Frequency–energy plot and targeted energy transfer analysis of coupled bistable nonlinear energy sink with linear oscillator

Abstract

The nonlinear energy sink (NES), which is proven to perform rapid and passive targeted energy transfer (TET), has been employed for vibration mitigation in many primary small- and large-scale structures. Recently, the feature of bistability, in which two nontrivial stable equilibria and one trivial unstable equilibrium exist, is utilized for passive TET in what is known as bistable NES (BNES). The BNES generates a nonlinear force that incorporates negative linear and multiple positive or negative nonlinear stiffness components. In this paper, the BNES is coupled to a linear oscillator (LO) where the dynamic behavior of the resulting LO-BNES system is studied through frequency–energy plots (FEPs), which are generated by analytical approximation using the complexification-averaging method and by numerical continuation techniques. The effect of the length and stiffness of the transverse coupling springs is found to affect the stability and topology of the branches and indicates the importance of the exact physical realization of the system. The rich nonlinear dynamical behavior of the LO-BNES system is also highlighted through the appearance of multiple symmetrical and unsymmetrical in- and out-of-phase backbone branches, especially at low energy levels. The superimposed wavelet frequency spectrums of the LO-BNES response on the FEP have verified the robustness of the TET mechanism where the role of the unsymmetrical NNM backbones in TET is clearly observed.