Optimal design of unimorph and segmented piezoelectric cantilevers for energy harvesting

Segmented piezoelectric layers attached to supporting cantilever beams offer the possibility of optimizing the harvester design from different perspectives with respect to a single layer covering the entire length. Indeed, a suitable selection of the length and position of the piezoelectric patch may increase their effectiveness, save piezoelectric material, and reduce costs from the life-cycle perspective of device disposal. A linear reduced-order model (ROM) for unimorph and stepped piezoelectric energy harvesters with a proof mass is developed to evaluate the power output under transversal ground excitation. The electromechanical PDEs derived by Hamilton’s principle are transformed into a system of uncoupled ODEs using the exact bending modes of an equivalent piecewise uniform, multilayered Bernoulli–Euler beam. The model is validated comparing its analytical voltage-to-acceleration transfer function with that experimentally identified for various resistive loads and tip masses under harmonic excitation. Such a validated ROM allows for fast and accurate computation of the sensitivity of frequency transfer functions with respect to patch length and position, highlighting the optimal combinations of parameters to maximize voltage, electrical power, or piezoelectric material efficiency.