The critical phenomena in a hysteretic model due to the interaction between hysteretic damping and external force

A self-excited system involving a van der Pol-type damping and a hysteretic damper representing restoring force is investigated in this paper. The influence of external force on the dynamic behavior of the hysteretic system is analyzed in detail. Numerical simulations show that, under an external force, the original hysteretic system can exhibit the so-called critical phenomena, where the hysteretic resorting force of the system may no longer obey the traditional piecewise function form. This new finding reveals that the system's behavior changes dramatically when an external force is present. Modified bilinear force paths are proposed to accommodate the new phenomena. It is shown that a hysteretic system can exhibit more complex dynamical behavior when an external forcing is applied, and that the critical phenomena may exist even when the system reaches its steady state. A study is presented on the necessary condition for the existence of the critical phenomena. More interestingly, it has been found that the hysteretic forcing can suppress chaotic motions, suggesting an alternative approach to control chaos.