Accurate reduced-order modeling of MEMS and NEMS microactuators under dynamic electrostatic loading and large strokes

This work investigates the static and dynamic behavior of microbeam when actuated by a DC load superimposed to an AC harmonic load. When modeling the micro electromechanical system, the use of nonlinear terms like third-order nonlinearities can be sometimes ambiguous. In this study we demonstrate that neglecting third-order nonlinearities and nonlinear inertia in the equation of motion leads to accurate results and low computational cost. We derive the governing equation of motion using both linear and nonlinear Euler Bernoulli beam theory with two possible configurations: cantilever and doubly-clamped. A Reduced Order Models (ROMs) based on Differential Quadratic Method (DQM) decomposition is utilized to simulate dynamic response of microbeam. Besides, we employ the Finite Difference Method (FDM) to discretize the orbits of motion and solve the resulting nonlinear algebraic equations. The stability of captured orbits is determined by combining the FDM discretization with Floquet theory. A comparison is then deduced between results found by applying the DQM-FDM decomposition and results found in the literature.