Analysis of Piezoelectric Energy Harvesters of a Moderate Aspect Ratio With a Distributed Tip Mass

Various mathematical beam models have been proposed for the efficient analysis of a piezoelectric energy harvester (PEH) and carrying out parameter study but there appears no beam model suitable for a PEH of a moderate width-to-length aspect ratio with a distributed tip mass, and so, moderate width-to-length aspect ratios and distribution effects of a tip mass over a finite length will be mainly focused on in the present beam analysis. To deal with a wide range of aspect ratios, the material coefficients appearing in the constitutive equations of a PEH beam will be interpolated by those of the limiting plane-strain and plane-stress conditions. The key idea in the interpolation is to derive the interpolation parameter analytically by using the fundamental frequency of a cantilevered beam of moderate aspect ratios. To deal with the distribution effects of a tip mass over a finite length, the use of a set of polynomial deflection shape functions is proposed in the assumed mode approach. The equations to predict the electrical outputs based on the proposed enhanced beam model are explicitly expressed in template forms, so one can calculate the outputs easily from the forms. The validity and accuracy were checked for unimorph and bimorph PEHs by comparing the results from the developed beam model, the conventional beam model, and a three-dimensional finite element model. The comparisons showed substantial improvements by the developed model in predicting the electrical outputs.