Pull-in analysis of electrostatically actuated curved micro-beams with large deformation

This paper investigates the pull-in behavior of an electrostatically actuated geometrically nonlinear micro-beam with an initial curved configuration. The theoretical formulation is based on an arc-coordinate system and does not involve any assumptions. The nonlinear governing equations are derived by considering the static equilibrium of an infinitesimal element and are then solved through the use of the differential quadrature method (DQM) and an iterative algorithm. Pull-in parameters (pull-in voltage, pull-in gap and pull-in mode) are obtained numerically for both fixed¿fixed and cantilever micro-beams. The present analysis is validated through direct comparisons between the present results and the existing numerical and experimental results. A parametric study is conducted to examine the effects of large deformation, the arc length, radius of curvature, initial gap and the boundary condition on the pull-in characteristics of micro-beams. The numerical results show that for micro-beams with a long arc length, neglect of geometrical nonlinear deformation will lead to significantly underestimated pull-in voltage and pull-in gap.