A general modal approach for the development of optimal multi-layer stacked vibration energy harvesters

Piezoelectric vibration energy harvesters with multi-layer stacked structures have been developed. They consist of multi-layer beams, of zigzag configurations, with rigid masses attached between the beams. The rigid masses, which also serve as spacers, are attached to each layer to tune the frequencies of the harvester. Close resonance frequencies and considerable power output can be achieved in multiple modes by varying the positions of the masses. A modal approach is introduced to determine the modal performance conveniently using the mass ratio and the modal electromechanical coupling coefficient, and the required modal parameters are derived using the finite element method. Mass ratio represents the influence of modal mechanical behaviour on the power density. Since the modes with larger mass ratios cause the remaining modes to have smaller mass ratios and lower power densities, a screening process using the modal approach is developed to determine the optimal or near-optimal performance of the harvesters when altering mass positions. This procedure obviates the need for full analysis by pre-selecting the harvester configurations with close resonances and favourable values of mass ratio initially. Furthermore, the multi-layer stacked designs using the modal approach can be used to develop harvesters with different sizes with the power ranging from microwatts to milliwatts.