Random response of vibro-impact systems with inelastic contact

The probability density and statistics of random response are investigated for vibro-impact systems with inelastic contact in this paper. The inelastic contact is described through an empirical model incorporating highly non-linear and inelastic mechanical property of the impact interface, and the system response is determined through the stochastic averaging and energy dissipation balance technique. The inelastic contact force is separated into an elastic restoring component and a dissipative component; the former is expressed as the gradient of the potential energy preserved in the system while the latter is approximated by a damping force with energy-dependent damping coefficient through energy dissipation balance technique. The averaged Itô stochastic differential equation with respect to system total energy is then derived through stochastic averaging. The solution of the associated Fokker–Plank–Kolmogorov equation yields stationary probability density of system total energy, joint probability density of system displacement and velocity, as well as statistics of system response. The agreement between analytical results and Monte-Carlo simulations validates effectiveness of the proposed technique.

► Random responses of vibro-impact systems with inelastic contact are investigated.
► The inelastic contact is described through an empirical impact model.
► The methodology combines stochastic averaging and energy dissipation balance technique.