Static Deflection, Pull-in Instability and Oscillatory Behavior of the Electrostatically Actuated Microresonator with a Distributed Proof Mass Considering Non-Classical Theory

Abstract

In this paper, the static and vibration responses of a microresonator by considering distributed proof mass are investigated based on the modified couple stress theory (MCST). The microresonator has a proof mass placed on the end of micro-cantilever beam and the proof mass actuated by electrostatic actuation. Due to the large length of proof mass compared to beam length, the proof mass is considered as a lengthy mass in the modeling. Hence, the resultant force and moment acting on the proof mass can be calculated by integrating the density of the electrostatic force along the mass length. Considering the length effects of the proof mass, MCST and electrostatic actuation, the equation of dynamic motion is derived using the extended Hamilton principle. Using a model approximation, i.e., Galerkin decomposition method, the governing equations of static and oscillatory motions are reduced and the resultant equation is solved by analytical (multiple scale method) and numerical methods. The result shows that the developed model, that includes distributed proof mass and size dependency effects, improves the results of pull-in instability voltage, natural frequency and amplitude of vibration.