An experimental and theoretical investigation of the mechanical behavior of multilayer initially curved microplates under electrostatic actuation

We investigate the static and dynamic behavior of a multilayer clamped-free-clamped-free (CFCF) microplate, which is made of polyimide, gold, chromium, and nickel. The microplate is slightly curved away from a stationary electrode and is electrostatically actuated. The free and forced vibrations of the microplate are examined. First, we experimentally investigate the variation of the first natural frequency under the electrostatic direct current (DC) load. Then, the forced dynamic behavior is investigated by applying a harmonic alternating current (AC) voltage superimposed to a DC voltage. Results are shown demonstrating the transition of the dynamic response of the microplate from hardening to softening as the DC voltage is changed as well the dynamic pull-in phenomenon. For the theoretical model, we adopt a dynamic analog of the von Karman governing equations accounting for initial curvature imperfection. These equations are then used to develop a reduced-order model (ROM) based on the Galerkin procedure to simulate the mechanical behavior of the microplate. We compare the theoretical results with the experimental data and show excellent agreement among the results. We also examine the effect of the initial rise on the natural frequencies of first three symmetric-symmetric modes of the plate.