Dynamic flexoelectric effect on piezoelectric nanostructures

• Published in: European journal of mechanics, A, Solids A, Solids, 2018-09, Vol.71, p.404-409
• Main Authors: Nguyen, B.H., Nanthakumar, S.S., Zhuang, X., Wriggers, P., Jiang, X., Rabczuk, T.
• Format: Article
• Language: English
• Subjects: Beam model; Beam theory (structures); Dynamic flexoelectric; Electric polarization; Electric properties; Energy harvesting; Equations of motion; Flexoelectricity; Free vibration; Harvesters; Ion beams; Mathematical models; Nanostructured materials; Piezoelectricity; Resonant frequencies; Vibration analysis; Vibration mode
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2018.06.002

Flexoelectricity, which represents the spontaneous electric polarization induced by the strain gradient, is a universal electromechanical coupling effect regardless of symmetry in all dielectric material. In solid dielectric material, the contribution from flexoelectricity can be due to four related phenomena: static and dynamic bulk flexoelectricity, surface flexoelectricity and surface piezoelectricity. While the surface flexoelectric effect can be negligible, the magnitude of the remaining three phenomena are comparable. Presently, the role of the static bulk flexoelectric and surface piezoelectric effects in the energy harvesters has been intensively studied, the contribution from dynamic flexoelectric effect remains unclear. In this work, based on the conventional beam theory, equations of motion considering dynamic flexoelectric effect are investigated. Consequently, the free vibration of the simply supported beam is studied in order to examine the influence of the dynamic flexoelectricity on natural frequency. From the numerical studies, it is found that dynamic flexoelectric effect is more influential on thick beam model and higher vibration modes. In addition, the results show that the relation between the static and dynamic flexoelectric coefficients can also alter the free vibration response. •We investigate the role of dynamic flexoelectric coefficient in piezoelectric nanostructures.•The energy associated with flexodynamic tensor is included into the kinetic energy.•Based on beam theory, the equation of motion for Timoshenko and Euler-Bernoulli beam models is derived.•Free vibration analysis shows that the dynamic flexoelectricity is more influential on the thick beam and higher vibration modes.