Pull-in voltage for square membrane

[izyk]

Hi
I've got a problem with electrostatic simulation. I've simulated square memrane 300x300x5um, under the electrostatic force using TRANS126 element. (see the script below) I took all voltage values from 0V to pull-in.
I've also calculated the pull-in voltage using an equation:

Electrostatic pressure = permittivity * voltage^2 / ( 2 * ( gap - deflection)^2 )

In many articles this equation is used and was also compared with ANSYS, the difference was very small.

Unfortunately I have a ~20-30% diffrence. Can anyone check my script?

---------------------------------------

FINISH
/CLEAR

/CWD,'C:\temp\ansys'


!* membrane
Lm=300
Wm=300
Tm=5 !* Epaisseur de la membrane 3e-6 / 1e-6

!* membrane_division
b=30

!* electrode_distance
h=-0.3
dif=20

!* voltage
v=10

/PREP7

ET,1,SHELL63
R,1,Tm

ET,2,TRANS126

MP,EX,1,130e+9*1e-6
! MP,DENS,1,2330*1e-18
MP,PRXY,1,0.278

WPOFFS,0,0,dif
RECTNG,0,Lm,0,Wm
WPOFFS,0,0,-dif

LESIZE,ALL,,,b

TYPE,1
MSHAPE,0,2D
MSHKEY,1
AMESH,ALL

!* transducer

NSEL,S,LOC,Z,dif


CM,tr,NODE
ALLSEL,ALL

EMTGEN,'tr','EMTELM','EMTPNO','UZ',h,0,0.1,0.8854E-05

NSEL,S,LOC,Z,dif+h
D,ALL,,0,,,,UZ
D,ALL,VOLT,v

CMSEL,S,TR
D,ALL,VOLT,0


!* applying loads and BC

NSEL,S,LOC,X,0
NSEL,A,LOC,X,Lm
NSEL,A,LOC,Y,0
NSEL,A,LOC,Y,Wm

D,ALL,UX,0
D,ALL,UY,0
D,ALL,UZ,0
D,ALL,ROTX,0
D,ALL,ROTY,0
D,ALL,ROTZ,0

ALLSEL,ALL

FINISH

/SOLU
ANTYPE,STATIC

!* Pour prendre en compte le stress stiffening et les grandes déformations
! NEQIT,100
! CNVTOL, U, 1, 1e-3
! NLGEOM,ON
! SSTIF,ON

! SOLVE
FINISH

/POST1
PLNSOL,U,Z

!* Récupération de la flèche qui doit être <= au GAP h
NSEL,S,LOC,X,Lm/2
NSEL,R,LOC,Y,Wm/2
NSEL,R,LOC,Z,dif
*GET,CENTRE_INFERIEUR,NODE,0,NUM,MIN
FLECHE=UZ(CENTRE_INFERIEUR)
NSEL,ALL

 

[MemsGeek]

The electrostatic pressure equation is correct.

I admit I have not analyzed your mac file in detail, but the following questions come to mind:

1) Does the transducer element support higher order terms O(x^2) and higher, if not it may only be a linearized approximation. If this were the case I would expect ansys to predict a higher pull in voltage than those reported in the papers.

2) Are the boundary conditions the same as in the papers? I see that you restrained the slopes at the edges.