Suppression of dynamic pull-in instability in electrostatically actuated strain gradient beams

In this paper, vibration suppression of micro-or nano-scale beams subjected to nonlinear distributed electrostatic force is studied. For the sake of precision, we use the beam model derived from strain gradient elasticity theory aimed at prediction of size effect. In addition, the electrostatic force is considered with first order fringing field correction. The continuous model of the strain gradient beam is truncated by using Kantorovich method as a semi-analytical finite element method. A boundary control feedback law is proposed to suppress forced vibrations of the beam. Both measurements and actuations are taken place in the boundary to avoid spillover instabilities. Simulation results show that the proposed controller not only suppresses the forced vibration of the beam before crossing dynamic pull-in threshold, but also it extends the criterion for dynamic pull-in instability.