Modelling of dynamical systems with motion dependent discontinuities

The paper introduces two concepts for describing and solving dynamical systems with motion dependent discontinuities such as clearances, impacts, dry friction, or combination of these phenomena. The first approach assumes any dynamic system can be considered as continuous in a finite number of continuous subspaces, which together form so-called global hyperspace. Global solution is obtained by “gluing” local solutions obtained by solving the problem in the continuous subspaces. An efficient numerical algorithm is presented, and then used to solve dynamics of a piecewise oscillator, which has been also verified experimentally. The second approach considers that in reality the system parameters do not change in an abrupt manner. Therefore, a smooth contiunuous function is used to model a transition between the subspaces, in particular the sigmoid function is employed. This allows to control the degree of abruptness on the intersections of the continuous subspaces. An asymmetrical, piecewise linear oscillator has been examined to provide recommendations regarding validity of this approach.