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 loading and is shown to perform exceptionally well. Overall, the techniques presented herein provide designers with general and efficient computational frameworks for studying the effects of loading, shape, and imperfections on beam 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.
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January 2012
Research Papers
Modeling of Initially Curved Beam Structures for Design of Multistable MEMS
Matthew D. Williams,
Matthew D. Williams
Interdisciplinary Microsystems Group
, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611-6250,
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Fred van Keulen,
Fred van Keulen
Professor
Structural Optimization and Computational Mechanics Group,
Department of Precision and Microsystems Engineering
, Faculty of Mech., Maritime, & Material Eng., Delft University of Technology, 2628 CD Delft, The Netherlands
,
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Mark Sheplak
Mark Sheplak
Professor
Interdisciplinary Microsystems Group,
Department of Mech. and Aero.
Engineering, University of Florida, Gainesville, FL 32611-6250,
Search for other works by this author on:
Matthew D. Williams
Interdisciplinary Microsystems Group
, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611-6250,
Fred van Keulen
Professor
Structural Optimization and Computational Mechanics Group,
Department of Precision and Microsystems Engineering
, Faculty of Mech., Maritime, & Material Eng., Delft University of Technology, 2628 CD Delft, The Netherlands
,
Mark Sheplak
Professor
Interdisciplinary Microsystems Group,
Department of Mech. and Aero.
Engineering, University of Florida, Gainesville, FL 32611-6250, J. Appl. Mech. Jan 2012, 79(1): 011006 (11 pages)
Published Online: November 14, 2011
Article history
Received:
July 21, 2010
Revised:
April 18, 2011
Posted:
July 28, 2011
Published:
November 14, 2011
Online:
November 14, 2011
Citation
Williams, M. D., Keulen, F. V., and Sheplak, M. (November 14, 2011). "Modeling of Initially Curved Beam Structures for Design of Multistable MEMS." ASME. J. Appl. Mech. January 2012; 79(1): 011006. https://doi.org/10.1115/1.4004711
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