Nonlinear Vibration of Size Dependent Microresonators with an Electrostatically Actuated Proof Mass

In this paper, the dynamic and nonlinear vibration responses of a microresonator containing a microbridge with a proof mass located at its middle are studied. The proof mass of the microresonator is actuated by the electrostatic field in such a way that a direct voltage finds a certain equilibrium position and then be prompted to vibration under the alternative voltage. Due to the importance of the size dependency effect in analysis of the performance of microelectromechanical systems, the size dependent theory is used in the modeling of the microstructure. By adopting the modified couple stress theory and considering electrostatic actuation, the dynamic equation of motion is derived using the extended Hamilton’s principle. Further, with the approximation by Galerkin’s method, the governing equation for the static and oscillatory motion is reduced and the resultant equation is solved by analytical (multiple-scales) and numerical methods. In the analytical and numerical results, the effects of various parameters on the system response, including the midplane stretching and size dependent effects, and dependency of vibration response to initial conditions, are analyzed in detail.