Abstract
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 behaviour. 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.
Highlights
The solution of a structural design problem generally requires the evaluation of a set of parameters in order to fulfill several requirements, for instance, in terms of strength, serviceability and dynamic performance of the structural system at hand
The vector r collects the parameters of the seismic input stochastic model, obtained by using recently proposed analytical expressions of Power Spectral Density (PSD) consistent with assigned Response Spectra (RS), that cover most of the international building codes (Barone et al, 2015, 2019)
Outcomes of computational times for uncontrolled system show that a great reduction of more than 90% is achieved for each evaluation of response statistics, whereas the mean errors with respect to numerical integrations, in terms of both displacements and relative velocities, are negligible
Summary
The solution of a structural design problem generally requires the evaluation of a set of parameters in order to fulfill several requirements, for instance, in terms of strength, serviceability and dynamic performance of the structural system at hand. The paper is organized as in the following: in section 2 the probabilistic optimal design problem is firstly formulated in general form and particularized for the case of n-DOF linear structural systems controlled by means of m concurrent non-linear FVDs (Di Paola et al, 2007; Di Paola and Navarra, 2009); in Section 3, in order to take advantage of the random vibration theory, the classical SL approach is described for the problem at hand and a procedure for the analytical evaluation of the response statistics, useful for SL technique, is proposed for linear n-DOF non-classically damped systems; section 4 is devoted to numerical applications in which the reduction in computational effort and the accuracy of the proposed procedure are investigated and the optimal design of FVDs is performed for a plane shear-type five-story frame and for a three-dimensional building structure. In Appendix brief details on the deriving of RS-consistent analytical PSD function and the expressions for its evaluation are provided, along with the analytical expressions that lead to the evaluation of the cross-spectral moments in modal space, once the direct spectral moments are determined
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