Analytic treatment of a system with a vibro-impact nonlinear energy sink

This Communication reports on an approximate analytic procedure for analysis of transient damped response in a system comprising a primary linear oscillator and vibro-impact nonlinear energy sink (NES). Multiple-scale expansion reduces the problem in the first approximation to low-dimensional vibro-impact system with forcing and damping; the latter problem yields to direct analytic approach. The results computed by this way fairly correlate with direct numeric simulations. The analysis takes advantage of small ratio of the NES and the primary masses, but does not require the restitution coefficient to be close to unity. The proposed approach paves the way for efficient design of systems with vibro-impact NESs.