15

()

(Dynamic Design Analysis MethodDDAM)(Power Spectral DensityPSD,)

ANSYS6.1 10

15.1

15.1 Y 13.1 15.1

15.1

A3EX2.1 E 11 N/m2PRXY0.3DENS7.8 E 3 Kg/m3

2E-3 m 1.6E-5 m2 21.333E-12 m4 4E-3 m

4E-3 m

15.1 (Hz) 0.5 1.0 2.4 3.8 17 18 20 32 (10-3m) 0.01 0.016 0.03 0.02 0.005 0.01 0.015 0.01

15.2

ANSYS6.1 ANSYS6.1

15.2.1

PSD analysis of the beam - shell structureStructural

1 Utility Menu | File | Change Jobname Change Jobname () 15.2

15.2

2 Enter new jobname ()CH15

3 Utility Menu | File | Change Title Change Title () 15.3

15.3

4 Enter new title ()PSD analysis of the beam - shell structure

5 Utility Menu | Plot | ReplotPSD analysis of the beam - shell structure

6Main Menu | Preference Preference of GUI Filtering () Structural()

15.2.2

BEAM4 SHELL63

1Main Menu | Preprocessor | Element Type | Add/Edit/DeleteElement Types () Library of Element Types () 15.4

15.4

2Structural ShellElastic 4node 63 4

3 Library of Element Types ()Structural Beam3D elastic 4 3 Library of Element Types (

) 4

SHELL63,BEAM4 ( 15.5) Element Types ()

15.5

15.2.3

1Main Menu | Preprocessor | Real Constants Real Constants () Element Type for Real Constants () 15.6

15.6 3Type 1 SHELL63 SHELL63 Real Constant Set Number 1,for SHELL63 ( SHELL63) 15.07

15.7 SHELL63

4 Shell thickness at node I TK(I) () 2E-3 2E-3 m

5 Real Constants Set Number 1for SHELL63 ( SHELL63) SHELL63

6 2 Element Type for Real Constants ()Type 2 BEAM4

Real Constant Set Number 2,for BEAM4 ( BEAM4) 15.8

15.8 BEAM4 7AREA 1.6E-5IZZ IYY

21.333E-12TKZ TKY 4E-3 8 Real Constant Set Number 2,for BEAM4 ( BEAM4)

9 Real Constants ()Set 1 Set 2( 15.9)

15.9 Real Constants

13.2.4

EX DENS

1Main Menu | Preprocessor | Material Props | Material Models Define Material Model Behavior () 15.10

15.10

2 Structural Linear Elastic Isotropic 1 EX PRXY 15.11

15.11 3 15.11 EX 2.1E11PRXY 0.3 2.1E11 N/m2 0.3

4 Density( 15.10) Density for Material Number 1 (1) 15.12

15.12 1

5DENS 7.8E3 1 7.8E3 Kg/m3

6Define Material Model Behavior ()Material | Exit

7 ANSYS6.1 ANSYS Toolbar ()

15.2.5

ANSYS6.1 ANSYS6.1

1Main Menu | Preprocessor | Modeling | Create | Keypoints | In Active CS Create Keypoints in Active Coordinate System (),15.13

15.14 --

15.13 2 Keypoint number () 1

X,Y,Z 000 Tab 3 1 4 X,Y,Z

2000.6 3001.2

4001.8

5 Utility Menu | PlotCtrls | Pan Zoom Rotate ANSYS6.1 Pan-Zoom-Rotate (-

-) 15.14 6 15.15

15.15

7Main Menu | Preprocessor | Modeling | Create | Lines | Lines | Straight line Create Straight Line ()

8 12 L1 23 34 L2L3

9 Utility Menu | PlotCtrls | Numbering Plot Numbering Controls () 15.16

15.16 10 Plot Numbering Controls () Keypoint numbers()Line numbers () Area numbers ()On( 15.16)

11 Utility Menu | Multi-Plots 15.17

15.17 12Main Menu | Preprocessor | Meshing |

MeshTool Mesh Tool ()15.18

15.18

13Lines Line Attributes () 15.19

15.19 14Material number ()

Real constant set number () Element type number ()Material number 1Real constant set number 2Element type number 2 BEAM4

15Mesh Tool () Size Controls () Element Sizes on Picked Lines () Element Sizes on Picked Lines ()

15.20

15.20 16 No. of element divisions ()6 6

ANSYS6.1 15.21

15.21 17Mesh Lines Lines Mesh ()

18Utility Menu | PlotCtrls | NumberingPlot Numbering Controls () Elem/ Attrib numbering Element numbers

19 Utility Menu | Plot | Elements 15.22

15.22 20Main Menu | Preprocessor | Modeling | Copy | Lines Copy

Lines () Copy Lines () 15.23

15.23 21 Y-offset in active CS ( Y) 0.5Items to be copied () Lines and Mesh

22 20( 15.23) Y-offset in active CS 0.5 X-offset in active CS 0.5

23 Utility Menu | Select | Entities Select Entities () 15.24

15.24 Select Entities

24 Lines By LocationX coordinates

Min,Max 0.5 X 0.5 From Full

25 20 Copy Lines ()

26 Utility Menu | Select | Everything

27 Utility Menu | Plot | Replot 15.25

15.25

15.2.6

6 ANSYS6.1 ANSYS6.1

1 Utility Menu | PlotCtrls | Numbering Plot Numbering Controls

() Line numbers () Area numbers ()Off Elem/ Attrib numbering No numbering

Keypoint numbers ()On

2 Utility Menu | PlotCtrls | Viewing Direction ANSYS6.1 Viewing Direction () 15.26

15.26

3 XV,YV,ZV Coords of view point ()-0.5-0.91 Coord axis orientation ()X-axis down

13 15.27

15.27 4Main Menu | Preprocessor | Modeling |

Create | Arbitrary | Through KPs Create Area thru KPs ()2614 10

ANSYS6.1 2614 10 15.28

15.28

5 Main Menu | Preprocessor | Meshing | MeshTool Mesh Tool ()15.29

6 Element Attributes ()Global SET

15.29 Mesh Tool

15.30

15.30 7 Element type number ()Material number ()Real constant set number () Element coordinate sys ()Element type number1 SHELL63Material number1Real constant set number1Element coordinate sys0

8 Utility Menu | Select | Everything Below | Selected Areas

9Mesh Tool () Size Controls () Element Sizes on Picked Lines ()

Element Sizes on Picked Lines () ( 15.20)

10 No. of element divisions ()5

11MeshAreas Shape () Quad Free Areas Mesh ()

12 13 Utility Menu | Select | Everything

14 Utility Menu | Plot | Replot 15.31

15.31 15Main Menu | Preprocessor | Modeling | Copy | Areas Copy

Areas () Copy Areas () 15.32

15.32 16 X-offset in active CS ( X) 0.5Items to be copied () Areas and Mesh

17 15 Number of copies ()3 X-offset in active CS ( X)0.5

Z-offset in active CS ( Z) 0.6ANSYS6.1

18 Utility Menu | Plot | Multi-Plots- 15.33

15.33 19Main Menu | Preprocessor | Numbering Ctrls | Merge ItemsMerge Coincident or Equivalently Defined Items (

) 15.34

15.34 20 Type of item to be merge ()All

21Main Menu | Preprocessor | Numbering Ctrls | Compress Numbers Compress Numbers () 15.35

15.35 22 Label Item to be compressed ()All

ANSYS6.1 Main Menu | Preprocessor | Archive Model | WriteWrite Geometry/Loads for Archive( 2 )

15.3

15.3.1

1 Utility Menu | Select | Entities Select Entities ()NodesBy Location

Z coordinates Z 0

2Main Menu | Preprocessor | Loads | Define Loads | Apply | Structural | Displacement | On Nodes Apply U, ROT on Nodes () 15.36

15.36 3 DOFS to be constrained ()All

DOF

4 Utility Menu | Select | Everything Utility Menu | Plot | Replot 15.37

15.37 5 ANSYS

15.3.2

1Main Menu | Solution | Analysis Type | New Analysis New Analysis () Modal (Modal)

2Main Menu | Solution | Analysis Type | Analysis OptionsModal Analysis () 15.38

15.38

3Mode extraction method () Block Lanczos () No. of modes extract () 10

4 Expand mode shapes ()Yes No. of modes to expand ()10 10 Calculate elem results ()Yes

5 Block Lanczos Method () 15.39

15.39 6 End Frequency ()100

7Main Menu | Solution | Solve | Current LS/STATUS Command () Solve Current Load Step ()

8 Utility Menu | File | Close

9 Solve Current Load Step ()

10ANSYSANSYS

15.3.3

15.3.3.1 1Main Menu | Solution | Analysis Type | New Analysis New

Analysis ()( 15.40)

15.40

2 Spectrum Spectrum ()

3 Main Menu | Solution | Analysis Type | Analysis OptionsSpectrum Analysis () 15.41

15.41 4 PSD() No. of modes for solu ()10 Calculate elem stresses? ()Yes

5

15.3.3.2

1Main Menu | Solution | Load Step Opts | Spectrum | PSD | SettingsSettings for PSD Analysis (()) 15.42

15.42

2 Type of response spct ( )Displacement

3Main Menu | Solution | Load Step Opts | Spectrum | PSD | PSD vs Freq Table for PSD vs Frequency () 15.43

15.43 4 PSD vs Frequency () 15.44

15.44 5 FREQ1FREQ2FREQ8 0.501.02.43.8

171820 32PSD1PSD2PSD80.01e-30.02e-30.016e-30.02e-30.005e-30.01e-30.015e-3 0.01e-3

6 Utility Menu | List | Status | Solution | Spectrum Options 15.45

15.45 7Main Menu | Preprocessor | Loads | Define Loads | Apply | Structural |

Spectrum | Base PSD Excit | On Nodes Apply Base PSD on Nodes () 120395877 96(

ANSYS6.1 Z 0) Apply Base PSD on Nodes () 15.46

15.46 6 Excitation direction ()Nodal Y Y

7Main Menu | Solution | Load Step Opts | Spectrum | PSD | Calculate PF Calculate Participation Factors () 15.47

15.47

8 9Main Menu | Solution | Load Step Opts | Spectrum | PSD | Calc Controls PSD Calculation Controls () 15.48

15.48 10 Displacement solution ()Velocity solution () Acceleration solution ()Absolute

15.3.3.3 ()

1Main Menu | Solution | Solve | Current LS/STATUS Command () Solve Current Load Step ()()

2

3 Solve Current Load Step ()

4ANSYS ANSYS

15.3.4

PSD

1 1Main Menu | Solution | Analysis Type | New Analysis New

Analysis ()SpectrumSpectrum ()

2 Main Menu | Solution | Load Step Opts | Spectrum | PSD | Mode Combine PSD Combination Mehtod () 15.49

15.49 3 Significent threshold ()0.005 Combined

mode ()10 4Main Menu | Solution | Solve | Current LS/STATUS Command

() Solve Current Load Step ()() 5

6 Solve Current Load Step ()

7ANSYS ANSYS

15.4

ANSYS 6.1

15.4.1 POST1

(POST1)(Load Step )3 1()(Von Mises)

1Main Menu | General Postproc | Read Results | First Set ()

2Main Menu | General Postproc | List Results | Results Summary SET 15.50

15.50

3 4Main Menu | General Postproc | List Results | Nodal Solution

List Nodal Solution () 15.51

15.51 5DOF solutionAll DOFs DOF List Nodal Solution (

) PRNSOL Command () 15.52

15.52

6 PRNSOL Command () Utility Menu | File | Close

7Main Menu | General Postproc | List Results | Element Solution List Element Solution () 15.53

15.53

8 Item to listed ()LineElem resultsStructural ELEM

PRESOL Command () 15.54

15.54 9PRNSOL Command () Utility Menu | File | Close

10Main Menu | General Postproc | List Results | Reaction SoluList Reaction Solution () 15.55

15.55

11 Item to be listed ()ALL stru forc F

PRRSOL Command () 15.56

15.56 12PRRSOL Command () Utility Menu | File | Close

Load Step ()3 1 ()Von Mises ()

13Main Menu | General Postproc | Read Results | By Set NumberRead result by Datas Set Number 15.57Data set number12 3( 15.50 set 12 Loadstep3)

15.57 Read result by Datas Set Number

14Main Menu | General Postproc | Plot Results | Contour Plot | Nodal Solu Contour Nodal Solution Data () 15.58

15.58 15 Item to be contoured () Stress

Von Mises SEQV Von Mises 3 Von Mises 15.59

15.59 3 Von Mises 16Main Menu | General Postproc | List Results Sorted Listing | Sort

Nodes Sort Nodes () 15.60

15.60 17 Order in which to sort ()Descending order List sorted nodes for Results

Comp Sort nodes based on ()StressVon Mises SEQV Von Mises 15.61

15.61 Von Mises 18 3Von Mises65.975Mpa27Utility Menu | File | Close,

ANSYS6.1 3 Von Mises

15.4.2 POST26 PSD

(POST26) 13 GUI

1Main Menu | TimeHist Postpro(POST26) Spectrum Usage () 15.62

15.62 2 Create response power spectral density(PSD) ()

Time History Variables () 3Main Menu | TimeHist Postpro | Store Data Store Data from the

Results File () 15.63

15.63 4 Resolutio n of freq. vector ()1

5 Main Menu | TimeHist Postpro | Define Variables Define Time-History Variables () 15.64

15.64 6 Add Add Time-History Variables () 15.65

15.65 Nodal DOF result7 Define Nodal Data () 245 Define Nodal Data () 15.66

15.66 8 Ref number of variable ()2, Node number ()245 User-specified label ()UY245 Data item ()DOF solutionTranslation UY Define Nodal Data

9 Define Time-History Variables ()

10 Main Menu | TimeHist Postpro | Calc Resp PSD Calculate Response PSD () 15.67

15.67 11 Reference number of resulting variables ()3 Reference no. of variables to be operated ()2

Type of response PSD ()Displacement Ref. w.r.t. which resp PSD is calculated Absolute value 3 15.68

15.68 12 Calculate Response

PSD ()(Reference number of resulting variables4) Type of response PSD ()Velocity 4

13 Calculate Response PSD ()(Reference number of resulting variables5) Type of response PSD ()Acceleration 5

14Main Menu | TimeHist Postpro | Settings | Graph Graph Settings () 15.69Maximum Time ()4

15.69 15 Utility Menu | PlotCtrls | Style | Graphs | Modify Axes Axes

Modifications for Graph Plots () 15.70

15.70 16 X-axis label (X)FrequencyFrequencyY-axis label (Y)Displacement-YDisplacement-Y

17 Main Menu | TimeHist Postpro | Graph Variables Graph

Time-History variables () 15.71

15.71

18 1st variable to graph ()3 ANSYS6.1 245 15.72

15.72 245Y 19 1518 Axes Modifications for Graph Plots () Y-axis label (Y)Velocity-YGraph Time-History variables () 1st variable to graph ()4 245 Y 15.73

15.73 245 Y 20 1518 Axes Modifications for Graph Plots () Y-axis label (Y)Acceleration-YGraph Time-History

variables () 1st variable to graph ()5 245 Y 15.74

15.74 245 Y

15.4.3 POST26

ANSYS6.1 (/) 245 240 Y

1Main Menu | TimeHist Postpro | Reset Postproc 15.75

15.75 2 Main Menu | TimeHist Postpro | Define Variables Define

Time-History Variables () 3 Add Add Time-History Variables () ( 15.6415.65)

4Nodal DOF result Define Nodal Data () 245

Define Nodal Data () 15.66 5 Ref number of variable ()2, Node number ()245 User-specified label ()UY245 Data item ()DOF solutionTranslation UY Define Nodal Data

6 25 240 Ref number of variable3Node number ()240 User-specified labelweiUY240 240 Y

3 Define Nodal Data 15.76 Define Time-History Variables ()

15.76 7 Main Menu | TimeHist Postpro | Calc Covariance Calculate

Covariance () 15.77 Reference number of resulting variables ()4 Ref. no. of variables to be operated on ()23

15.77 8 Type of response PSD ()DisplacementRef. w.r.t. which

covariance is calculated () Absolute value

ANSYS6.1 Output Window () 15.78

15.78

ANSYS Toobar ANSYS6.1

15.4.4

(Load Step)3 1 Von Mises 65.975Mpa 27 SteinbergMiner

T3e5 15 +0v

6074.36831.0 01 eTvn == +

6220.1271.0 02 eTvn == +

6195.00433.0 03 eTvn == + (1994.12)Q235A P-S-N( 2.1-1)

1 65.975Mpa +=1N

2 131.95Mpa 64.52 eN = 3 197.925Mpa 57.33 eN =

0.1753.057.36195.0

64.5622.16074.3

3

3

2

2

1

1

LSTR,2,3 LSTR,3,4 * TYPE,2 MAT,1 REAL,2 ESYS,0 LESIZE,ALL,,,6,1, LMESH,ALL LGEN,2,ALL,,,,0.5,,,0 LGEN,2,ALL,,,0.5,,,,0 LSEL,R,LOC,X,0.5 LGEN,2,ALL,,,0.5,,,,0 LSEL,ALL * /VIEW,1,-0.5,-0.9,1 /VUP,1,Y /REPLOT * A,2,6,14,10 TYPE,1 MAT,1 REAL,1 ESYS,0 ALLSEL,BELOW,AREA LESIZE,ALL,,,5,1 AMESH,1 * AGEN,2,1,,,0.5 AGEN,2,ALL,,,,,0.6 ASEL,R,LOC,Z,1.2 AGEN,2,ALL,,,,,0.6 ALLSEL,ALL * NUMMEG,ALL,,, NUMCMP,ALL NSEL,R,LOC,Z,0 D,ALL,,,,,,ALL ALLSEL,ALL

* /SOLU ANTYPE,2 MODOPT,LANB,10,0,100, ,OFF EQSLV,SPAR MXPAND,10, , ,1 LUMPM,0 PSTRES,0 SOLVE FINISH * /SOLU ANTYPE,8 SPOPT,PSD,10,1 PSD PSDUNIT,1,DISP,386.4, * PSDFRQ,1, ,0.5,1.0,2.4,3.8,17 PSDFRQ,1, ,18,20,32, , * PSDVAL,1,0.01e-3,0.02e-3,0.016e-3,0.02e-3,0.005e-3 PSDVAL,1,0.01e-3,0.015e-3,0.01e-3, , * NSEL,R,LOC,Z,0 D,ALL,UY,1.0 ALLSEL,ALL * PFACT,1,BASE, PSDRES,DISP,ABS PSDRES,VELO,ABS PSDRES,ACEL,ABS * SOLVE FINISH * /SOLU ANTYPE,8 PSDCOM,0.005,10 PSD SOLVE FINISH

* /POST1 SET,FIRST SET,LIST PRNSOL,DOF, PRESOL,ELEM PRRSOL,F SET, , ,1, , , ,12, 3 PLNSOL,S,EQV,0,1 NSORT,S,EQV,0,1, ,0 PRNSOL,S,PRIN FINISH * /POST26 FILE FILE,'CH13','rst','.' /UI,COLL,1 NUMVAR,200 STORE,PSD,1 1 NSOL,2,245,U,Y,UY-245 RPSD,3,2,,1,1, RPSD,4,2,, 2,1, RPSD,5,2,,3,1, * PLTIME,0,4 /AXLAB,X,Frequency /AXLAB,Y,Displacement-Y PLVAR,3 245 Y /AXLAB,X,Frequency /AXLAB,Y,Velocity-Y PLVAR,4 245 Y /AXLAB,X,Frequency /AXLAB,Y,Acceleration-Y PLVAR,5 245 Y RESET POST26 NSOL,2,245,U,Y,UY-245 2 245 Y NSOL,3,240,U,Y,UY-240 3 240 Z * CVAR,4,2,3,1,1,

*GET,U245,VARI,4,EXTREM,CVAR FINISH