Effect of Dispersion Forces on Dynamic Stability of Electrostatically Actuated Micro/Nano-Beams in Presence of Mechanical Shocks

Abstract

Dispersion forces such as van der Waals and Casimir interactions become important when the size of structures shrinks. Therefore, the effective design of micro and nano-sized structures depends on appropriate consideration of these forces. In the current research, we analyzed the effect of dispersion forces on the dynamic behavior of a micro/nanobeam actuated by electrostatic forces subject to a mechanical shock. We used the Euler–Bernoulli beam theory including nonlinearities due to mid-plane stretching in our model. The equation of motion is solved using time-dependent finite element method, and pull-in forces are calculated. The stability regimes are evaluated as the set of three force parameters in which the beam elasticity overcomes the external forces, and the beam is able to vibrate without hitting the substrate. Results show that the design of the beam should be such that the three sets of non-dimensional parameters that determine the intensity of shock, dispersion, and electrostatic force do not fall above the stability limit to avoid pull-in instability. Our results have applications in the design of electrostatically actuated micro/nanobeams in mechanical shock environments such as accelerometers.