Effect of flexoelectricity on the Pull-in instability of beam-type NEMS

Considering the increasing number of smart materials in advanced industries and technologies, the need to investigate the use of these materials is felt more and more. The flexoelectric effect is one of the most important phenomena created in micro-scale beams, which will have a significant effect on the results and should be investigated. Therefore, in this article, the Pull-in instability in the beam-type microelectromechanical systems has been investigated under the flexoelectric effect. The governing equations of the system have been derived based on the theory that is founded on the strain gradient theory for the Euler-Bernoulli beam model. This beam is under the effect of intermolecular Casimir force and electrostatic force. The equations and boundary conditions related to them have been non-dimensionalized first in direct and indirect flexoelectric effect. With the help of the differential quadrature method, the Pull-in voltage's critical parameters and the system's free-standing behavior have been studied. Among the significant results obtained from this research, it is possible to mention the Pull-in voltage increase due to the flexoelectric effect reduction. Also, in the indirect state of the flexoelectric effect, the increase in the initial applied voltage causes a decrease in the Pull-in voltage.