SPEEDING UP THE STOCHASTIC LINEARISATION FOR SYSTEMS CONTROLLED BY NON-LINEAR PASSIVE DEVICES

The response of structures under dynamic loadings is often improved by introducing passive control devices, such as fluid viscous dampers, tuned liquid column dampers, non-linear energy sinks. These devices can operate through the dissipation of the input energy or by changing the dynamic characteristics of the main structure to which they are attached involving several different physical mechanisms. Nevertheless, the large-scale use and design of these devices have been limited by the computation difficulties due to the presence of inherent non-linearities in their constitutive laws. To overcome this limitation, it is common to replace non-linear equations of motion of controlled systems with linear equivalent counterparts by using well-established procedures as Stochastic Linearisation techniques. Most of Stochastic Linearisation algorithms operate recursively, since the values of the equivalent linear parameters depend implicitly on response statistics. Hence, the computational burden required for the analyses increases, also due to the fact that controlled systems are very often non-classically damped. Calculations are therefore carried out numerically, since analytical solutions for response statistics are available only for a limited class of problems. In this study, taking advantage of a model for Power Spectral Density functions of earthquake loads consistent to Response Spectra, a procedure to speed up the Stochastic Linearisation technique by avoiding numerical evaluations of response statistics is proposed. Firstly, Stochastic Linearisation schemes for on general Multi-Degree-Of-Freedom not-classically-damped structural systems controlled by multi passive control devices are derived and the general algorithm to evaluate response statistics is presented. Then, applications have been carried out in order to assess the validity of the proposed approach in terms of accuracy and its ability in reducing the computational effort, approaching the design procedure of passive control devices coherently with the provisions of seismic building codes.