Fundamental power limits of piezoelectric energy harvesters based on material strength

The mathematical models used to predict power produced from piezoelectric energy harvesters have seen continued refinement in the last decade. Despite this, we have been unable to give general power limits for the technology. This is due in large part to the fact that power output is heavily dependent on acceleration magnitude and frequency, as well as the internal damping of the harvester itself. The existing power models all assume some magnitude of excitation acceleration, that scales the harvested power, usually by the square of its magnitude. We know that this excitation can only be taken to the point at which the harvester is damaged, and no longer produces power. The power produced at this excitation acceleration magnitude thus represents the power-harvesting limit of the technology. In this paper, we seek to relate acceleration, displacement, stress, and harvested power in a way that provides a general limit for the technology. We will show that, based on the ultimate strength of the material, there is an upper limit on the excitation acceleration. Then using this expression for allowable excitation acceleration, we are able to develop an expression for the upper limit of harvestable power. The resulting expression for power capabilities is independent of acceleration magnitude and harvester mechanical damping. It does, however, depend on the acceleration frequency and beam design. Using this expression, we then explore the power harvesting limits of the technology across a range of input frequencies and beam sizes.