Closed-form solutions for forced vibrations of piezoelectric energy harvesters by means of Green’s functions

In this article, the closed-form solutions are obtained for the forced vibrations of cantilevered unimorph piezoelectric energy harvesters. A tip mass is attached at the free end, and the moment of its inertia to the fixed end is considered. Timoshenko beam assumptions are used to establish a coupled electromechanical model for the harvester. Two damping effects, transverse and rotational damping effects, are taken into account. Green’s function method and Laplace transform technique are used to solve the coupled electromechanical vibration system. The conventional case of a harmonic base excitation is considered, and numerical calculations are performed. The present model is validated by comparing its predictions with the existing data, the experimental results, and the finite element method solutions. The influences of shear deformation and rotational inertia on the predictions are discussed. The effect of load resistance on the electrical power is studied, and the optimal load resistances are obtained. Ultimately, the optimal schemes are proposed to improve electricity generation performance for the soft piezoelectric materials: PZT-5A/5H.