Surface energy and thermal stress effect on nonlinear vibration of electrostatically actuated circular micro-/nanoplates based on modified couple stress theory

Electrostatically actuated circular micro-/nanoplates are commonly used in micro-/nanoswitches and pumps. This paper models the thermal and size effects on the nonlinear vibration behavior of electrostatically actuated circular micro-/nanoplates. Surface elasticity and modified couple stress theories are simultaneously applied to the modeling. A reduced-order model incorporating temperature change is derived and solved numerically. Results show that the material length scale, surface energy, negative temperature change, and geometry nonlinear strain increase frequency and pull-in voltage of the plate. However, Casimir force and positive temperature change reduce the frequency of the plate. Moreover, the effects of surface energy, material length scale and temperature change on frequency become more obvious for thinner plates. The influence of the geometrically nonlinear strain on the frequency is significant for large initial gap to thickness ratio of the plate.