Towards a Semi-analytical Model of a Tapered Piezoelectric Energy Harvester with an Arbitrary Proofmass

In this paper, we present a semi-analytical vibrational model of a tapered piezoelectric energy harvester (TPEH) with an arbitrarily shaped proofmass. The model presented here extends a similar model without a proofmass derived in our previous work. The proofmass extension influences the eigen-analysis of the system by modifying the characteristic equation via the proofmass contribution to the boundary conditions and by updating the actuation of the system that now includes the proofmass inertia terms. The electromechanical state space model consequently derived can be simulated using a temporal solver for CAD of TPEH with a proofmass.