Correction factor of lumped parameter model for linearly tapered piezoelectric cantilever

Abstract

Distributed parameter model (DPM) gives an accurate representation of the vibration response of piezoelectric cantilevers. Nevertheless, lumped parameter model (LPM) has been widely used because of its simple mathematical representation. However, researchers developed a correction factor for LPM because of its inaccurate power output prediction of the piezoelectric harvesters. The developed correction factors were limited to the rectangular and exponentially tapered piezoelectric beams because the DPM of other shaped beams are rather complicated to derive. This paper presents a correction factor for linearly tapered piezoelectric cantilever beam using a finite element model (FEM) approach. Validation of the developed FEM is accomplished using two analytical models from literature of rectangular and exponentially tapered shapes with tip mass. Results show an excellent agreement between the FEM and the related DPM. The FEM of a linearly tapered piezoelectric cantilever is then built and the error of using the uncorrected LPM for different tapered ratios is investigated. Correction factors of different taper ratios subjected to various tip masses are developed. Comparisons between the corrected LPM and the FEM verify the estimation of the correction factor. Results show that FEM approach can be used to enhance the accuracy of LPM of piezoelectric cantilever harvesters.