Optimisation and performance comparison of direct and parametric piezoelectric energy harvester with geometrical nonlinearities

The behaviour and performance of a flexible beam piezoelectric energy harvester (PEH) in direct and parametric excitation, including the effect of geometrical nonlinearities, are addressed in this paper. First, the electromechanical modelling of the harvester is addressed. A Timoshenko geometrically exact model of a laminated piezoelectric beam in large rotation, including parametric excitation, is proposed, extending previous results of the literature. Then, considering cantilever boundary conditions, it is simplified under Euler–Bernoulli, inextensible assumptions and third order Taylor expansion, suitable for modal expansion. Two perturbation methods are tested to compute vibratory response under direct and parametric excitations. They are both found inaccurate for large amplitude oscillations, leading to a preference for numerical solving by continuation of periodic solutions. PEH behaviours and performances are finally carefully estimated regarding the optimal harvested power in a shunted resistor at resonance. Comparisons between direct and parametric forcing are proposed and the effect of geometrical nonlinearities is estimated. An interesting result is that the harvested power under parametric excitation cannot compete with the one under direct excitation.