Vibration analysis of flexoelectric micro-beams for energy harvesting

We develop a theoretical formulation of a flexoelectric cantilever beam model for energy harvesting by integrating the dynamic flexoelectric effect and surface effect. Electromechanical equations are derived from Hamilton’s principle using the assumed-modes method, incorporating strain gradient–induced polarization and surface residual stress. Voltage–frequency responses indicate that dynamic flexoelectricity enhances higher-mode output, while surface stress shifts the resonance to higher frequencies with increased voltage. The combined effects enable efficient, broadband, and tunable energy harvesting at the micro- and nano-scales.