With the development of nanotechnology, nanoactuators have recently re-stimulated a surge of scientific interests in research communities. One of the interesting transduction mechanisms that showed high efficiency at the nanoscale was flexoelectricity. In fact, the flexoelectric effect in dielectric solids couples polarization and strain gradient, rather than polarization and strain for piezoelectricity, to convert mechanical stimulus into electricity and vice cersa. The objective of the current work is to develop a complete comprehensive electromechanical model of a nanobeam whose for piezoelectrically-actuated nanocantilever sensor in which both the flexoelectricity and piezoelectricity effects will be tzken into consideration. Starting from the enthalpy density function, the Hamilton’s principle is applied to drive the governing coupled equations with appropriate boundary conditions. Then, we investigate the free vibration of the mechanism by formulating the eigenvalue problem associated with the coupled partial differential equations. Using the Galerkin procedure we develop both the static and dynamic of our structure. The results show that a certain aspect ratio flexoelectric effect significantly increases the performance of the nanoactuator.
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