Near-elastic vibro-impact analysis by discontinuous transformations and averaging

We show how near-elastic vibro-impact problems, linear or nonlinear in-between impacts, can be conveniently analyzed by a discontinuity-reducing transformation of variables combined with an extended averaging procedure. A general technique for this is presented, and illustrated by calculating transient or stationary motions for different harmonic oscillators with stops or clearances, and self-excited friction oscillators with stops or clearances First- and second-order analytical predictions are derived, and shown to agree to estimated accuracy with results of numerical simulation.