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

Abstract

The main focus of this study is the development of an adapted complex variable method in the vicinity of equilibrium in bistable NES. A simplified chaos trigger model is established to describe the distance between the stable phase cycle and the pseudo-separatrix. An analytical expression can predict the excitation threshold for chaos occurrence. The relative positions between the chaos trigger threshold line and the Slow Invariant Manifold (SIM) structure can express the distribution of response regimes under growing harmonic excitation. This topological structure implies the alternation of the response regime and helps to classify the bistable NES. The experiment compares the analytical result of intra-well oscillation with the numerical result in the frequency domain. The experimental response regimes under different input energy levels and frequency domains have been observed and give ideas to guide the optimal design of a bistable NES. It is shown that the modest bistable NES possesses strong robustness to frequency perturbation.