Abstract
In the present paper, the frictional vibrations in a mechanical system are studied theoretically using the average method when the friction-velocity characteristic curves are given by several types of function. The steady-state vibrations, or limit cycles, obtained from the average method are compared with the corresponding approximate motions regarded as the positively exact solutions, which are obtained from the piecewise linear system with the friction-velocity characteristic curves approximated by a polygon having numerous segments. Moreover, the effectiveness of the use of the average method in the theoretical analysis of frictional vibrations is shown in three types of friction-velocity functions when the nonlinearities in the system are not too large. Successively, the influences of the discontinuity between the maximum static friction and the kinetic friction without slipping are investigated for the amplitude curves of limit cycles. Lastly, in the case where such a discontinuity does not exsist, an easily revisable method is offered in which almost exact solutions can be obtained by modifying the solved curves estimated from the average method.
