Symmetry and Symmetry Breaking in Electrostatic MEMS

The use of electrostatic forces to provide actuation is a method of central importance in microelectromechanical systems (MEMS) and is of growing importance in nanoelectromechanical systems (NEMS). The study of electrostatic actuation has led to numerous interesting experimental, theoretical, and numerical results. Yet, surprisingly, even simple electrostatically actuated systems have secrets to reveal. Here, we study the electrostatic deflection of an annular elastic membrane. We consider the so-called small aspect ratio approximate model of electrostatically deflected membranes. We ask whether or not solutions to this model automatically inherit the symmetry of the annular domain. Through a numerical investigation we show that in fact, asymmetric solutions exist. That is, there is a symmetry breaking bifurcation present in this model for the electrostatically deflected annular system.