Second-order phononic topological insulators and optimal energy harvesting

In the present work, we explore the possibility of using first- and second-order phononic topological insulators (TIs) as substrates for piezoelectric energy harvesters. Square unit cells of C 4 v and C 2 v symmetry are designed adopting a genetic algorithm based topology optimization method. In the case of first-order TIs, the interface between unit cells that are topologically distinct serves as the ideal location for placing piezoelectric patches, as it enables energy localization. While, in the case of second-order TIs, the piezoelectric patches are placed at the corners of interfaces between topologically opposite unit cells. The electrical energy output over a frequency range is maximized by such strategical placement of piezoelectric patches. In addition, we propose a stepped plate with thickness varying along the direction of the topological interface, in order to widen the operational frequency range. The numerical simulations corroborate the efficiency of the proposed ideas for an energy harvesting system and opens new avenues in applications of phononic topological metamaterials.