Response of sliding structures with restoring force to stochastic excitation

The stochastic response of a rigid structure with a restoring force resting on a frictional foundation and excited by stationary or evolutionary white noise is studied analytically and by Monte Carlo simulation. The degree of accuracy and range of applicability of the following three analytical methods is established: (1) Equivalent Linearization Method, (2) stationary solution of the Fokker-Planck equation and (3) direct closed form stochastic linearization of a viscoplasticity model. It is demonstrated that the Viscoplasticity Model is a very accurate and effective tool for studying sliding base isolation systems for all levels of excitation and any value of the coefficient of friction μ. However, the Equivalent Linearization Method also gives accurate predictions even for relatively low levels of excitation when the coefficient of friction is less than 0.1.