An Efficient Stochastic Linearisation Procedure for the Seismic Optimal Design of Passive Control Devices

The seismic response of structures is often enhanced by introducing passive control devices that can operate through the dissipation of the input energy or by modifying the dynamic characteristics of the main structure. The inherent non-linearities in the constitutive laws of some of them lead to computation difficulties and have limited the large-scale use and design of these devices. In this study, a procedure for the optimal design of multi passive control devices is proposed. The general case of linear Multi-Degree-Of-Freedom (MDOF) not-classically-damped structural systems controlled by Fluid Viscous Dampers (FVD) are investigated in a stochastic framework. The procedure consists of evaluation of the device optimal pattern by minimizing an objective function related to the dampers cost and subjected to a constraint on the structural behavior. For each configuration, the complete probabilistic characterization of the response is achieved by employing random vibration theory, Stochastic Linearisation (SL) techniques and a novel analytic model which provides closed-form PSD functions of earthquakes accelerations coherent to response spectra suggested by seismic codes. Exploiting this model, a procedure to speed up the Stochastic Linearisation technique by avoiding any numerical integration is proposed. Applications on MDOF building structures have been carried out to validate the proposed approach in terms of accuracy and reduction of the computational effort and to obtain optimal pattern of the passive control device coherently with the provisions of seismic building codes.