Modeling of Initially Curved Beam Structures for Design of Multistable MEMS

TitleModeling of Initially Curved Beam Structures for Design of Multistable MEMS
Publication TypeJournal Article
Year of Publication2012
AuthorsWilliams, M. D., F. Van Keulen, and M. Sheplak
JournalJournal of Applied Mechanics
Start Page011006
Date Published01/2012

This article describes a mathematical model and two solution methodologies for efficiently predicting the equilibrium paths of an arbitrarily shaped, precurved, clamped beam. Such structures are common among multistable microelectromechanical systems (MEMS). First, a novel polynomial-based solution approach enables simultaneous solution of all equilibrium configurations associated with an arbitrary mechanical loading pattern. Second, the normal flow algorithm is used to negotiate the particularly complex nonlinear equilibrium paths associated with electrostatic loadingand is shown to perform exceptionally well. Overall, the techniquespresented herein provide designers with general and efficient computational frameworks for studying the effects of loading, shape, and imperfections onbeam behavior. Sample problems motivated from switch and actuator applications in the literature demonstrate the methodologies' utility in predicting the nonlinear equilibrium paths for structures of practical importance.

Refereed DesignationRefereed