Modeling and Experimental Validation of Bi-Stable Beam Based Piezoelectric Energy Harvester

We have previously proposed a bi-stable nonlinear oscillator based piezoelectric energy harvester to address the challenges of low-frequency, low-g vibration energy harvesting at MEMS scale. The compressive residual stress in micro-fabricated thin films could be employed to induce buckling in doubly clamped beams. The buckled beams with two equilibriums can snap through at low frequencies and enhance the power generation. This paper focuses on the modeling of the dynamics of the bi-stable oscillator based energy harvesters. An electromechanical lumped model has been built by Lagrange’s formulation and lumped parameters have been solved explicitly. More particularly, the model considers multi-layer thin films and the residual stress in these films, to be readily applicable to MEMS device design. Harmonic functions as the approximate solutions have been used to analytically solve for the frequency responses of the nonlinear oscillations. Two modes of oscillations predicted by the analytical model have been validated by testing a meso-scale prototype.