Targeted energy transfer analysis of a nonlinear oscillator coupled with bistable nonlinear energy sink based on nonlinear normal modes

Abstract

The nonlinear energy sink (NES), which has been proven to conduct quick and passive targeted energy transfer (TET), has been implemented in several structures to reduce vibration. For an NES to perform efficiently via targeted energy transfer (TET), the vibration levels must surpass a well-defined threshold; otherwise, the NES will perform inefficiently. The bistable NES (BNES) produces a nonlinear force with a negative linear and a positive nonlinear stiffness component. This investigation examines the energy flow characteristics of a bistable nonlinear energy sink coupled with a nonlinear oscillator (NO). Where frequency–energy graphs (FEPs) demonstrated the nonlinear normal modes (NNMs) and dynamic behaviour of the resultant NO-BNES system. At low energy levels, the emergence of many symmetrical and asymmetrical in-phase and out-of-phase backbone branches is emphasized. The superimposed wavelet frequency spectra of the NO-BNES response on the FEP have validated the robustness of the TET mechanism, where the contribution of the asymmetrical NNM backbones in TET can be viewed with clarity. Comparing the BNES and cubic NES by superimposing the wavelet frequency spectra on FEPs and energy dissipation efficiency reveals that the BNES performs better in TET.