Symmetry breaking in an initially curved micro beam loaded by a distributed electrostatic force

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Abstract

The asymmetric buckling of a shallow initially curved stressfree micro beam subjected to distributed nonlinear deflectiondependent electrostatic force is studied. The analysis is based on a two degrees of freedom reduced order (RO) model, resulting from the Galerkin decomposition with linear undamped eigenmodes of a straight beam used as the base functions. Simple approximate expressions are derived defining the geometric parameters of beams for which an asymmetric response bifurcates from the symmetric one. The necessary criterion establishes the conditions for the appearance of bifurcation points on the unstable branch of the symmetric response curve;the sufficient criterion assures a realistic asymmetric buckling bifurcating from the stable branches of the curve. It is shown that while the symmetry breaking conditions are affected by the nonlinearity of the electrostatic force, its influence is less pronounced than in the case of the symmetric snap-through criterion. A comparison between the RO model results and those obtained by direct numerical analysis shows good agreement between the two and indicates that the obtained criteria can be used to predict non-symmetric buckling in electrostatically actuated bistable micro beams.

Original languageEnglish
Title of host publicationASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012
Pages57-66
Number of pages10
DOIs
StatePublished - 2012
EventASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012 - Chicago, IL, United States
Duration: 12 Aug 201212 Aug 2012

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume5

Conference

ConferenceASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012
Country/TerritoryUnited States
CityChicago, IL
Period12/08/1212/08/12

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