Shape improvement for piezoelectric energy harvesting applications

We aim at using variable shape cantilever beam to improve the efficiency of energy harvesting from ambient vibration in wireless grid sensor applications. The cantilever beam is composed of an active layer composed of a piezoelectric material and a metallic layer (unimorph design). A tip mass attached to the free end of the cantilever beam is added to increase the inertial forces of the structure. The introduction of the variable shape design is motivated by the fact that prismatic shape beams are not efficient since only the part near to the clamped side can produce electrical power thanks to the presence of stresses. By varying the geometry of the beam we redistribute the stress along the beam's length in order to increase the harvested power. In this work, the equations of motion and associated boundary conditions are derived using Hamilton Principle. We analyze the statics and dynamics of the variable geometry beam. In order to maximize the harvested energy, we discuss the influence of the system's and excitation's parameters on the dynamic problem. Besides, we found that harvested energy is maximized for an optimum electric load resistance. Concerning the beam's shape, this work reveals that it should be as truncated as possible. In fact, trapezoidal cantilever with base and height dimensions equal to the base and length dimensions of a rectangular beam will have a higher strain and maximum deflection for a given load.