Vibration analysis of electrostatically actuated nonlinear microbridges based on the modified couple stress theory

In this paper natural frequency of electrostatically actuated microbridges is investigated based on the modified couple stress theory. Nonlinear formulation of Euler–Bernoulli microbeam is derived using Hamilton’s principle. By considering the von-Karman strain, the nonlinearities caused by the mid-plane stretching are included in the formulation. To confirm the model, results of static deflection and natural frequency of microbeams are calculated using modified couple stress theory and compared to those evaluated based on the classical theory and experimental observations. At first, from experimental results of static deflection of a microcantilever, estimation for length scale parameter of polysilicon is presented. Using this value of length scale, natural frequency of microbridges under electrostatic actuation is calculated on the basis of the modified couple stress theory and compared with experimental results. The results of the modified couple stress theory are in very good agreement with experimental findings while the difference between the results predicted based on the classical theory and experimental findings is considerable.