Dynamics modeling of microbeams under electrostatic load

This paper investigates the features of different techniques to model the dynamic behaviour of microbeams electrostatically actuated to identify the frequency shifting due to the electromechanical coupling. A first model with a single degree of freedom of double clamped microbeam is investigated: the analytic solution of the linearized equation of motion is compared to the numerical one of the nonlinear problem, solved by the Newmark method. FEM models are then introduced and compared to Newmark numerical integrations. A new procedure for a fast estimation of the frequency has been developed: a parabolic curve (frequency vs. voltage) approximates the actual characteristic by means of two interpolation points, corresponding to the steady-state frequency (pure mechanical actuation) and to a generic voltage, for which the Newmark method is applied once.