion and grazing motion are obtained. By the use of generic mappings between different boundaries including stick and non-stick motions, periodic motions of the Fermi accelerator can be constructed, and corresponding local stability and bifurcations can be discussed according to mapping dynamics. Finally, different acceleration behaviors including periodic, chatter and stick motions are presented and illustrated.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2019