Nonlinear behavior analysis of electrostatically actuated multilayer anisotropic microplates with residual stress

Electrostatically actuated microplates with multilayer and material anisotropy properties, are widely employed in microelectromechanical systems. However, previous theories rarely consider the aforementioned properties simultaneously, hindering their widespread application. This paper proposes a general theoretical model for electrostatically actuated rectangular multilayer anisotropic microplates subjected to residual stress and hydrostatic pressure by combining the classical laminated thin plate theory, Galerkin method and a partial expansion approach for nonlinear electrostatic force. This model enables successful establishment of closed-form expressions for the main mechanical behaviors, e.g. the pull-in voltage, static deflection, and resonant frequency. Validation of these expressions, using finite element method simulations and experimental results, shows significant improvement in the analysis accuracy (15 times higher) compared to those theories neglecting the material anisotropy, as well as excellent applicability across a wide range of DC voltages and dimensions. Additionally, the influences of electrostatic softening effects and scale effects on the theories are also discussed.