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.