Resonance and energy transfer in forced vibro-impact systems with linear compliance

We address a non-stationary dynamic of a vibro-impact oscillator with linear compliance under harmonic excitation. The analytic treatment is based on the well-known approximation of isolated resonance. To this end, an appropriate set of action–angle variables is formulated for the single degree of freedom conservative vibro-impact oscillator with linear compliance. At the next stage, the dynamics of the forced system is considered in conditions of a primary 1:1 resonance, common in most applications. The approximation of the isolated resonance reduces the dynamics to a planar resonance manifold with foliation induced by a global invariant derived for the 1:1 isolated resonance flow. This foliation allows for an appropriate description of the steady-state, modulated and transient responses, and their bifurcations. The results are verified with direct numeric simulations.