Energy Harvesting Based on Piezoelectric Patched Beams Under Moving-Mass Excitation

This paper develops a reduced-order electromechanical model for piezoelectric energy harvesting from a beam traversed by a moving mass. The beam is described by the Euler–Bernoulli theory, and the coupled equations of motion are derived through modal expansion combined with the linear piezoelectric constitutive relations. Unlike most existing formulations, the model accounts for non-uniform transit by including moving-mass acceleration, accommodates an arbitrary number of piezoelectric patches distributed along the span, and incorporates von Kármán strain–displacement relations. So, moderately large deflections and mid-plane stretching as well as various boundary conditions may be investigated within the same framework. The resulting coupled nonlinear ordinary differential equations are integrated in time using a numerical solver. On the other hand, predictions of midpoint deflection, output voltage, and harvested power are validated against the COMSOL Multiphysics Finite element model. The experimental setup has been established, and a dedicated laboratory experiment provides additional verification under controlled conditions. Parametric analyses investigating the individual and combined effects of the mass ratio, velocity ratio, acceleration profile, patch length, patch position, number of patches, and external load resistance are elaborated. Distributed multi-patch configurations are shown to recover more energy than a single-centered patch once higher modes contribute appreciably to the response. Design charts relating the governing parameters to the harvested power are constructed for each set of support conditions. These results are intended to assist the preliminary sizing and placement of piezoelectric transducers on some practical energy harvesting applications.