On the accuracy of lumped parameter model for tapered cantilever piezoelectric energy harvesters with tip mass

The objective of this paper is to investigate the effect of tip mass ratios on the vibration response of the tapered piezoelectric cantilever beams using the lumped parameter model. Finite element analysis is used in this study to compare the finite element model with the lumped parameter model for different taper ratios of piezoelectric cantilever beam subjected to different tip mass ratios. Validation is done by comparing the finite element model with referenced distributed parameter models for 1) rectangular piezoelectric cantilever beam with different tip mass ratios and 2) different taper ratios of piezoelectric cantilever beam in the absence of tip mass. Deflection error percentage is obtained in this work as a key parameter to understand how tip mass can affect the accuracy of the lumped parameter model. It represents the difference between the normalized deflection of lumped parameter model and finite element model for the tapered piezoelectric cantilever. Results showed that when the taper ratio of the piezoelectric cantilever beams increases, the deflection error percentage increases in the absence of tip mass. When tip mass is added, the deflection error between the finite element model and the lumped parameter model decreases drastically leading to more accurate results in the vibration response of the beam.