On forward and reverse coupling of vibrating piezoelectric energy harvesters

Abstract

This document provides information about the analysis of effects coupling the mechanical and the electrical phenomena going on inside a piezoelectric energy har- vester. Two characteristics are exploited in energy harvesting: direct piezoelectric effect where stress is resulting by the application of an electric field and reverse effect showing an electric field resulting by stress application. Piezoelectric patches, bonded on beams free to vibrate under a mechanical stimulus, can be used as active elements. Point-wise material characteristics are described by symmetric matrices coupling together stress and electric field to the strain and the electric polarisation leading to reciprocal direct and reverse effects. Under operating conditions, the stress and electric field values applied to the material patch are not uniform and do not have the same spatial pattern resulting in a non reciprocal interaction. An explanation of this phenomenon is attempted by applying the Euler-Bernoulli beam theory model that allows the computation of two geometrical coefficients for direct and inverse interactions under uniform stress distribution. Com- parisons versus experiments carried out on a Macro Fiber Composite piezoelectric patch show that the model is able to estimate the effect.