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Pull‐in voltage analysis for an electrostatically actuated extensional microbeam with large deflection
Author(s) -
Wang Y.G.,
Lin W.H.
Publication year - 2010
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200900380
Subject(s) - microbeam , boundary value problem , nonlinear system , deflection (physics) , method of mean weighted residuals , shooting method , mechanics , residual stress , voltage , bernoulli's principle , materials science , mathematical analysis , physics , classical mechanics , mathematics , galerkin method , optics , composite material , quantum mechanics , thermodynamics
This paper presents an analysis of pull‐in behavior for nonlinear microelectromechanical coupled microbeams. Based on the accurate geometrically nonlinear theory of Euler‐Bernoulli beams, a distributed electromechanical model that accounts for electrostatic fringing field, finite deformation, and residual stress, is proposed. The governing differential equations, in conjunction with the corresponding boundary conditions, constitute a nonlinear two‐point boundary value problem which is solved numerically by shooting method. Taking the applied voltage as an unknown and the maximum deflection as a control parameter, the characteristic relations of applied voltage vs. deflection are successfully obtained. In order to confirm the model results, several case studies are compared with available published simulations, showing a good reliability. The influences of various parameters, such as the initial gap‐length ratio, fringing field effect, residual stress, on the pull‐in parameters have been studied with this method. Numerical results show that the proposed method is accurate and stable, which is an effective method to analyze the deformation of a microbeam.