Dynamics of a Canonical Electrostatic MEMS/NEMS System

The mass-spring model of electrostatically actuated microelectromechanical systems (MEMS) or nanoelectromechanical systems (NEMS) is pervasive in the MEMS and NEMS literature. Nonetheless a rigorous analysis of this model does not exist. Here periodic solutions of the canonical mass-spring model in the viscosity dominated time harmonic regime are studied. Ranges of the dimensionless average applied voltage and dimensionless frequency of voltage variation are delineated such that periodic solutions exist. Parameter ranges where such solutions fail to exist are identified; this provides a dynamic analog to the static “pull-in” instability well known to MEMS/NEMS researchers.