Stochastic dynamics of linear structures with nonlinear damper devices (PIS method)

Passive control introducing energy absorbing devices into the structure has received considerable attention in recent years. Unfortunately the constitutive law of viscous fluid dampers (Force-Velocity relationship) is highly nonlinear, and even supposing that the structure behaves linearly, the whole system has inherent nonlinear properties. Usually the analysis is performed by inserting some equivalent linear viscous damping (Soong and Costantinou, 1994; Lee et al., 2004), by equating the energy of the nonlinear viscous damping and the equivalent one in a single cycle of vibration. Recently Di Paola et al. (2005) proposed a stochastic linearization technique for the case of seismic ground motion. In this paper the effect of the non-Gaussianety of the response due to the inherent nonlinearity of the damper device will be studied in detail via Path Integral Solution (PIS) method. In order to achieve this goal the PIS method is handled via short time Gaussian approximation, in this way the conditional probability density function, for small intervals, follows a Gaussian distribution also in the case of nonlinear systems.