Optimal design of nonlinear energy sinks for SDOF structures subjected to white noise base excitations

Nonlinear Energy Sinks (NESs) have recently received increasing attention from researchers because of their capability to passively absorb a significant amount of energy over a wide range of frequencies. In most studies, the dynamic response of the main structure coupled with one or more NESs is analysed for impulsive loading. In this paper, the performance of the NES attached to a Single Degree of Freedom (SDOF) system, under random Gaussian white noise base excitations, is investigated through several numerical simulations. In order to determine the optimal configuration for the device, four different objective functions are considered. Sensitivity analyses with respect to the intensity of the random loads, the mass ratio and the main parameters of the primary structure are presented. The authors propose an approximate design approach based on the use of the Statistical Linearization Technique, and an accurate empirical formulation linking the NES optimal parameters to the characteristic of the main structure and the random excitation. Numerical results are validated by Monte Carlo simulations. Finally, a numerical application for a 2-DOFs system equipped with a NES has been presented in order to investigate the applicability of the proposed empirical approach for Multi Degrees of Freedom structures.