Nonlinear Vibrations of an Electrostatically Actuated Microresonator in an Incompressible Fluid Cavity Based on the Modified Couple Stress Theory

In this paper, the size-dependent resonant behavior of a microcantilever immersed in an incompressible fluid cavity is investigated. The nonclassical modified couple stress theory (MCST) is employed to capture the effects of length scale. The microbeam is deflected by applying a bias direct current (DC) voltage and then driven to vibrate around its deflected position by a harmonic alternating (AC) voltage. Regarding the nonlinear electrostatic force and the fluid pressure exerted upon the microbeam, the governing equations of the system are derived based on the MCST. Multiple scales method is used to obtain an approximate analytical solution for nonlinear resonance curves. Initially, the effect of length scale parameter on the dynamic response of system is studied, and then, a parametric study is conducted to evaluate the effects of MCST as well as the fluidic confinement on the resonance curves. The obtained results reveal that the frequency response along with the softening behavior of the system decreases when MCST is used. It is shown that the resonance amplitude obtained by the MCST is considerably smaller than those obtained by the classical theory (CT). Finally, it is found that the dynamic stability margins of the system could be extended by the size effect perspective.