Mathematical Models of Mechanical Systems with Discontinuities

The chapter outlines two models 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” together 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 contiunuous function is used to model transitions between the subspaces. The sigmoid function is employed allowing to control the degree of abruptness. An unsymmetrical, piecewise linear oscillator has been used to examine this method providing ultimately recommendations regarding validity of this approach.