The Study Of Dynamics And Stability Of A Dry Friction Vibration System

In this paper, we study the dynamics behavior and the periodic motion of a dry friction system. The contents are listed as follows:In Chapter 1, we introduce the present situation and the achievement about the study of the system with dry friction, which involve some basic concepts, such as the switch boundary, grazing bifurcation. Besides, we elaborate the general method for studying the stability of the periodic motion in non-smooth system.In Chapter 2, we analyze the nonlinear characteristic of the dry friction, and then set up the model of a two-degree-of-freedom system with dry friction. Our studying will focus on the dynamics characteristic of the system. We list the conditions about the full stick state, full slip state, half stick state, and establish the differential equations which correspond with the studied system.In Chapter 3, we study the stability of the periodic motion of the system with dry friction under the full slip state with the help of Floquet Theory. Firstly we study the stability of the periodic motion of one-degree-of-freedom system with linear dry friction under the full slip state. Then we extend the study to two-degree-of-freedom system. According to the relation how the trajectories pass the switch boundaries, the periodic motion of two-degree-of-freedom system with dry friction can be classified into three kinds, which are denominated as not-crossing, single-crossing, double-crossing cases in this paper. Subsequently, we give the examples them and study the stability of them respectively. Finally, we briefly introduce the methods to study the stability of periodic motion of the system with non-linear dry friction under the full slip state.In Chapter 4, by means of MATLAB we carry out the numerical simulation of the system with dry friction we have mentioned above, and obtain the phase portraits of periodic motion in the system under the stick state or slip state. In addition, we get the phase portraits of periodic motion under the full slip state, and analyze their stability.