Research On The Stick-Slip Motion Of The Dry Friction Self-Excited Vibration System Based On Filippov Differential Inclusion

In practical engineering there are a lot of self-excited vibration phenomenon caused by the dry friction, and often be harmful. In order to reduce the adverse effects of self-excited vibration, improve the security and stability of engineering system, the study of dry friction self-excited vibration is particularly important. But as a result of non-smoothness of dry friction, the friction oscillator contains the bond complex stick-slip motions. This paper mainly uses Filippov theory, discusses the existence condition of the sliding motion and calculates the sliding motion speed of the dry friction oscillator. Then by using calculation results, we simulate the sliding motion of the dry friction oscillator. In this paper, the main work and achievements include the following four parts:1. The classification of non smooth dynamical systems, the history and development of differential inclusion theory, the research status and achievements of the research on the self excited vibration of dry friction are introduced.2. Filippov theory are introduced. They mainly including the structure of the set value mapping, Filippov solution and the existence, the relationship between the differential inclusion and dry friction model.3. Filippov sliding motion on a co-dimension 1 discontinuity surface is considered. We give sufficient conditions under which ? is attractive. And under these conditions we obtained the velocity formula of the sliding motion of a system on a discontinuous surface. Then, the periodic sliding motion of a single degree of freedom dry friction system is simulated by using the analytical calculation results.By numerical simulation, we find that when the velocity of the driving belt is increasing, the sliding motion of the system is gradually lost, and the mass tends to be static. Because the system is symmetrical about the speed, the change of the speed direction of the drive belt can be similar to the theoretical and simulation results.4. Filippov sliding motion on a co-dimension 2 discontinuity surface is studied. We give sufficient conditions under which ? is nodal attractive. And under these conditions we obtained the velocity formula of the sliding motion of intersection of two discontinuous surfaces. Then, the periodic sliding motion of two degree of freedom dry friction system is simulated by using the analytical calculation results. By numerical simulation, we find that when the velocity of the driving belt is increasing, the viscoelastic periodic sliding motion of the two masses are gradually disappeared as before, the two mass vibration tends to be static. This is similar to the conclusion on a co-dimension 1 discontinuity surface. Changing the symmetry of the system structure, almost synchronous motion of the two mass is changed, and the movement of the system is more complex.