Asymptotic and Numerical Analysis of Electrostatic Buckling of Cantilevers

Nawaf Bou-Rabee, California Institute of Technology

Photo of Nawaf Bou-Rabee

In this poster presentation, we consider the electrostatic actuation of a fixed-free cantilever beam. The effects of nonlinear and linear bending forces are taken into account. We assume the parallel-plate capacitor approximation which implies that the electrostatic force is inversely related to the square of the distance between the beam and the electrostatic surface. With these models from linear and nonlinear beam theory, we identify a turning point at a critical value of the dimensionless critical voltage, i.e., the pull-in or snap-down voltage.

This problem is motivated by the pull-in instability in micro-electro-mechanical systems (MEMS) and nano-electro-mechanical systems (NEMS). Electrostatic forces are one of the common ways of moving structures at the micro/nano-scales. The pull-in instability, however, limits the stable range of motion of electrostatic structures. The pull-in phenomenon occurs because the elastostatic forces in the components of the device cannot balance the nonlinear electrostatic force.

Abstract Author(s): Nawaf Bou-Rabee and Louis Romero