Topology optimum design of unimorph piezoelectric cantilevered Mindlin plates as a vibrating electric harvester

Abstract

An FEM-based topology optimization approach is proposed to calculate the topologies of a substrate plate and a piezoelectric layer used for vibrating unimorph cantilevered plate-like electricity generators (energy harvesters). The Mindlin plate theory was combined with a topology optimization algorithm to consider the shear effect. Each optimum topology for a plate and a piezoelectric layer is computed and combined by reflecting the natural frequencies of the substrate plate, electromechanical couplings of piezoelectric materials, tip masses and method of moving asymptotes. The piezoelectric coefficients such as elasticity, piezoelectric coupling and capacitance are interpolated by element density variables. The cantilevered plate generators with optimal topologies were designed for three piezoelectric materials such as PZT, PMN-PT and PMN-PT single crystal fiber MFC, and their voltage outputs were compared using a developed FEM-based optimization code to investigate the suitable material for harvesters.