/COM,ANSYS MEDIA REL. 2024R2 (05/10/2024) REF. VERIF. MANUAL: REL. 2024R2 /VERIFY,VM310 /TITLE,VM310, ELECTROSTATIC-STRUCTURAL ANALYSIS OF A MEMS PARALLEL-PLATE CAPACITOR /COM, /COM, REF: ANY ELECTROSTATICS TEXTBOOK /COM, PI=ACOS(-1) K=3 ! SPRING CONSTANT PER UNIT AREA, KG/(UM^2 S^2) M=1E-6 ! PLATE MASS PER UNIT AREA, KG/UM^2 L=10 ! PLATE LENGTH, UM D=1 ! CAPACITOR THICKNESS, UM PER=8.854E-6 ! FREE SPACE PERMITTIVITY, PF/UM VLP=10 ! VOLTAGE APPLIED IN A LINEAR PERTURBATION ANALYSIS, VOLT FLP=15 ! FORCE APPLIED IN A LINEAR PERTURBATION HARMONIC ANALYSIS, UN FRQ=20 ! FREQUENCY OF HARMONINC LOAD, HZ NS1=40 ! TOTAL NUMBER OF SUBSTEPS FOR NONLINEAR STATIC ANALYSIS NS2=25 ! SUBSTEP TO RESTART FROM IN LINEAR PERTURBATION ANALYSIS TOL=1E-6 ! CONVERGENCE TOLERANCE IN NONLINEAR STATIC ANALYSIS A=L**2 ! PLATE AREA, UM^2 ! TO CREATE WHITE BACKGROUND /RGB,INDEX,100,100,100, 0 /RGB,INDEX, 80, 80, 80,13 /RGB,INDEX, 60, 60, 60,14 /RGB,INDEX, 0, 0, 0,15 /PREP7 ET,1,226,1001 KEYOP,1,4,1 BLOCK,,D,,L,,L ESIZE,,1 VMESH,1 /SHOW,PNG /VIEW,1,1,1,1 EPLOT /SHOW,CLOSE EMUNIT,EPZRO,1 MP,EX,1,1E-6 MP,PRXY,1,0 MP,PERX,1,PER D,ALL,UY,0,,,,UZ NSEL,S,LOC,X,0 D,ALL,UX,0 D,ALL,VOLT,0 NSEL,S,LOC,X,D CP,NEXT,UX,ALL CP,NEXT,VOLT,ALL NLOAD=NDNEXT(0) NSEL,ALL ET,2,14 ! LINEAR SPRING WITH UX,UY,UZ DOFS ET,3,21,,,2 ! MASS WITH UX, UY, UZ DOFS *GET,NMAX,NODE,0,NUM,MAX NSEL,S,LOC,X,D *GET,NMAXS,NODE,0,COUNT,MAX R,2,K*A/NMAXS ! NODAL STIFFNESS R,3,M*A/NMAXS ! NODAL MASS _J=0 *DO,_I,1,NMAXS N1=NDNEXT(_J) _J=N1 N2=N1+NMAX N,N2,NX(N1)+1,NY(N1),NZ(N1) D,N2,UX,0 TYPE,2 REAL,2 E,N2,N1 TYPE,3 REAL,3 E,N1 *ENDDO ALLSE FINISH /COM, /COM, ****************************************** /COM, *** NONLINEAR *** /COM, *** STATIC ANALYSIS *** /COM, ****************************************** /COM, /SOLU D,NLOAD,VOLT,500 ALLSE ANTYPE,STATIC OUTRES,ALL,ALL RESCONTROL,DEFINE,ALL,ALL NLGEOM,ON NSUB,NS1 CNVTOL,U,1.,TOL ARCLEN,ON ARCTRM,U,.95*D,NLOAD,UX SOLVE FINISH /POST26 NSOL,3,NLOAD,VOLT,,VOLT NSOL,4,NLOAD,U,X,'UX VS VOLT' FILLDATA,5,,,,-D/3,0 VARNAM,5,'PULL-IN UX' PRVAR,3,4 /SHOW,PNG XVAR,3 /AXLAB,X,VOLTAGE /AXLAB,Y,DISPLACEMENT PLVAR,4,5 /SHOW,CLOSE VGET,VEC1,3 VGET,VEC2,4 *GET,NS,ACTIVE,0,SET,NSET VPI=0 UPI=0 RATIO=0 *DO,I,1,NS,1 *IF,VEC1(I),GT,VPI,THEN VPI=VEC1(I) UPI=-VEC2(I) *ENDIF U1=-VEC2(I) V1=(D-U1)*SQRT(2*K*U1/PER) RATIO=RATIO+V1/VEC1(I) *ENDDO RATIO=RATIO/NS FINISH PARSAV /COM, /COM, ****************************************** /COM, *** LINEAR PERTURBATION *** /COM, *** STATIC ANALYSIS *** /COM, ****************************************** /COM, /SOLU ANTYP,STATIC,RESTART,1,NS2,PERTURB PERTURB,STATIC SOLVE,ELFORM D,NLOAD,VOLT,VLP SOLVE FINISH PARRES /POST1 FILE,,rst SET,1,NS2 UBI=-UX(NLOAD) *GET,VBI,NODE,NLOAD,VOLT *GET,QBI,NODE,NLOAD,RF,CHRG C=-QBI/VBI FILE,,rstp SET,LAST ULP=-UX(NLOAD) FINISH PARSAV /COM, /COM, ****************************************** /COM, *** LINEAR PERTURBATION *** /COM, *** MODAL ANALYSIS *** /COM, *** (RESONANCE) *** /COM, ****************************************** /COM, /SOLU ANTYP,STATIC,RESTART,1,NS2,PERTURB PERTURB,MODAL SOLVE,ELFORM D,NLOAD,VOLT,0 MODOPT,LANB,1 MXPAND SOLVE FINISH PARRES /POST1 SET,LAST *GET,FRQ1,MODE,1,FREQ FINISH PARSAV /COM, /COM, ****************************************** /COM, *** LINEAR PERTURBATION *** /COM, *** MODAL ANALYSIS *** /COM, *** (ANTI-RESONANCE) *** /COM, ****************************************** /COM, /SOLU ANTYP,STATIC,RESTART,1,NS2,PERTURB PERTURB,MODAL SOLVE,ELFORM DDELE,NLOAD,VOLT MODOPT,LANB,1 MXPAND SOLVE FINISH PARRES /POST1 SET,LAST *GET,FRQ2,MODE,1,FREQ FINISH PARSAV /COM, /COM, ****************************************** /COM, *** LINEAR PERTURBATION *** /COM, *** HARMONIC ANALYSIS *** /COM, *** (ACTUATOR MODE) *** /COM, ****************************************** /COM, /SOLU ANTYP,STATIC,RESTART,1,NS2,PERTURB PERTURB,HARM SOLVE,ELFORM D,NLOAD,VOLT,VLP NSUB,1 HARFRQ,FRQ SOLVE FINISH PARRES /POST1 FILE,,rstp SET,LAST UHR=-UX(NLOAD) FINISH PARSAV /COM, /COM, ****************************************** /COM, *** LINEAR PERTURBATION *** /COM, *** HARMONIC ANALYSIS *** /COM, *** (SENSOR MODE) *** /COM, ****************************************** /COM, /SOLU ANTYP,STATIC,RESTART,1,NS2,PERTURB PERTURB,HARM SOLVE,ELFORM DDELE,NLOAD,VOLT F,NLOAD,FX,-FLP NSUB,1 HARFRQ,FRQ SOLVE FINISH PARRES /POST1 FILE,,rstp SET,LAST VHR=VOLT(NLOAD) FINISH ! ANALYTICAL SOLUTION VPI_TAR=SQRT(8*K*D**3/(27*PER)) UPI_TAR=D/3 DBI=D-UBI C_TAR=PER*A/DBI KR=K-PER*VBI**2/DBI**3 ! ELECTROSTATICALLY SOFTENED STIFFNESS F=PER*VBI**2/(2*DBI**2) ULP_TAR=2*F/KR*VLP/VBI FRQ1_TAR=1/(2*PI)*SQRT(KR/M) FRQ2_TAR=1/(2*PI)*SQRT(K/M) W=2*PI*FRQ UHR_TAR=2*F/(-W**2*M+KR)*VLP/VBI VHR_TAR=-(FLP/A)/(-W**2*M+K)*VBI/DBI /OUT,vm310,vrt /COM, /COM, ---------------------------- VM310 RESULTS COMPARISON ---------------------- /COM, /COM, | TARGET | MECHANICAL APDL | RATIO /COM, | | | /COM, NONLINEAR STATIC ANALYSIS: /COM, | | | *VWRITE,VPI_TAR,VPI,VPI/VPI_TAR (2X,'PULL-IN VOLTAGE',6X,'|',2X,F8.3,4X,'|',4X,F8.3,7X,'|',2X,F9.6) *VWRITE,UPI_TAR,UPI,UPI/UPI_TAR (2X,'PULL-IN DISPLACEMENT',1X,'|',2X,F9.6,3X,'|',4X,F9.6,6X,'|',2X,F9.6) *VWRITE,RATIO (2X,'VOLT-DISP CURVE',6X,'|',14X,'|',19X,'|',2X,F9.6) *VWRITE,C_TAR,C,C/C_TAR (2X,'CAPACITANCE AT V_DC',2X,'|',1X,E12.6,1X,'|',3X,E12.6,4X,'|',2X,F9.6) /COM, | | | /COM, LINEAR PERTURBATION STATIC ANALYSIS: /COM, | | | *VWRITE,ULP_TAR,ULP,ULP/ULP_TAR (2X,'DISPLACEMENT',9X,'|',1X,E12.6,1X,'|',3X,E12.6,4X,'|',2X,F9.6) /COM, | | | /COM, LINEAR PERTURBATION MODAL ANALYSIS (RESONANCE): /COM, | | | *VWRITE,FRQ1_TAR,FRQ1,FRQ1/FRQ1_TAR (2X,'FREQUENCY',12X,'|',2X,F9.3,3X,'|',4X,F9.3,6X,'|',2X,F9.6) /COM, | | | /COM, LINEAR PERTURBATION MODAL ANALYSIS (ANTI-RESONANCE): /COM, | | | *VWRITE,FRQ2_TAR,FRQ2,FRQ2/FRQ2_TAR (2X,'FREQUENCY',12X,'|',2X,F9.3,3X,'|',4X,F9.3,6X,'|',2X,F9.6) /COM, | | | /COM, LINEAR PERTURBATION HARMONIC ANALYSIS (ACTUATOR MODE): /COM, | | | *VWRITE,UHR_TAR,UHR,UHR/UHR_TAR (2X,'DISPLACEMENT',9X,'|',1X,E12.6,1X,'|',3X,E12.6,4X,'|',2X,F9.6) /COM, | | | /COM, LINEAR PERTURBATION HARMONIC ANALYSIS (SENSOR MODE): /COM, | | | *VWRITE,VHR_TAR,VHR,VHR/VHR_TAR (2X,'VOLTAGE',14X,'|',2X,F9.5,3X,'|',3X,F9.5,7X,'|',2X,F9.6) /COM, /OUT *LIST,vm310,vrt