Cantilever Beam

Cantilever Beam - 1-Dimensional ModelPull-in voltage...

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Unformatted text preview: 1-Dimensional ModelPull-in voltage 213278=AkgVPIThe system will be unstable when a moving plate is displaced g/32-Dimensional ModelBernoulli-Euler beam bending theory(1)small deflection for which the radius of curvature equals the inverse of the second-derivative of deflection(2)no shear deformation from the transverse loading(3)no in-plane curvature adjustment due to transverseextension or compression of the thickness(4)the supports are ideally fixed(5)membrane effects from stress-stiffening are negligible(6)anticlastic curvature along a beams width w isgeometrically insignificantThe coupled electromechanical equationwhere the fringing-field correction ff = 0.65g/wfor cantilevers (stress-free)for beams( 29ffgVgTgIE+-=-122224~==tT3121tE=Algebra equationB : bending parameter S : stress parameterSimulation methods(1)finite-difference MATLAB scripts(2)Rayleigh-Ritz energy methods( 29ffgVgSgB+-=-121212224Table 1. Closed-form M-TEST models for ideal test structuresTable 2. Numerical constants used in Table 13-Dimensional ModelThe effects which should be considered id 3D model(1)Plate Effect(2)Support Compliance(3)Stress-Gradients Through Film ThicknessPlate effect (2D Bernoulli-Euler mechanics)3423EtqLtip=Support ComplianceBuilt-in support found in conformal deposition processes of MEMS fabricationBuilt-in residual stress(1)Increase structure compliance(2)Increaserotate in the presence ofexternal momentsStress-Gradients Through Film ThicknessNonuniform stresses in the film thickness createbuilt-in moments, which is released cantilevers cause them to curl out of plane.Because the stress-gradients is assumed to be uniform in-planeDue to linearity for small deflectionsModified coefficient for VPI2220006347.5096.1++CCCRgLRgLf2D VersionModel Navigator2D Multiphysics -MEMS Module>Structural Mechanics>Plane Strain COMSOL Multiphysics>Deformed Mesh>Moving Mesh (ALE) Frame (ale) MEMS Module>Electrostatics>Electrostatics Geometry...
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This note was uploaded on 09/19/2011 for the course MEM 900 taught by Professor Asdf during the Spring '11 term at Drexel.

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Cantilever Beam - 1-Dimensional ModelPull-in voltage...

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