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Energy harvesting from vibration of Timoshenko nanobeam under base excitation considering flexoelectric and elastic strain gradient effects

S.A.M. Managheb, S. Ziaei-Rad and R. Tikani

Journal of Sound and Vibration, Volume 421, February 2018, Pages 166-189



The coupling between polarization and strain gradients is called flexoelectricity. This phenomenon exists in all dielectrics with any symmetry. In this paper, energy harvesting from a Timoshenko beam is studied by considering the flexoelectric and strain gradient effects. General governing equations and related boundary conditions are derived using Hamilton's principle. The flexoelectric effects are defined by gradients of normal and shear strains which lead to a more general model. The developed model also covers the classical Timoshenko beam theory by ignoring the flexoelectric effect. Based on the developed model, flexoelectricity effect on dielectric beams and energy harvesting from cantilever beam under harmonic base excitation is investigated. A parametric study was conducted to evaluate the effects of flexoelectric coefficients, strain gradient constants, base acceleration and the attaching tip mass on the energy harvested from a cantilever Timoshenko beam. Results show that the flexoelectricity has a significant effect on the energy harvester performance, especially in submicron and nano scales. In addition, this effect makes the beam to behave softer than before and also it changes the harvester first resonance frequency. The present study provides guidance for flexoelectric nano-beam analysis and a method to evaluate the performance of energy harvester in nano-dielectric devices.



A. Energy harvesting; B. Flexoelectricity; C. Electromechanical coupling; D. Strain gradient; E. Timoshenko beam theory; F. Short circuit natural frequency; G. Open circuit natural frequency


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