Dynamics analysis and parameter optimization of a nonlinear energy sink with geometrically nonlinear inerters

Abstract This paper studies a nonlinear energy sink (NES) with geometrically nonlinear inerters (GNI-NES) to improve the vibration absorption performance. The force-displacement relation of the geometrically nonlinear inerters mechanism (NIM) is obtained, and a dynamic model is established for the coupled system. The dynamic responses of the system are solved using the harmonic balance method (HBM) and the Runge-Kutta method. The vibration absorption performance of the system is evaluated using displacement transmissibility, and the parameters are analyzed. Then, the grey wolf algorithm is used to obtain the optimal system parameters. The results show that compared with the cubic NES, the proposed GNI-NES achieves the lower peak value, and exhibits better vibration stability compare to the cubic NES. Furthermore, these outcomes enhance our comprehension of the operations of the NIM and aid in crafting more effective designs of nonlinear passive vibration mitigation systems employing inerters.