Towards incorporating impact losses into random vibration analyses: a model problem

A benchmark model random vibration problem is considered for an SDOF system with a one-sided inelastic barrier at its equilibrium position under Gaussian white-noise excitation. An analytical solution is obtained for an expected response energy by cycle-to-cycle application of the method of moments with successive conditional and unconditional averaging. The solution, valid both for small and `not very smallʹ impact losses, leads to a formula for the equivalent viscous damping factor, which may be used to account for impact losses. Monte-Carlo simulation results show that this formula provides generally better accuracy than one obtained by stochastic averaging. They also illustrate applicability of the formula for certain more complicated random vibration problems.