On the nonlinear dynamics of pre-stressed nanoelectromechanical resonators

Motivated by the lack of sufficient accuracy in the nonlinear dynamics of the pre-stressed nano electromechanical resonators, in the present article, the concept of the dynamic instability in the pre-stressed nanoelectromechanical resonators comprehensively is investigated while the emphasis is placed on investigating the effect of the applied electric voltage. A class of nonlinear the Mathieu-Hill equation is established to determine the bifurcations while an axial parametric load is applied to excite the system. The results emphasize that the existence of different stable states allows to occur the saddle node, the supercritical, and subcritical pitchfork bifurcations.