Usefulformulas for springsProperty of cross sectionshape

4 k 3E I second moment of areaalsocalled moment of inertia

pop ke KELILax Stifter

Beam cross section

7 a I bias k 3 by Eabpa3 Lecture I

DT I 24

what about other shapesRoark's Fornular for stress and strain

Useful formula Table in bCourses

see examples

Torque Torsion beamton

rotation angle at free end

T JELLofG E

2CHUIE Poisson's ratio

J Jf r DA e Polarmoment of inertia

Table 10 1 of Roark's use symbol K J

I F Izard

Iab J ab3 336 11 Ita for azb

Revisit Gap Closing ActuatorParallel Plate actuator

Electrostatic force

I 6h Fe 3 ztcv51 543 fztz g.AE

I 4TH springrestoring tone

Fs k zF n i

Fns stabilityAnalysisstable For simplicity let f go 8

Tinstantaneous gap spacingI

T go3 Free Fs Fe

DS.fikt kcgo g E A

g g ogtfo8 OFnee should haveopposite

GI sign to og

2Fgegt_co

Free 2FretTg ogfog EOVIA t zgj.grC k t An og

O

EoRAGI k

rateFor point D 3 Ts small f go 3 is large stable

For 3 is close to go f go 3 smallunstable.se

UiMe WeT5moWwmis too large What happens

Fe Fspring for all 3 Plate pulled all thewaydow

pull in conditionFind pull in voltage

FFree O

SFngety o g go 3

3 EoV2A oketo 8 TgsFree 1

IT 3 f kteargas solve.LV g

k toVg EogVf Igcgo g E

80g I I o 8 32go go 8mA

Maximum plate displacement 3 max 3 goPull In voltage VPI

ktqo g E o Vps

Vpz

Fg

rain

I l

i f Fs for s Vpsr

to go 3

Transfer Curvesis loop

go q

are

Full solution of Fs Fe 2

VEGF3 a

in Ei nInstabletestable

µ

Vps Voltage

Pull out voltageFor pullout FszFe at displacement 3 80 8D

kcgo gd A_got

vpoIdeal value Vpo isaffected

EoA by adhesive force

3

Yo I F gi g9 aT