Qualitative analysis of the response regimes and triggering mechanism of bistable NES

The main focus of this study is the development an adapted complex variable method with respect to equilibrium point in bistable nonlinear energy sink (NES), which mainly investigated vicinity 1:1 resonance. A simplified chaos trigger model established describe distance between stable phase cycle and pseudo-separatrix. An analytical expression can predict excitation threshold for occurrence. relative positions line slow invariant manifold structure interpret distribution response regimes under growing harmonic excitation. degeneration be demonstrated by qualitative analysis method, helps classify NES. experiment confirms result intra-well oscillation frequency domain. characteristic weak, modest, strong NES are identified experimental results.