Applied Nonlinear Dynamics of Non - Smooth Mechanical Systems

This paper introduces practically important concept of local non-smoothness where any dynamical system can be considered as smooth in a finite size subspace of global hyperspaceΩ. Global solution is generated by matching local solutions obtained by standard methods. If the dynamical system is linear in all subspaces then an implicit global analytical solution can be given, as the times when non-smoothness occurs have to be determined first. This leads to the necessity of solving a set of nonlinear algebraic equations. To illustrate the non-smooth dynamical systems and the methodology of solving them, three mechanical engineering problems have been studied. Firstly the vibro-impact system in a form of moling device was modelled and analysed to understand how the progression rates can be maximised. Periodic trajectories can be reconstructed as they go through three linear subspaces (no contact, contact with progression and contact without progression). In the second application frictional chatter occurring during metal cutting has been examined via numerical simulation method. The analysis has shown that the bifurcation analysis can be very useful to make an appropriate choice of the system parameters to avoid chatter. The last problem comes from rotordynamics, where nonlinear interaction between the rotor and the snubber ring are studied. The results obtained from the developed mathematical model confronted with the experiment have shown a good degree of correlation.