- /TITLE,VM237, PIEZOELECTRIC-CIRCUIT ANALYSIS
- JPGPRF,500,100,1 ! MACRO TO SET PREFS FOR JPEG PLOTS
- /SHOW,JPEG
- /COM, ---------------------------------------------------------------
- /COM, FINITE ELEMENT MODEL OF A PIEZOELECTRIC CIRCULAR PLATE
- /COM, ---------------------------------------------------------------
- A=1E-3 ! RADIUS, M
- T=0.1E-3 ! THICKNESS, M
- /COM,
- /COM, MATERIAL PROPERTIES OF LEAD ZIRCONATE TITANATE (PZT-5A)
- /COM,
- /COM, -- MATERIAL MATRICES (POLAR AXIS ALONG Y-AXIS): IEEE INPUT
- /COM,
- /COM, [s11 s13 s12 0 0 0 ] [ 0 d31 0 ] [ep11 0 0 ]
- /COM, [s13 s33 s13 0 0 0 ] [ 0 d33 0 ] [ 0 ep33 0 ]
- /COM, [s12 s13 s11 0 0 0 ] [ 0 d31 0 ] [ 0 0 ep11]
- /COM, [ 0 0 0 s44 0 0 ] [ 0 0 d15]
- /COM, [ 0 0 0 0 s66 0 ] [ 0 0 0 ]
- /COM, [ 0 0 0 0 0 s44] [d15 0 0 ]
- /COM,
- /COM, - COMPLIANCE COEFFICIENTS, M2/N
- S11=16.4E-12
- S12=-5.74E-12
- S13=-7.22E-12
- S33=18.8E-12
- S44=47.5E-12
- S66=44.3E-12
- /COM, - PIEZOELECTRIC STRAIN COEFFICIENTS, C/N
- D15=5.84E-10
- D31=-1.71E-10
- D33=3.74E-10
- /COM, - RELATIVE PERMITTIVITY AT CONSTANT STRESS
- EP11=1730
- EP33=1700
- /COM, - DENSITY, KG/M3
- RHO=7750
- /NOPR
- /PREP7
- /COM,
- /COM, -- MATERIAL MATRICES (POLAR AXIS ALONG Y-AXIS): ANSYS INPUT
- /COM,
- /COM, [s11 s13 s12 0 0 0 ] [ 0 d31 0 ] [ep11 0 0 ]
- /COM, [s13 s33 s13 0 0 0 ] [ 0 d33 0 ] [ 0 ep33 0 ]
- /COM, [s12 s13 s11 0 0 0 ] [ 0 d31 0 ] [ 0 0 ep11]
- /COM, [ 0 0 0 s44 0 0 ] [d15 0 0 ]
- /COM, [ 0 0 0 0 s44 0 ] [ 0 0 d15]
- /COM, [ 0 0 0 0 0 s66] [ 0 0 0 ]
- TB,ANEL,1,,,1 ! ANISOTROPIC ELASTIC COMPLIANCE MATRIX
- TBDA,1,S11,S13,S12
- TBDA,7,S33,S13
- TBDA,12,S11
- TBDA,16,S44
- TB,PIEZ,1,,,1 ! PIEZOELECTRIC STRAIN MATRIX
- TBDA,2,D31
- TBDA,5,D33
- TBDA,8,D31
- TBDA,10,D15
- TB,DPER,1,,,1 ! DIELECTRIC PERMITTIVITY AT CONSTANT STRESS
- TBDA,1,EP11,EP33
- TBLIS,ALL ! LIST INPUT AND CONVERTED MATRICES
- MP,DENS,1,RHO ! DENSITY
- ET,1,PLANE223,1001,,1 ! PIEZOELECTRIC AXISYMMETRIC ELEMENT TYPE
- RECT,,A,,T
- ESIZE,T ! MESH SOLID MODEL
- NUMSTR,NODE,10
- AMESH,1
- ! APPLY STRUCTURAL BC, SIMPLY SUPPORTED PLATE
- NSEL,S,LOC,X
- D,ALL,UX,0
- NSEL,S,LOC,X,A
- NSEL,R,LOC,Y,0
- D,ALL,UY,0
- NSEL,ALL
- ! APPLY ELECTRIC BC
- NSEL,S,LOC,Y,0
- CP,1,VOLT,ALL ! COUPLE BOTTOM ELECTRODE
- *GET,NBOT,NODE,0,NUM,MIN ! GET MASTER NODE ON BOTTOM ELECTRODE
- NSEL,S,LOC,Y,T
- CP,2,VOLT,ALL ! COUPLE TOP ELECTRODE
- *GET,NTOP,NODE,0,NUM,MIN ! GET MASTER NODE ON TOP ELECTRODE
- NSEL,ALL
- D,NBOT,VOLT,0 ! GROUND BOTTOM ELECTRODE
- D,NTOP,VOLT,1 ! APPLY 1V LOAD ON TOP ELECTRODE
- FINI
- /SOLU
- ANTYPE,STATIC ! STATIC ANALYSIS
- SOLVE
- FINI
- /POST1
- *GET,QT,NODE,NTOP,RF,CHRG ! GET TOTAL CHARGE ON TOP ELECTRODE
- CP=ABS(QT) ! CAPACITANCE CP=Q/V, WHERE V=1V
- EPZ0=8.854E-12 ! FREE SPACE PERMITTIVITY
- PI=3.1415 ! PI CONSTANT
- C=EP33*EPZ0*PI*A**2/T ! ANALYTICAL CAPACITANCE
- /COM, 2-D CAPACITANCE (ANALYTICAL) =%C%, F
- /COM, 2-D CAPACITANCE (ANSYS) = %CP%, F
- FINI
- /COM, ---------------------------------------------------------------
- /COM, FINITE ELEMENT MODEL OF RLC-CIRCUIT
- /COM, ---------------------------------------------------------------
- /PREP7
- DDELE,NTOP,VOLT ! DELETE VOLTAGE LOAD ON TOP ELECTRODE
- ET,2,CIRCU94,0 ! DEFINE A RESISTOR
- R=3000 ! RESISTANCE, OHM
- R,1,R
- N,1
- TYPE,2
- REAL,1
- E,1,NTOP
- ET,3,CIRCU94,1 ! DEFINE AN INDUCTOR
- L=15 ! INDUCTANCE, H
- R,2,L
- N,2
- TYPE,3
- REAL,2
- E,2,1
- ET,4,CIRCU94,4 ! DEFINE A VOLTAGE SOURCE
- V=1 ! VOLTAGE LOAD, V
- R,3,V
- N,3
- TYPE,4
- REAL,3
- E,2,NBOT,3
- FINI
- /SOLU
- ANTYPE,TRANS ! TRANSIENT ANALYSIS
- NSUB,100 ! NUMBER OF TIME STEPS
- TIME,2E-3 ! ANALYSIS TIME, S
- TINTP,,0.25,0.5,0.5 ! INTEGRATION PARAMETERS FOR A PIEZOELECTRIC ANALYSIS
- OUTRES,ALL,ALL
- SOLVE
- FINI
- /GOPR
- /COM, ANALYTICAL SOLUTION:
- /COM, V_C = 1-EXP(-D*T)*COS(B*T)-D/B*EXP(-D*T)*SIN(B*T)
- /COM, WHERE:
- D=R/(2*L)
- B=SQRT(1/(L*C)-D**2)
- /NOPR
- /POST26
- NUMVAR,20
- NSOL,2,NTOP,VOLT,,V_C_ANSYS
- ! DERIVE EXACT SOLUTION
- *DIM,WORK1,ARRAY,100
- *DIM,WORK2,ARRAY,100
- FILLDATA,3,,,,1 ! 1
- EXP,4,1,,,,,,-D,-1 ! -EXP(-D*T)
- PROD,5,1,,,,,,B ! B*T
- VGET,WORK1(1),5
- *VFUN,WORK2(1),COS,WORK1(1)
- VPUT,WORK2(1),6 ! COS(B*T)
- *VFUN,WORK2(1),SIN,WORK1(1)
- VPUT,WORK2(1),7 ! SIN(B*T)
- ADD,8,6,7,,,,,,D/B ! COS(B*T) + D/B*SIN(B*T)
- PROD,9,4,8 ! -EXP(-D*T)*[COS(B*T) + D/B*SIN(B*T)]
- ADD,10,3,9,,V_C_EXACT ! 1-EXP(-D*T)*[COS(B*T) + D/B*SIN(B*T)]
- ! PRINT AND PLOT ANSYS AND EXACT VOLTAGE ACROSS THE PZT CAPACITOR
- PRVAR,2,10
- PLVAR,2,10
- /NOPR
- *DIM,VCE,ARRAY,5 ! EXACT SOLUTION FOR RESULTS TABLE
- *DIM,VCA,ARRAY,5 ! ANSYS SOLUTION FOR RESULTS TABLE
- *GET,VCE(1),VARI,10,RTIME,0.18E-3
- *GET,VCE(2),VARI,10,RTIME,0.40E-3
- *GET,VCE(3),VARI,10,RTIME,0.88E-3
- *GET,VCE(4),VARI,10,RTIME,0.13E-2
- *GET,VCE(5),VARI,10,RTIME,0.186E-2
- *GET,VCA(1),VARI,2,RTIME,0.18E-3
- *GET,VCA(2),VARI,2,RTIME,0.40E-3
- *GET,VCA(3),VARI,2,RTIME,0.88E-3
- *GET,VCA(4),VARI,2,RTIME,0.13E-2
- *GET,VCA(5),VARI,2,RTIME,0.186E-2
- *DIM,LABEL,CHAR,5
- *DIM,VALUE,,5,3
- LABEL(1) = '1.8E-2s','4.0E-2s','8.8E-2s','1.3E-1s','1.86E-1s'
- *VFILL,VALUE(1,1),DATA,VCE(1),VCE(2),VCE(3),VCE(4),VCE(5)
- *VFILL,VALUE(1,2),DATA,VCA(1),VCA(2),VCA(3),VCA(4),VCA(5)
- *VFILL,VALUE(1,3),DATA,ABS(VCA(1)/VCE(1)),ABS(VCA(2)/VCE(2)),ABS(VCA(3)/VCE(3)),
- ABS(VCA(4)/VCE(4)),ABS(VCA(5)/VCE(5))
- /OUT,vm237,vrt
- /COM
- /COM,------------------- VM237 RESULTS COMPARISON ---------------------
- /COM,
- /COM, | TARGET | ANSYS | RATIO
- /COM,
- /COM, VC for t @ ...
- /COM
- *VWRITE,LABEL(1),VALUE(1,1),VALUE(1,2),VALUE(1,3)
- (1X,A8,' ',F12.4,' ',F12.4,' ',1F5.3)
- /COM,----------------------------------------------------------------
- /OUT
- FINI
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