Energy harvesting performance of acoustic energy harvesters consisting of flexoelectric plates and defect-state phononic crystals

Purpose: This paper introduces a novel analysis model for a sound energy harvester that goes beyond the traditional methods based on piezoelectric or electromagnetic effects. The proposed model utilizes both piezoelectric and flexoelectric effects and consists of a flexoelectric vibrating plate and a phononic crystal with defect points to enhance the power of sound energy harvesting. Methods: Using plane wave expansion and supercell methods, this paper obtains the defect band frequencies and corresponding acoustic pressure distribution of the defective state phononic crystal. By applying the Hamiltonian principle, the electromechanical control equations for the double-layer flexoelectric plate are derived. The Galerkin method is employed to solve these equations, providing an approximate closed-form solution for voltage output. Finite-element simulations validate the theoretical results. Conclusion: The study reveals a significant enhancement (3.66 times) in voltage output for the sound energy harvester at the micro-nano-scale through the combined effects of flexoelectricity and piezoelectricity. The presence of defect state phononic crystal results in 4.24-fold, 11.60-fold, and 2.55-fold increases in voltage output, power output, and energy conversion efficiency, respectively, for the flexoelectric sound energy harvester. Additionally, optimal laying schemes and load resistance for the flexoelectric layer are provided.