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Shock and Vibration
Volume 2017, Article ID 4157085, 7 pages
Research Article

Flexoelectric Effect on Vibration of Piezoelectric Microbeams Based on a Modified Couple Stress Theory

Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China

Correspondence should be addressed to Ying Luo; nc.ude.sju@gniyoul

Received 12 October 2016; Accepted 12 February 2017; Published 16 March 2017

Academic Editor: Paulo B. Gonçalves

Copyright © 2017 Xingjia Li and Ying Luo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A novel electric Gibbs function was proposed for the piezoelectric microbeams (PMBs) by employing a modified couple stress theory. Based on the new Gibbs function and the Euler-Bernoulli beam theory, the governing equations which incorporate the effects of couple stress, flexoelectricity, and piezoelectricity were derived for the mechanics of PMBs. The analysis of the effective bending rigidity shows the effects of size and flexoelectricity can greaten the stiffness of PMBs so that the natural frequency increases significantly compared with the Euler-Bernoulli beam, and then the mechanical and electrical properties of PMBs are enhanced compared to the classical beam. This study can guide the design of microscale piezoelectric/flexoelectric structures which may find potential applications in the microelectromechanical systems (MEMS).