Impacts of Small-Scale Effect and Nonlinear Damping on the Nonlinear Vibrations of Electrostatic Microresonators.

Although the small-scale effect and nonlinear damping on the nonlinear vibration of microbeam electrostatic resonators are important, they have been overlooked by researchers. We use the slender beam model including the small-scale effect and nonlinear damping to investigate the nonlinear vibrations of the electrostatic resonators in the present paper. We apply the Galerkin method on a nonlinear partial differential equation to obtain the nonlinear ordinary differential equations for the first and third modes. The two equations include constant terms. The multiple-scale method is used to obtain the approximate analytical solutions of the two equations. The approximate analytical solutions discover the effects of driving electric field, small-scale effect, and nonlinear damping on structural vibrations. The results suggest that the small-scale effect, the direct current (DC) voltage, and the alternating current (AC) voltage have some critical effects on the vibrations of microresonators.