On developing an optimal design procedure for a bimorph piezoelectric cantilever energy harvester under a predefined volume

•The width is to be set to the maximum possible width.•The length is to be set to the maximum possible length.•The material selected for the middle layer is of high density.•An initial total thickness is to be obtained so as to give the required resonance frequency.•The tip mass and the final thickness are to be obtained by simultaneously increasing both while keeping the resonance frequency constant until the optimal load equals the required load. A typical vibration harvester is tuned to operate at resonance in order to maximize the power output. There are many design parameter sets for tuning the harvester to a specific frequency, even for simple geometries. This work studies the impact of the geometrical parameters on the harvested power while keeping the resonance frequency constant in order to find the combination of the parameters that optimizes the power under a predefined volume. A bimorph piezoelectric cantilever is considered for the study. It consists of two piezoelectric layers and a middle non-piezoelectric layer and holds a tip mass. A theoretical model was derived to obtain the system parameters and the power as functions of the design parameters. Formulas for the optimal load resistance that provide maximum power capability at resonance and anti-resonance frequency were derived. The influence of the width on the power is studied, considering a constant mass ratio (between the tip mass and the mass of the beam). This keeps the resonance frequency constant while changing the width. The influence of the ratio between the thickness of the middle layer and that of the piezoelectric layer is also studied. It is assumed that the total thickness of the cantilever is constant and the middle layer has the same mechanical properties (elasticity and density) as the piezoelectric layer. This keeps the resonance frequency constant while changing the ratio between the thicknesses. Finally, the influence of increasing the free length as well as of increasing the mass ratio on the power is investigated. This is done by first, increasing each of them individually and secondly, by increasing each of them simultaneously while increasing the total thickness under the condition of maintaining a constant resonance frequency. Based on the analysis of these influences, recommendations as to how to maximize the geometrical parameters within the available volume and mass are presented.