The optimal distribution of axial strain amplitude in a piezoelectric vibrating energy harvester

This study considers the optimal distribution of strain amplitude in a piezoelectric vibrating energy harvester (PVEH) that maximizes the harvested energy. In many previous studies, it was tacitly assumed that a uniform distribution of axial strain in the piezoelectric layer ensures that the harvested energy is maximal. Though this assumption is intuitive, it was not supported by analysis. In this work, we derive and present a formal analytic proof confirming that, for a given amount of energy in the vibrating structure, a uniform distribution of strain in the piezoelectric layer ensures that the harvested energy is maximal.