Optimization Under Uncertainty of Nonlinear Energy Sinks

Abstract

Nonlinear Energy Sinks (NESs) are a promising technique for passively reducing the amplitude of vibrations. Through nonlinear stiffness properties, a NES is able to passively absorb energy. Unlike a traditional Tuned Mass Damper (TMD), NESs do not require a specific tuning and absorb energy from a wide range of frequencies. However, each NES is only efficient over a limited range of excitations. In addition, NES efficiency is extremely sensitive to perturbations in design parameters or loading, demonstrating a nearly discontinuous efficiency. Therefore, in order to optimally design a NES, uncertainties must be accounted for. This thesis focuses on optimally selecting parameters to design an effective NES system through optimization under uncertainty. For this purpose, a specific algorithm is introduced that makes use of clustering techniques to segregate efficient and inefficient NES behavior. SVM and Kriging approximations as well as new adaptive sampling techniques are used for the optimization under uncertainty. The variables of the problems are either random design variables or aleatory variables. For example, the excitation applied to the main vibrating system is treated as aleatory. In an effort to increase the range of excitations for which NESs are effective, a combination of NESs configured in parallel is considered. Optimization under uncertainty is performed on several examples with varying design parameters as well as different numbers of NESs (from 1 to 10). Results show that combining NESs in parallel is an effective method to increase the excitation range over which a NES is effective.