Coupling nonlinearities and dynamics between the hybrid tri-stable piezoelectric energy harvester and nonlinear interfaced circuit

Tri-stable piezoelectric vibration energy harvester (T-PVEH) recently has been widely investigated due to its good electro-mechanical performance. However, most studies emphasizing the mechanical configuration usually only regard the interfaced circuit as equivalent to a linear resistance load. The coupling nonlinearities and dynamics between the T-PVEH and the nonlinear interfaced circuit are yet to be well understood. Considering a hybrid T-PVEH interfacing with a nonlinear AC-DC rectifying circuit, this paper aims to derive its electro-mechanical equations to characterize the mechanical and energetic dynamics, as well as the coupling nonlinearities between the mechanical terminal and electrical terminal, which can be helpful to optimize the T-PVEH configuration and the circuit topology, so as to enhance the energy harvesting efficiency and effective broadband. The general harmonic balance solutions and the Jacobian matrix used to estimate the solution stability are presented based on the derived electro-mechanical equations. The influences of the magnetic distance, coupling constant and load resistance on the mechanical and energetic dynamics are simulated. The contradiction between the bandwidth and efficiency caused by the coupling nonlinearities is also analyzed. The results show that proper selection of the magnetic distance, load resistance and coupling constant in their suitable range is beneficial to enhance the effective bandwidth and harvested power of the global inter-well motions. It also shows that strong coupling constant with large load resistance will introduce additional mechanical damping and stiffness, attenuating the response amplitude and effective bandwidth of the system. Experimental results show reasonable agreement with the simulations. The rectified voltage obtained by experiment is 2.6 V, which meets the power supplying demand of the low-powered electronic devices.