On the limiting of vibration amplitudes by a sequential friction-spring element

The possibility of using an additional sequentially connected friction spring element in order to reduce vibration amplitudes both for the self-excited oscillations and for the forced vibrations is discussed in the paper. The analysis is based on the averaging technique for systems with “slave variables” and demonstrates two main effects: damping during slipping in the additional element and fast switching between different natural frequencies due to alternating sticking/slipping phases. Analytic predictions for the oscillations’ amplitudes are obtained as steady state solutions of the equations governing slow motions of the system. The obtained analytic results enable optimal choice of friction in order to achieve maximal damping effect in case of the forced vibrations. The reasonable choice of the friction by the self-excited vibrations is a compromise between the acceptable amplitude and the robustness of the corresponding limit cycle. The asymptotic results are confirmed by numeric simulations.