Efficient targeted energy transfer of bistable nonlinear energy sink: application to optimal design

This paper is dedicated to the optimal design of a bistable nonlinear energy sink (NES) for the vibration control of a periodically excited linear oscillator. This system with negative linear and cubic nonlinear coupling is analytically studied with the method of multiple scales. As a result, a slow invariant manifold is obtained and is applied to predict four typical response regimes at different energy levels. Moreover, asymptotic analysis and Melnikov analysis are, respectively, used to obtain the thresholds of these typical responses. Through their efficiency comparison, it is observed that the bistable NES can be efficient and robust in a broad range of excitation amplitude. With the Hilbert transform and wavelet transform, targeted energy transfer with transient or permanent 1:1 resonance is found to be responsible for the effectiveness of such responses as strongly modulated response and 1:1 resonance. Finally, an optimal design criterion and a corresponding parameter configuration are proposed to guide the application of this type of NES.