7 i byee147/fa19/coeee147.wp... · 2019. 10. 2. · roark's fornular for stress and strain...
TRANSCRIPT
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