PS5-11-solution

PS5-11-solution - Homework Solution #5 MEMS MECE E4212...

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Unformatted text preview: Homework Solution #5 MEMS MECE E4212 Problem #1 A kg V PI 27 8 3 = (3) g : the gap in the absence of any voltage or spring constant k : the spring constant A: the surface area 3 3 3 4 3 L Ebh L EI k = = ( ) ( ) ( ) ( ) 3 3 6 1000 4 6 10 6 50 9 160 = E E E E k m N k / 2 = Pull in occurs at 3 2 g g PI = m g 10 = , 12 854 . 8 = = E (a) ) 6 50 )( 6 100 )( 12 854 . 8 ( 27 ) 6 10 )( / 2 ( 8 3 = E E E m E m N V PI V V PI 7 . 115 = (b) ( ) 10 3 2 3 2 = = g g PI m g PI 67 . 6 = (c) Limitation: not parallel plates for large deflections, and also not a point load, so should be valid for small deflections only. (d) Graduate Students The spring force is given by: ( ) d d k F S = , where 3 3 L EI k = and 3 12 1 bt I = . The electrostatic force is given by: 2 2 2 d AV F r E = Force vs. Displacement 0.00 6.00 12.00 18.00 24.00 30.00 0.00 2.00 4.00 6.00 8.00 10.00 Tip Displacement (microns) Force (micro N) Spring Force Electrostatic Force (EF), 20V...
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This note was uploaded on 02/05/2012 for the course APMAE 4200 taught by Professor R during the Fall '11 term at Columbia.

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PS5-11-solution - Homework Solution #5 MEMS MECE E4212...

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