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.