Analytical modeling and simulations of a piezoelectric nanorod for energy harvesting via Eringen's differential model

In this paper, an analytical model is formulated to analyze the linear longitudinal forced vibration response of a PZT nano-generator acting on its 33-mode for energy harvesting and the effects of both steady-state and transient vibration response of the nano-generator are taken into consideration. Computer simulations are carried out to investigate the generated power, voltage and current originating from the excitation of the base motion. The effects of the excitation frequency, whether it is in the near resonance domain or not, the resistance of the electrical circuit and the nanorod's aspect ratio on the vibration response and electrical response of the nanogenerator are evaluated. For this purpose, Eringen's differential model, Hamilton's principle, the linear piezoelectricity theory and the classical rod theory are employed to derive the governing equation of motion together with the equivalent electrical equation. Then, the derived equations are solved using the Laplace transform method and several results such as the peak voltage as a function of the exciting frequency are shown to demonstrate the effectiveness of the proposed methodology.