Pull-in Voltage of Electrostatically-Actuated Microbeams in Terms of Lumped Model Pull-in Voltage Using Novel Design Corrective Coefficients

Abstract

In this paper, we present a study of the static and dynamic responses of a fixed–fixed and cantilever microbeam (using both the lumped and the distributed models) to a DC and a step DC voltage. A Galerkin-based step by step linearization method and a Galerkin-based reduced order model have been used to solve the governing static and dynamic equations, respectively. The calculated static and dynamic pull-in voltages have been validated by previous experimental and theoretical results and a good agreement has been achieved. The introduction of novel design corrective coefficients, independent of the beam’s material and geometric properties, results in a closed form relationship between static pull-in voltage of the lumped model and static & dynamic pull-in voltages of the distributed models, and takes into account the residual stresses, axial force and damping effects. Multiplying these design coefficients with the static pull-in voltage of the lumped model, the static and dynamic pull-in voltage of a given microbeam can be obtained without the need to solve the nonlinear governing equations.