Random vibration of Coulomb oscillators subjected to support motion with a non-Gaussian moment closure method

The response of one-degree-of-freedom systems with frictional devices (Coulomb oscillators) undergoing Gaussian support motion (earthquake) is investigated by adopting a moment equation approach in the context of Ito's calculus. Such equations contain expectations of the signum function of the velocity. In order to evaluate them, the joint probability density function of the variables is expanded in a truncated series of modified Hermite polynomials, which allows the computation of the response moments. The truncation is equivalent to neglecting the Hermite moments of the variables beyond a given order. Starting from the response moments so calculated, approximate marginal and joint PDF, mean upcrossing rate functions, and the largest value distributions can be constructed. Conversely, the estimates of the response correlations require the evaluation of a first-order differential system, which also is written by using Ito's rule. The results of the applications compare well with the simulation, and show that the assumption of Gaussian response is unacceptable and non-conservative.