Bifurcation boundaries analysis of the thin-walled internal resonance energy harvester

Abstract

The dynamic instability of the thin-walled 1: 2 internal resonant piezoelectric vibration energy harvester is investigated. Previously work (Nie et al., 2019) derived the nonlinear electromechanical-coupled governing equations and validated them experimentally. The modulation equations are performed by the method of multiple scales. The system stability is obtained from the eigenvalues of the Jacobi matrix. Then, three types of bifurcation boundaries of the system are determined analytically and simulated numerically via Routh–Hurwitz criterion. Results show that internal resonance complicates the dynamic properties of the bifurcation region. For a large external excitation, new saddle node bifurcation regions appear in the stability diagram. Moreover, the new saddle node and Hopf bifurcation regions may intertwine. Furthermore, as the acceleration excitation increases, the system can be observed to transition to stable–unstable–stable states. The system’s high and low branch responses are fed back by the system’s large and small initial conditions. The system’s periodic and quasi-periodic motions are characterized by time response, FFT, phase trajectory, and Poincaré map. The study of the stability boundary of the piezoelectric energy harvester contributes to the harvesting of energy from ambient vibrations over a broader frequency range.