Dynamic analysis of stochastic friction systems using the generalized cell mapping method

Friction systems are a kind of typical non-linear dynamical systems in the actual engineering and often generate abundant dynamics phenomena. Because of non-smooth characteristics, it is difficult to handle these systems by conventional analysis methods directly. At the same time, random perturbation often affects friction systems and makes these systems more complicated. In this context, we investigate the steady-state stochastic responses and stochastic P-bifurcation of friction systems under random excitations in this paper. And in order to retain the non-smooth of friction system, the generalized cell mapping (GCM) method is first used to the original stochastic friction systems without any approximate transformation. To verify the accuracy and validate the applicability of the suggested approach, we present two classical nonlinear friction systems, i.e., Coulomb force model and Dahl force model as examples. Meanwhile, this method is in good agreement with the Monte Carlo simulation method and the computation time is greatly reduced. In addition, further discussion finds that the adjustable parameters can induce the stochastic P-bifurcation in the two examples, respectively. The stochastic P-bifurcation phenomena indicate that the stability of the friction system changes very sensitively with the parameters. Research of responses analysis and stochastic P-bifurcation has certain significances for the reliability and stability analysis of practical engineering.