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ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison
to ANSYS Mechanical results
Dave JohnsonPenn State Erie
9/11/2017 1
Disk modal and harmonic analyses• Steel disk - 75 mm radius and 3mm radius
center hole, and 0.34 mm thickness
9/11/2017
• 1421 SHELL 181 elements• Modulus = 200,000 Mpa• Poisson’s Ratio = 0.3• Density = 7.85E-9 tonnes/mm3
TOTAL MASS: 0.471E-04 (tonne)
• Support: simply-supported, (no translation: UX = UY = UZ = 0) at the edge of the hole
2
Hand calc for verification and validation of modal analysis results
Reference: Mark’s Standard Handbook for Mechanical Engineers, 8th ed., p. 5-75
• For a flat circular plate – constrained at the center, the “umbrella” mode (zero nodal diameters) is predicted by:
9/11/2017
Where:• E = elastic modulus (N/mm2)• r = plate radius (mm)• g = gravity acceleration (mm/s2)• ν = Poisson’s ratio• t = plate thickness (mm)
3
Hand calc for verification and validation of modal analysis results
*** FREQUENCIES FROM BLOCK LANCZOS ITERATION ***
MODE FREQUENCY (HERTZ)FREQUENCY RANGE REQUESTED= 0.00 500.001 31.028364525952 31.156689302753 53.417788778604 79.034945984505 79.04406402341
9/11/2017
~3.2% differenceHand calc vs. FEA
4
Modal Analysis Results*** FREQUENCIES FROM BLOCK LANCZOS ITERATION ***
MODE FREQUENCY (HERTZ)
FREQUENCY RANGE REQUESTED= 0.00000 500.000
1 31.02836452595
2 31.15668930275
3 53.41778877860
4 79.03494598450
5 79.04406402341
6 183.3880216411
7 183.4157944991
8 298.3216528279
9 322.7271830757
10 322.8378280898
11 336.4477549042
12 336.9226420643
13 496.8088338095
14 497.05947940599/11/2017
In the frequency range of interest, we observe 14 modes: 31 < fn < 497 Hz
5
Harmonic Analysis Setup• Method: Mode Superposition• Load (1 N) on keypoint in z-direction at edge (at
3 o’clock position)• use all (14) modes from 0 to 500 Hz,
solve 100 substeps• 0.03 damping ratio
(minimal, structural value)• perform an expansion
pass after the harmonic analysis solution
9/11/2017 6
Harmonic Analysis ResultsZ-deformation at
node where the harmonic load is applied– Linear vs. Log ?
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Note: the Mode Superposition Solutionused 14 modes (in range 0 – 500 Hz), and
max. amplitude (27.59 mm) occurred @ 30 Hz
Harmonic Analysis Results - 2Use modes from twice the range of interest,
i.e., 0 – 1000 Hz (26 modes were found)
9/11/2017 8
Note: the Mode Superposition Solutionused 26 modes (in range 0 – 500 Hz), and
max. amplitude (27.62 mm) occured @ 30 Hz
Harmonic Analysis Results - 3Used the FULL Method, not Mode Superposition
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Note: the FULL Method Solution, maximumamplitude (33.07 mm) occurred @ 30 Hz
ANSYS Mechanical ComparisonModal linked to Harmonic (B-C) vs. Harmonic (D & E)
9/11/2017
Structural Steel properties from WB library
Same geometry, constraint, and loading
Similar mesh: 1433/1422 SHELL181 elements
TOTAL MASS = 0.47072E-04 (tonne)
[same as ANSYS Mechanical APDL model]
10
ANSYS Mechanical Comparison
9/11/2017
Modal linked to Harmonic (B-C) vs. Harmonic (D & E)
11
(Split to make vertex for loading)
ANSYS Mechanical ComparisonModal linked to Harmonic (Schematic Objects B-C)
9/11/2017 12
Compared to ANSYS Mechanical APDL Results:*** FREQUENCIES FROM BLOCK LANCZOS ITERATION ***
MODE FREQUENCY (HERTZ)
FREQUENCY RANGE REQUESTED= 0.00 500.0
1 31.02836452595
2 31.15668930275
3 53.41778877860
4 79.03494598450
5 79.04406402341
6 183.3880216411
7 183.4157944991
8 298.3216528279
9 322.7271830757
10 322.8378280898
11 336.4477549042
12 336.9226420643
13 496.8088338095
14 497.0594794059
ANSYS Mechanical ComparisonModal linked to Harmonic (Schematic Objects B-C)
9/11/2017 13
Note: (default) uses log scale for Amplitude,Solution used 14 modes (in range 0 – 500 Hz),and max. amplitude (18 mm) occurs @ 30 Hz
ANSYS Mechanical ComparisonHarmonic without Modal (Schematic Object D)
9/11/2017 14
Note: (default) uses log scale for Amplitude,Solution used 26 modes (in range 0 – 1000 Hz),and max. amplitude (26 mm) occurs @ 35 Hz
ANSYS Mechanical ComparisonHarmonic without Modal (Schematic Object E)
using FULL Method
9/11/2017 15
NOTE: different damping input under Analysis Settings (α = 11 and β = 2e-5) see next slide, and max. amplitude (18.2 mm) occurs @ 30 Hz
Full Harmonic, Damping Input
For this example:
9/11/2017 16
From ANSYS Help > Mechanical APDL >Structural Analysis Guide > 1.2.1 Alpha & Beta Damping (Rayleigh Damping)
Comparing Results
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Comparing Results
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Comparing ResultsMaximum Response occurs at 30 or 35 Hz and
the Next Highest Response occurs at 80 Hz
9/11/2017 19
Conclusions/Observations• Mechanical (WB) default method for Harmonic
Analysis is Mode Superposition. The ANSYS default method is Full
• Mechanical (WB), Harmonic Analysis without linked Modal Analysis, uses 2x the user-requested frequency range, i.e., requested 0 – 500 Hz, and WB used modes from 0 – 1000 Hz
• Mechanical (WB), default Frequency Response plot format uses a log scale for the y-axis (for the Amplitude)
9/11/2017 20
Conclusions/ObservationsWhy ?• Does the Full Method
show higher max. values, in general ?
• Is Mechanical MSUP-26 max. value at 35 Hz ?
• Should we care about variations at higher frequencies where the amplitude is much less ?
9/11/2017 21
finish
/clear
/PREP7
ET,1,SHELL181 ! use 3D 4-node thin shell element
!*
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,EX,1,,200000 ! modulus in MPa
MPDATA,PRXY,1,,0.3 ! Poisson's ratio
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,DENS,1,,7.85e-9 ! density in tonnes/mm^3
sect,1,shell,,
secdata, 0.34,1,0.0,3 ! shell thickness 0.34 mm
secoffset,MID
seccontrol,,,, , , ,
PCIRC,75,3,0,360, ! 75 mm outer radius, 3 mm radius center hole
SMRT,6 ! Smart size for meshing
ESIZE,5,0, ! Global element size
MSHAPE,0,2D !
MSHKEY,0 ! allow "free" meshing
!*
AMESH,all ! create the mesh
FINISH
/SOLU
ANTYPE,2 ! Modal analysis
MODOPT,LANB,50 ! use (default) Block Lanczos method
EQSLV,SPAR
MXPAND,50, , ,0 ! extract & expand up to 50 modes
LUMPM,0
PSTRES,0
!*
MODOPT,LANB,50,0,500, ,OFFbv ! frequency range 0 - 500 Hz
lsel,s,,,5,8,1
DL,all, ,UX, ! constraints on edge of hole
DL,all, ,UY,
DL,all, ,UZ,
lsel,all
solve
save,disk_modal,db
finish
/POST1
set,list
finish
/SOLU
ANTYPE,3 ! Harmonic Analysis
!*
HROPT,MSUP, , ,0 ! Mode Superposition Method
HROUT,ON
LUMPM,0
!*
HROPT,MSUP,14,1,0 ! use (all) 14 modes from modal analysis
HROUT,ON,OFF,0
!*
FK,1,FZ,1, ! Harmonic load amplitude
HARFRQ,0,500, ! Frequency range
NSUBST,100, ! substep thru freq range
KBC,1 ! step change boundary conditions
!*
ALPHAD,0,
BETAD,0,
DMPRAT,0.03, ! 3% damping ratio
DMPSTR,0,
MDAMP,1, , , , , , ,
!*
solve
finish
save,disk_harmonic,db
/SOLU
!*
EXPASS,1 ! Harmonic Analysis Expansion Pass
NUMEXP,ALL,0,500,1 ! Frequency range
HREXP,ALL,
!*
SOLVE
/POST26 ! Time History Postprocessor
*GET,nn,KP,1,ATTR,NODE
NSOL,2,nn,U,Z,
!*
LINES,200
PRCPLX,1 ! print Amplitude/Phase vs. Real/Imaginary results
/AXLAB,Y,UZ Deformation (mm)
/title, disk harmonic analysis - w/linear y-axis (default)
plvar,2
prvar,2
/GROPT,LOGY,ON
/title, disk harmonic analysis - w/log y-axis to match WB
plvar,2
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