Nonlinear Dynamics of Electrostatically Actuated Coupled MEMS Parallel Cantilever Resonators

Abstract

This paper deals with the nonlinear response of a coupled cantilever system composed of two micro beams electrostatically actuated. The AC frequency of actuation is near natural frequency of the cantilevers. The two cantilevers are identical. Lagrange equations are used to develop a mathematical model of the system. These equations of motion are nondimensionalized and subjected to the method of multiple scales in order to find steady state solutions. Alternating Current (AC) and Direct Current (DC) actuation voltages are applied between the first cantilever and ground plate with DC voltage applied between the first and second cantilevers. Amplitude-frequency and phase-frequency responses of the system are provided for typical micro beam system structures.