Self-Excited Forced Vibrations with Solid Friction of Nonconstant-Speed Sliding System. Analysis by Piecewise Linear Approximation Method in the Case of Linear Friction-Velocity Characteristics

Self-excited forced vibrations with solid friction of a block lying on a surface moving at nonconstant speed are treated theoretically using a piecewise linear approximation method for the case of linear friction-velocity characteristics. In the previous report, various characteristics of these vibrations were analyzed theoretically using an averaging method. The present report concerns the substantiation of the validity of the application of the averaging method to the analysis of a frictional vibration system. The friction-velocity characteristic functions are assumed to be linear with three kinds of slopes : positive, zero and negative. The motions of a block in the system are studied for two cases : first, the case in which the maximum static friction is equal to the kinetic friction without slipping, and second, the case in which it differs. The steady-state vibrations are obtained with regard to the stick and slip motions of the block. The distributions of various types of these vibrations occurring in the system are shown in several figures, and the amplitude curves of the displacement waves are described in terms of the frequency ratio Ω and the speed of the moving surface Y0/Y.