Periodic solutions and the avoidance of pull-in instability in nonautonomous microelectromechanical systems

We study periodic solutions of a one-degree of freedom microelectromechanical system (MEMS) with a parallel-plate capacitor under T-periodic electrostatic forcing. We obtain analytical results concerning the existence of T-periodic solutions of the problem in the case of arbitrary nonlinear restoring force, as well as when the moving plate is attached to a spring fabricated using graphene. We then demonstrate numerically on a T-periodic Poincaré map of the flow that these solutions are generally locally stable with large “islands” of initial conditions around them, within which the pull-in stability is completely avoided. We also demonstrate graphically on the Poincaré map that stable periodic solutions with higher period nT, n > 1 also exist, for wide parameter ranges, with large “islands” of bounded motion around them, within which all initial conditions avoid the pull-in instability, thus helping us significantly increase the domain of safe operation of these MEMS models.