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ANSYS Mechanical-APDL HarmonicAnalysis Example and Comparisonto ANSYS Mechanical resultsDave JohnsonPenn State Erie9/11/20171
Disk modal and harmonic analyses Steel disk - 75 mm radius and 3mm radiuscenter hole, and 0.34 mm thickness 1421 SHELL 181 elementsModulus 200,000 MpaPoisson’s Ratio 0.3Density 7.85E-9 tonnes/mm3TOTAL MASS: 0.471E-04 (tonne) Support: simply-supported,(no translation: UX UY UZ 0)at the edge of the hole9/11/20172
Hand calc for verification andvalidation of modal analysis resultsReference: Mark’s Standard Handbook for MechanicalEngineers, 8th ed., p. 5-75 For a flat circular plate – constrained at the center, the“umbrella” mode (zero nodal diameters) is predicted by:Where: E elastic modulus (N/mm2) r plate radius (mm) g gravity acceleration (mm/s2) ν Poisson’s ratio t plate thickness (mm)9/11/20173
Hand calc for verification andvalidation 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 79.03494598450 3.2% difference5 79.04406402341Hand calc vs. FEA9/11/20174
Modal Analysis Results*** FREQUENCIES FROM BLOCK LANCZOS ITERATION ***9/11/2017MODEFREQUENCY (HERTZ)FREQUENCY RANGE REQUESTED 4497.05947940590.00000500.000In the frequencyrange of interest, weobserve 14 modes:31 fn 497 Hz5
Harmonic Analysis Setup Method: Mode Superposition Load (1 N) on keypoint in z-direction at edge (at3 o’clock position) use all (14) modes from 0 to 500 Hz,solve 100 substeps 0.03 damping ratio(minimal, structural value) perform an expansionpass after the harmonicanalysis solution9/11/20176
Harmonic Analysis ResultsZ-deformation atnode where theharmonic loadis applied– Linear vs. Log ?Note: the Mode Superposition Solutionused 14 modes (in range 0 – 500 Hz), andmax. amplitude (27.59 mm) occurred @ 30 Hz9/11/20177
Harmonic Analysis Results - 2Use modes from twice the range of interest,i.e., 0 – 1000 Hz (26 modes were found)Note: the Mode Superposition Solutionused 26 modes (in range 0 – 500 Hz), andmax. amplitude (27.62 mm) occured @ 30 Hz9/11/20178
Harmonic Analysis Results - 3Used the FULL Method, not Mode SuperpositionNote: the FULL Method Solution, maximumamplitude (33.07 mm) occurred @ 30 Hz9/11/20179
ANSYS Mechanical ComparisonModal linked to Harmonic (B-C) vs. Harmonic (D & E)Structural Steel propertiesfrom WB librarySame geometry, constraint,and loadingSimilar mesh: 1433/1422SHELL181 elementsTOTAL MASS 0.47072E-04 (tonne)[same as ANSYS MechanicalAPDL model]9/11/201710
ANSYS Mechanical ComparisonModal linked to Harmonic (B-C) vs. Harmonic (D & E)(Split to make vertex for loading)9/11/201711
ANSYS Mechanical ComparisonModal linked to Harmonic (Schematic Objects B-C)Compared to ANSYS Mechanical APDL Results:*** FREQUENCIES FROM BLOCK LANCZOS ITERATION ***MODEFREQUENCY (HERTZ)FREQUENCY RANGE REQUESTED 8088338095497.05947940590.00500.012
ANSYS Mechanical ComparisonModal linked to Harmonic (Schematic Objects B-C)Note: (default) uses log scale for Amplitude,Solution used 14 modes (in range 0 – 500 Hz),and max. amplitude (18 mm) occurs @ 30 Hz9/11/201713
ANSYS Mechanical ComparisonHarmonic without Modal (Schematic Object D)Note: (default) uses log scale for Amplitude,Solution used 26 modes (in range 0 – 1000 Hz),and max. amplitude (26 mm) occurs @ 35 Hz9/11/201714
ANSYS Mechanical ComparisonHarmonic without Modal (Schematic Object E)using FULL MethodNOTE: different damping input under AnalysisSettings (α 11 and β 2e-5) see next slide,and max. amplitude (18.2 mm) occurs @ 30 Hz9/11/201715
Full Harmonic, Damping InputFrom ANSYS Help Mechanical APDL Structural Analysis Guide 1.2.1 Alpha & Beta Damping (Rayleigh Damping)For this example:9/11/201716
Comparing Results9/11/201717
Comparing Results9/11/201718
Comparing ResultsMaximum Response occurs at 30 or 35 Hz andthe Next Highest Response occurs at 80 Hz9/11/201719
Conclusions/Observations Mechanical (WB) default method for HarmonicAnalysis is Mode Superposition. The ANSYSdefault method is Full Mechanical (WB), Harmonic Analysis withoutlinked Modal Analysis, uses 2x the user-requestedfrequency range, i.e., requested 0 – 500 Hz, andWB used modes from 0 – 1000 Hz Mechanical (WB), default Frequency Responseplot format uses a log scale for the y-axis (for theAmplitude)9/11/201720
Conclusions/ObservationsWhy ? Does the Full Methodshow higher max.values, in general ? Is Mechanical MSUP-26max. value at 35 Hz ? Should we care aboutvariations at higherfrequencies where theamplitude is much less ?9/11/201721
ll,,secdata, 0.34,1,0.0,3secoffset,MIDseccontrol,,,, , , ,! use 3D 4-node thin shell element! modulus in MPa! Poisson's ratio! density in tonnes/mm 3! shell thickness 0.34 mmPCIRC,75,3,0,360,! 75 mm outer radius, 3 mm radius center FINISH! Smart size for meshing! Global element size!! allow "free" meshing/SOLUANTYPE,2! create the mesh! Modal analysisMODOPT,LANB,50! use (default) Block Lanczos methodEQSLV,SPARMXPAND,50, , ,0! extract & expand up to 50 modesLUMPM,0PSTRES,0!*MODOPT,LANB,50,0,500, ,OFFbv ! frequency range 0 - 500 Hzlsel,s,,,5,8,1DL,all, ,UX,DL,all, ,UY,DL,all, ,UZ,lsel,allsolvesave,disk modal,dbfinish/POST1set,listfinish! constraints on edge of hole
/SOLUANTYPE,3!*HROPT,MSUP, , 0,BETAD,0,DMPRAT,0.03,DMPSTR,0,MDAMP,1, , , , , , ,!*solvefinishsave,disk ALL,!*SOLVE! Harmonic Analysis! Mode Superposition Method! use (all) 14 modes from modal analysis! Harmonic load amplitude! Frequency range! substep thru freq range! step change boundary conditions! 3% damping ratio! Harmonic Analysis Expansion Pass! Frequency range/POST26! Time History *LINES,200PRCPLX,1! print Amplitude/Phase vs. Real/Imaginary results/AXLAB,Y,UZ Deformation (mm)/title, disk harmonic analysis - w/linear y-axis (default)plvar,2prvar,2/GROPT,LOGY,ON/title, disk harmonic analysis - w/log y-axis to match WBplvar,2
ANSYS Mechanical-APDL Harmonic Analysis Example and Comparison to ANSYS Mechanical results Dave Johnson Penn 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/mm 3 TOTAL MASS:
