Nonlinear energy sink and Eurocode 8: an optimal design approach based on elastic response spectra

In this paper, the authors propose novel empirical formulae for the optimal design of Nonlinear Energy Sinks (NESs) to control seismic induced vibrations in structures. While large part of the existing literature on NES for seismic applications is based on deterministic analyses of the structural response to recorded ground motions, herein the effectiveness of the device is studied in a stochastic framework. In fact, the seismic excitation has been modeled using a response spectra consistent power spectral density function, taking into account design spectra prescribed into Eurocode 8. Statistics of the structural response have been determined by Monte Carlo Simulations, performing nonlinear time-domain analyses to investigate the dependence of the optimal NES parameters on the main characteristics of the primary system and on the seismic load amplitude. The outcomes of these analyses have been translated into empirical expressions allowing for computing the optimal NES stiffness and damping. Since these are closed-form relationships depending on the main structure and the response spectra parameters, their use allows for an immediate estimate of the NES optimal design configuration, avoiding demanding numerical analyses and making their implementation suitable for practical engineering purposes. The accuracy of the design formulae has been tested by comparison with numerical optimisations for a set of possible configurations of the main structure and for varying intensity of the external excitation. Although the proposed relationships have been extrapolated from single degree of freedom system responses, applications to multi degree of freedom structures is quite straightforward, as shown through two case studies involving the analysis of a 2D multistorey structure and a 3D multi-bay frame controlled by two orthogonal NESs.