Electromechanical Modeling of Cantilevered Piezoelectric Energy Harvesters for Persistent Base Motions

This chapter investigates electromechanical modeling of cantilevered piezoelectric energy harvesters excited by persistent base motions. The modeling approaches are divided here into two sections as lumped parameter modeling and distributed parameter modeling. The first section discusses the amplitude-wise correction of the existing lumped parameter piezoelectric energy harvester model for base excitation. For cantilevers operating in the transverse and longitudinal vibration modes, it is shown that the conventional base excitation expression used in the existing lumped parameter models may yield highly inaccurate results in predicting the vibration response of the structure. Dimensionless correction factors are derived to improve the predictions of the coupled lumped parameter piezoelectric energy harvester model. The second section of this chapter presents coupled distributed parameter modeling of unimorph and bimorph cantilevers under persistent base excitations for piezoelectric energy harvesting. Closed-form solutions are obtained by considering all vibration modes and the formal representation of the direct and converse piezoelectric effects. Steady state electrical and mechanical response expressions are derived for arbitrary frequency excitations. These multi-mode solutions are then reduced to single-mode solutions for excitations around the modal frequencies. Finally, the analytical expressions derived here are validated experimentally for a cantilevered bimorph with a proof mass.