Nonlinear dynamics of dry friction oscillator subjected to combined harmonic and random excitations

The dynamics of a nonlinear single degree freedom oscillator on a moving belt subjected to combined harmonic and random excitations is numerically investigated. The dynamics is described by differential equations with discontinuities due to dry friction between the mass and the belt. The discontinuous oscillator is modelled as a Filippov system. Discontinuity induced bifurcations such as the adding sliding bifurcations due to harmonic excitation and stochastic bifurcations like the P and D bifurcations are investigated by numerically integrating the equations of motion using an adaptive time stepping method. A bisection approach is used to accurately determine the discontinuity point, and a Brownian tree approach is used to follow the correct Brownian path. The associated Fokker–Planck (FP) equation is solved by the finite element method. The largest Lyapunov exponent is computed by using the Müller jump matrix and the Wedig algorithm. The effects of the system parameters on the dynamics of the system are investigated.