Time–frequency analysis of friction-induced vibration under reciprocating sliding conditions

A time–frequency analysis can give an overall view of the behaviour of friction-induced vibration. In this paper, short-time Fourier transform (STFT), Wigner–Ville distribution (WVD), Choi–Williams distribution (CWD) and Zhao–Atlas–Marks distribution (ZAMD) are applied to analyze time–frequency characteristics of friction-induced vibration. The result shows that there is always a frequency change in the time–frequency presentation of vibration in the location where the vibration is bounded. The frequency changes in time–frequency presentations are associated with nonlinearity of vibration systems. The nonlinearity may be counted as the evidence to support the consideration that friction-induced vibrations are bounded by limit cycles due to the system nonlinearity. Based on the time–frequency presentations of vibrations, it may be concluded that the friction vibration system is generally a linear system in the phase of vibration initiation but is a nonlinear system in the phases of vibration being bounded and disappearance.