Discontinuity Induced Bifurcations in Nonlinear Systems

摘要

Nonlinear systems involving impact, friction, free-play, switching etc. are discontinuous and exhibit sliding and grazing bifurcations when periodic trajectories interact with the discontinuity surface which are classified into crossing sliding, grazing sliding, adding sliding and switching sliding bifurcations depending on the nature of the bifurcating solutions from the sliding surface. The sudden onset of chaos and the stick-slip motion can be explained in terms of these bifurcations. This paper presents numerical and numerical-analytical methods of studying the dynamics of harmonically excited systems with discontinuous nonlinearities representing them as Filippov systems. The switch model based numerical integration schemes in combination with the time domain shooting method are adopted to obtain the periodic solutions and the bifurcations.