An investigation of the static and dynamic behavior of electrically actuated rectangular microplates

•The nonlinear mechanical behavior of microplates under electrostatic actuation.•A reduced-order model of the von–Karman equations, enabling investigation of the nonlinear behavior of the plate.•The forced vibration of the plate is being presented here for the first time (never studied before).•Analytical results are presented and compared for some cases with a finite-element model.•We show results for the response of the plate under superharmonic and subharmonic resonances.

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the effect of different non-dimensional design parameters. The static results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased. Finally, near-square plates are studied to understand the effect of geometric imperfections of microplates.