{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PS5-11-solution

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

This preview shows pages 1–3. Sign up to view the full content.

Homework Solution #5 MEMS – MECE E4212 Problem #1 A kg V PI ε 27 8 3 0 = (3) 0 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 0 3 2 g g PI = m g µ 10 0 = , 12 854 . 8 0 = = E ε ε (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 0 = = g g PI m g PI µ 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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The spring force is given by: ( ) 0 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 0 2 d AV F r E ε ε = 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 EF, 40V EF, 60V EF, 80V EF, 100V EF, 115.7V, Pull-in Voltage EF, 140 V Problem #2 (a) Gage factor: ( ) l l d R R L L R R GF ε ρ ρ ν ε + + = = = 2 1 / / where A L R ρ = , dA A L d A L dL A dR 2 ρ ρ ρ + = , A dA
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online