Stochastic Bifurcation Analysis of a Duffing Oscillator with Coulomb Friction Excited by Poisson White Noise

Abstract The stochastic analysis of the response of frictionally damped Duffing oscillator subjected to Poisson white noise (PWN) and its stochastic bifurcation analysis are considered. The behaviour of the stochastic attractors is examined through the stationary solution of the corresponding generalized Fokker-Planck-Kolmogorov (FPK) or Kolmogorov-Feller (KF) equation. A finite element (FE) scheme has been used for the solution of the FPK equation, using C 1 continuity shape functions. Parametric studies are carried out to gain insights into the effects of the Coulomb friction, and arrival rates of the underlying Poisson process of PWN. The results of FE solution are shown to be in good agreement with the results of Monte Carlo simulation (MCS).