Dynamic effects of weights on vibration reduction by a nonlinear energy sink moving vertically

A nonlinear energy sink (NES) is a promising device to reduce structural vibrations. If a nonlinear energy sink moves vertically, in principle, its weight cannot be ignored together with the initial deformation due to the static equilibrium. The present work investigates dynamic effects of the weight on the vibration of a structure coupled with a nonlinear energy sink, which is modeled as a 2-degree-of-freedom system. Free vibration is numerically examined. Forced vibration is analytically explored via the method of harmonic balance with numerical validations. It is found that the freely vibrating frequency is larger than the natural frequency of the structure except for an unreasonably small NES mass if the weight is considered, while it is smaller if the weight is ignored. It is also found that the steady-state response of the primary structure in the case considering the weight is smaller than that in the case ignoring the weight, but the difference decreases with the increase of the excitation amplitude. The experimental results demonstrate that considering the weight leads to more accurate predictions. (C) 2019 Elsevier Ltd. All rights reserved.