Designing maximum power output into piezoelectric energy harvesters

Energy harvesting from vibrational sources has been the focus of extensive research in the last decade, but fundamental questions remain concerning the design of these harvesters. We consider a piezoelectric bimorph energy harvester and seek to translate design requirements, such as mass and target natural frequency, into beam dimensions that maximize power output. Our method centers around optimizing the thickness of the piezoelectric layers of a beam relative to the total beam thickness, otherwise known as the thickness ratio. This method uses approximations for the fundamental frequency and mode shape. This allows for the development of algebraic expressions for the modal parameters required for the prediction of power output. The resulting expression for power is fully defined by the fixed system level requirements and the only unknown parameters, the piezoelectric thickness ratio and the damping ratio. We show in an example case that, for typical damping ratio values, the ideal thickness ratio is not significantly affected by changes in the damping ratio. As such, the method requires a simple sweep of the thickness ratio in order to determine the beam design which maximizes the power. We develop the design method for both systems where the piezoelectric material is continuous and where the thickness is selected from a discrete set of values. Because our method produces a single algebraic expression for the power, the resulting beam design can be developed extremely quickly from a set of design requirements, and thus does not require optimization algorithms. We also show that our design method achieves more power output and requires less piezoelectric material than an approach which maximizes the coupling coefficient.