ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison

to ANSYS Mechanical results

Dave JohnsonPenn State Erie

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Disk modal and harmonic analyses Steel disk - 75 mm radius and 3mm radius

center hole, and 0.34 mm thickness

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1421 SHELL 181 elements Modulus = 200,000 Mpa Poissons 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: Marks 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:

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Where: E = elastic modulus (N/mm2) r = plate radius (mm) g = gravity acceleration (mm/s2) = Poissons 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

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~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 oclock 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

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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)

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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)

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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

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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)

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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)

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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)

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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

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NOTE: different damping input under Analysis Settings ( = 11 and = 2e-5) see next slide, and max. amplitude (18.2 mm) occurs @ 30 Hz

Full Harmonic, Damping Input

For this example:

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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

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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)

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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 ?

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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

ANSYS M-APDL Harmonic Analysis Example and Comparison to WBANSYS Mechanical-APDL Harmonic Analysis Example and Comparison to ANSYS Mechanical resultsDisk modal and harmonic analysesHand calc for verification and validation of modal analysis resultsHand calc for verification and validation of modal analysis resultsModal Analysis ResultsHarmonic Analysis SetupHarmonic Analysis ResultsHarmonic Analysis Results - 2Harmonic Analysis Results - 3ANSYS Mechanical ComparisonANSYS Mechanical ComparisonANSYS Mechanical ComparisonANSYS Mechanical ComparisonANSYS Mechanical ComparisonANSYS Mechanical ComparisonFull Harmonic, Damping InputComparing ResultsComparing ResultsComparing ResultsMaximum Response occurs at 30 or 35 Hz and the Next Highest Response occurs at 80 HzConclusions/ObservationsConclusions/Observations

Disk_Input