Theoretical and experimental study on the combination internal resonance of L-shaped piezoelectric vibration energy harvester

In this work, the dynamic behaviors of L-shaped piezoelectric vibration energy harvester that result from the combination internal resonance are numerically, analytically and experimentally presented. The electromechanically coupled governing equations of the energy harvester were employed in accordence with our previous study. The multi-branch approximate responses of the system are derived by using the method of multiple scales. The stability of the system is determined by the eigenvalues of the Jacobi matrix. Parameterized analyses are conducted on the output response as the external excitation frequency approaches the differential combination frequency of the energy harvester. The effects of acceleration excitation and external resistance on the output performance of the system are analyzed. The nonlinear responses of the system under various initial conditions are numerically analyzed using time response curves, spectrograms, Poincaré maps, and bifurcation diagrams. The effects of external resistance and external excitation frequency on the attractor basin are investigated. The particular nonlinear phenomena identified in the theory are experimentally verified for the combination resonance. The broad frequency range of the LPEH ranges from 15 Hz to 16.82 Hz. The study of combination resonance and internal resonance of the piezoelectric energy harvester will help to understand its complex vibration characteristics and predict the dynamic behavior.