2022/01/05 by Hermann A. G. Schenk, Schenk, Hermann A. G., A. P. Melnikov +11
Engineering · Physics and Astronomy · #Advanced MEMS and NEMS Technologies #Applied Physics (physics.app-ph) #FOS: Physical sciences #Force Microscopy Techniques and Applications #Mechanical and Optical Resonators
paper · pdf · doi:10.48550/arxiv.2201.01627
openalex publication_date 2022/01/05 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In a previous publication we demonstrated that the stable and unstable equilibrium states of prismatic Coulomb actuated Euler-Bernoulli micro-beams, clamped at both ends, can successfully be simulated combining finite element analysis (FEM) with continuation methods. Simulation results were experimentally scrutinised by combining direct optical observations with a modal analysis regarding Euler-Bernoulli eigenmodes. Experiment and simulation revealed convincing evidence for the possibility of modelling the physics of such a micro-beam by means of lumped parameter models involving only a single degree of freedom, the Euler-Bernoulli zero mode. In this paper we present the corresponding analytical single degree of freedom lumped parameter model (LPM). This comprehensive model demonstrates the impact of the beam bending on the nature of the Coulomb singularity, allows for an easy and accurate computation of the pull-in voltage in the presence of stress stiffening and is apt for efficient frequency response computations. Our method to derive the zero-mode LPM is based on a Chebyshev-Edgeworth type method as is common in analytical probability theory. While used here for a very particular purpose, this novel approach to non-linear dynamic systems has a much broader scope. It is apt to analyse different boundary conditions, electrostatic fringe field corrections and squeeze film damping, to name a few applications.