Electrostatic Beam Model Jan Lienemann and Jan G. Korvink IMTEK – Institute for Microsystem Technology, Albert Ludwig University Georges K¨ ohler Allee 103, D-79 110 Freiburg, Germany Tel. +49 761 203 7390, Fax. +49 761 203 7382, lieneman@imtek.de March 30, 2003 Abstract In this short report we detail how to derive the nonlinear dynamic system equations for a beam subject to electrostatic actuation. We start from the FEM discretization of a linear beam and a point charge approach for the electrostatics. Lagrange methods are used to couple the energy domains. Contents 1 The System 1 2 FEM Discretization of the Beam 2 2.1 FEM setup ........................................... 2 2.2 Stress, strain and displacement ................................ 2 2.3 Discretization ......................................... 3 3 Electrostatic Actuation 6 4 Nonconservative Work 7 5 Equations of Motion 7 6 Implementation 8 6.1 Node numbering ....................................... 8 6.2 Building of matrices ..................................... 8 6.3 Boundary conditions ..................................... 10 7 Summary 11 1 The System V in s Figure 1: System setup 1