Discontinuity-induced bifurcations in a piecewise-smooth capsule system with bidirectional drifts

Abstract

Discontinuous friction and impact exist in a variety of piecewise-smooth dynamical systems that exhibit rich and complex nonlinear phenomena. This paper aims to study the discontinuity-induced grazing and adding-sliding bifurcations in a piecewise-smooth capsule system subjected to bidirectional drifts. For this purpose, analytical and semi-analytical onset conditions of the impact-induced grazing and the frictioninduced adding-sliding bifurcations are investigated by solving explicitly the underlying piecewise-linear model. In this way, parametric relations revealing the occurrence mechanisms of transitions of the system from stationary to forward progression can be derived. This analytical approach is verified numerically using path-following techniques for piecewise-smooth dynamical systems. The numerical investigation includes a parametric study of the observed average capsule velocity and power consumption suggesting optimal choices for system operation.