Simplified design of nonlinear energy sinks for MDOF structures excited by white noise base excitations

Passive control devices are often used to protect slender and flexible structures from dynamic actions, including earthquakes, wind and waves. The Nonlinear Energy Sink (NES) has recently received increasing attention from researchers because of its capability to passively and irreversibly absorb a significant amount of energy from the primary system over a wide range of frequencies. In this paper, the application of two NESs acting in orthogonal directions is considered to mitigate the response of a multi degree of freedom structure. Parameters for each NES are obtained by considering a single degree of freedom structure, whose mass and frequency are designed based on the fundamental mode of the original structure along the direction of action of the device, and applying the empirical expressions proposed in Oliva et al. (2017). Compared to standard Monte Carlo simulations, the use of these expressions requires a significant lower computational effort, making their implementation suitable for practical engineering purposes. A numerical application on a three-dimensional building is presented to demonstrate the effectiveness of the proposed method. The NESs performance is analysed varying the direction of the ground motion, showing the potential of this passive control system in civil engineering applications. Results are reported in terms of statistics of the structural response, determined by Monte Carlo simulation, and analysis of the energy dissipated by the control devices.