Topology optimization of piezoelectric materials and application to the cantilever beams for vibration energy harvesting

A new design analysis method based on FEM and a topology optimization for piezoelectric materials was developed for the unimorph cantilevered energy harvesters which can produce the maximum electric power outputs. The optimum topology of a piezoelectric material layer on the harvesting beam has been calculated by considering natural frequencies of beams, electromechanical couplings of piezoelectric materials, tip masses and MMA (method of moving asymptotes). The piezoelectric coefficients such as elasticity, capacitance and piezoelectric coupling were interpolated by element density variables in the topology optimization. The optimum design method was verified by vibration tests and measuring voltage outputs of the harvester and a good correlation between two results has been obtained. The effects of beam geometric parameters and several piezoelectric materials (PZT, PVDF, PMN-PT and piezoelectric fiber composites) on power generation were also investigated. The beam with PMN-PT generated the largest voltage and the next largest is PZT, MFC and PVDF, respectively.