115469704-ansys

DYNAMICS

for ANSYS 7.0

Workshop Supplement

Inventory Number: 001810

First Edition ANSYS Release: 7.0

Published Date: March 14, 2003

Registered Trademarks: ANSYS® is a registered trademark of SAS IP Inc.

All other product names mentioned in this manual are trademarks or registered trademarks of their respective manufacturers.

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Workshop Supplement

DYNAMICS

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Table of Contents

Introductory Workshop

Galloping Gertie -------------------------------------------- W-5

Modal Analysis Workshop

Plate with a Hole -------------------------------------------- W-17


Model Airplane Wing -------------------------------------------- W-23

Harmonic Analysis Workshop

Fixed-Fixed Beam -------------------------------------------- W-27

Transient Analysis Workshop

Bouncing Block -------------------------------------------- W-35

Restarting a Transient Workshop

Bouncing Block -------------------------------------------- W-43

Response Spectrum Workshop

Workbench Table -------------------------------------------- W-49

Random Vibration Workshop

Model Airplane Wing -------------------------------------------- W-55

Pre-stressed Modal Analysis Workshop

Pre-Stressed Disc -------------------------------------------- W-61

Modal Cyclic Symmetry Workshop

Spiral Bevel Gear -------------------------------------------- W-67

Introductory

Workshop

Galloping Gertie

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… Galloping Gertie

Objective

• To get an idea of the steps involved in a typical dynamic analysis.

• The Tacoma Narrows bridge, also known as the Galloping Gertie

is famous for its spectacular collapse in 1940. In this workshop,

we will examine a model of the bridge and calculate its natural

frequencies and mode shapes. We will then simulate the wind

storm and vortex shedding that caused the bridge‟s collapse by

doing a harmonic analysis.

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Instructions

1. Enter ANSYS in the working directory specified by your instructor.

2. Start by reading input from the file gallop.inp.

Utility Menu: File > Read Input from… choose gallop.inp

– This will create the model and perform a static analysis to prestress the bridge.

– The next step is to do a modal analysis.

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3. Enter Solution and change analysis type to Modal:

Solution > Analysis Type > New Analysis… choose Modal.

4. Set the following analysis options.

Solution > Analysis Type > Analysis Options...

accept the default (Block Lanczos)

10 modes to extract

10 modes to expand

Calculate element stresses

Include prestress effects… press OK

Accept defaults on the next dialog (Options for Block Lanczos Modal Analysis)

5. Solve.

Solution > Solve > Current LS

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6. Plot the first few mode shapes.

General Postproc > Read Results > By Pick …

General Postproc > Plot Results > Contour Plot > Nodal Solu ...



Mode 3 – SX stress Mode 1 – SX stress

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7. Enter Solution and choose harmonic analysis.

Solution > Analysis Type > New Analysis…

8. Set the following analysis options.

Solution > Analysis Type > Analysis Options...

Select the Mode superposition solution method

Defaults for all others (including subsequent dialog box)

9. Set frequency and substep options:

Solution > Load Step Opts > Time/Frequenc > Freq and Substps...

Harmonic frequency range = 0 to 0.4

Number of substeps = 40

Stepped boundary conditions

10. Set constant damping ratio = 0.01.

Solution > Load Step Opts > Time/Frequenc > Damping…



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11. Apply a load vector for mode superposition

with a scale factor of 100. Solution > Define Loads > Apply > Load Vector > For Mode Super…

(close the warning message window)

12. Solve: Solution > Solve > Current LS

13. Save the ANSYS database for the Variable

Viewer in Step 14.

Utility Menu: File > Save as Jobname.db …

14. Enter POST26 (TimeHist Postproc). The

Variable Viewer will start automatically.

Specify the results file name, i.e. gallop.rfrq,

by clicking on File > Open Results) Select “gallop.rfrq” as the results file, then click [Open]

Select “gallop.db” as the ANSYS database, then click [Open]



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15. Create a scalar parameter to represent the center node: At command

line type in ncen = node(0,0,0) .

16. Define a variable (a vector) using the Variable Viewer that will contain

the UZ displacements of the center node:



a. Click on the “Add Data” button

b. Double click on “Nodal Solution”

and “DOF Solution”, select “Z-

Component of displacement” and

enter “uz_mid” for the Variable

Name, and then click [OK]

c. Enter “ncen” followed by [Enter] in

the ANSYS Picker Menu, then [OK]

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16. (cont‟d).

The Variable Viewer should appear as follows:



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17. Graph the UZ-displacement vs frequency:

1. Select the line labeled “uz_mid” and then click on the “Graph Data” button

18. Close the Variable Viewer and then Exit ANSYS or go to step 19 if time

permits.



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Optional: Continue with the following steps to review the

deformed shape and stresses at 0.07 Hz frequency.

19. Read Input from… gallop_more.inp.

20. Enter POST1, read results for load step 1 substep 7, and plot the deformed

shape and stress contours. Repeat for the imaginary part as well.

21. Exit ANSYS.

Real Part Imaginary Part



SEQV stress SEQV stress

Modal Analysis

Workshop

Plate with a Hole

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Description:

Determine the first 10 natural

frequencies of the plate with a hole

shown. Assume the plate to be

radially constrained at the hole. The

plate is made of aluminum, with the

following properties:

– Young‟s modulus = 10 x 106 psi

– Density = 2.4 x 10-4 lbf-sec2/in4

– Poisson‟s ratio = 0.27


… Plate with a Hole

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Instructions

1. Clear the database and read input from plate.inp to create the model geometry and mesh.

Utility Menu: File > Clear & Start New… press OK, then answer Yes

Utility Menu: File > Read Input from… choose plate.inp

2. Define material properties.

Preprocessor > Material Props > Material Models…

• Double click through

– … Structural … Linear … Elastic … Isotropic

• EX = 10e6 (Young‟s modulus in psi)

• PRXY = 0.27 (Poisson‟s ratio)

• [OK]

– … Structural … Density

• DENS = 2.4e-4 (Density in lbf-sec2/in4)

• [OK]

• Exit the material GUI



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3. Choose modal analysis.

Solution > Analysis Type > New Analysis… choose Modal, then OK

4. Specify analysis options. Solution > Analysis Type > Analysis Options…

Use Block Lanczos method (default)

10 modes to extract

10 modes to expand

Yes to calculate element results… press OK

Accept defaults on the next dialog box

5. Radially constrain the hole. Utility Menu: Plot > Lines

Solution > Define Loads > Apply > Structural > Displacement > Symmetry B.C. > On Lines

Pick the lines around the hole and press OK in the Picker Menu

6. Start the solution. Solution > Solve > Current LS

Check solution information in the /STAT window, then press OK



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7. Review results. Start by listing the frequencies.

General Postproc > Results Summary

8. Plot the first mode shape.

General Postproc > Read Results > First Set

General Postproc > Plot Results > Deformed Shape

Choose “Def + undef edge” and press OK



Mode 1

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9. Plot and animate the next mode shape.

General Postproc > Read Results > Next Set

Utility Menu: Plot > Replot

Utility Menu: PlotCtrls > Animate > Mode Shape…

10 frames

Time delay = 0.05

(accept all other defaults)

10. Repeat above step for subsequent mode

shapes.



Mode 6

Modal Analysis

Workshop

Model Airplane Wing

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Description:

Determine the first five natural frequencies of the model airplane wing shown. Assume the wing to be fully fixed at Z=0. The wing has the following properties:

– Young‟s modulus = 38000 psi


– Density = 1.033 x 10-3 slugs/in3 = (1.033E-3)/12 lbf-sec2/in4


… Model Airplane Wing

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Instructions

1. Clear the database and read input from wing.inp to create the model

geometry and mesh.

2. Define material properties. Remember to use British in-lb-sec units.

3. Apply boundary conditions. Hint: Choose Apply Displacements on

Areas, pick the Z=0 area, and fix it in all DOF.

4. Extract (and expand) the first four natural frequencies using the

Block Lanczos method.



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5. Review all the mode shapes.



Mode 1

Mode 3

Mode 2

Mode 4

Harmonic Analysis

Workshop

Fixed-Fixed Beam

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… Fixed-Fixed Beam

Description:

• Determine the harmonic response of a steel beam carrying two

rotating machines which exert a maximum force of 70 lb at

operating speeds of 300 to 1800 rpm. The beam, 10 feet long, is

fully fixed at both ends, and the machines are mounted at its

“one-third” points. Assume a damping ratio of 2%.

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Instructions 1. Clear the database and read input from beam.inp to create the

beam model.

2. Specify harmonic analysis (full method) .

3. Fix the two ends of the beam and apply the two in-phase harmonic

forces of FY=70 lbs each at the 40-inch and 80-inch points along

the beam.

4. Specify a damping ratio of 0.02 (i.e. 2%).

Solution > Load Step Opts > Time/Frequenc > Damping

5. Specify 25 solutions between 5 and 30 Hz (300-1800 rpm).

Remember to step apply the loading.

Solution > Load Step Opts > Time/Frequenc > Freq and Substps …

6. Obtain the harmonic solution.

Solution > Solve > Current LS



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7. In Time history post processor plot UY displacements versus frequency for the two nodes at which the forces were applied.

NOTE: Use (Utility Menu > PlotCtrls >

Style > Graphs ) for changing graph

style / settings.

8. Find the critical frequency and phase angle.

TimeHist Postpro > List Variables

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9. In General Post processor review the deformed shape of the beam

at the critical frequency and phase angle.

1. Find the load step and substep for the critical frequency:

General Postproc > Result Summary

2. Issue the HRCPLX command to read in the results at the critical

frequency and phase angle:

HRCPLX,1,4,-25.3743

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9. (continued).

3. Plot the UY displacement:

General Postproc > Plot Results > Contour Plot > Nodal Solu

plns,u,y

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10. If time permits, repeat the analysis with forces that are 180° out of

phase.

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10. (continued).

HRCPLX,1,21,-98.2155

plns,u,y

Transient Analysis

Workshop

Bouncing Block

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Description:

• A 6x6x1-inch block is dropped on a 100-

inch long beam from a height of 100 inches.

Obtain a graph of the motion of the block as

it bounces on the beam. Assume a gap

stiffness of 2000 lb/in. The beam is fully

fixed at both ends, and the only load is

gravity, 386 in/sec2. The beam and the

block are made of the same material:

– Young‟s modulus = 1,000,000 psi

– Density = 0.001 lbf-sec2/in4



… Bouncing Block

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Instructions 1. Clear the database and read input from bounce.inp to build the

model.

2. Define a transient analysis (full method)

3. Fix the two ends of the beam in all directions.

4. Use APDL to calculate the integration time step (ITS):

kgap = 2000 - gap stiffness

mgap = 6*6*0.001 = 0.036 - mass of block

pi = acos(-1)

fgap = sqrt(kgap/mgap)/(2*pi) - gap frequency

its = 1/(fgap*30) - integration time step


… Bouncing Block

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5. Solve using two load steps.

• Load Step 1 (for non-zero initial acceleration):

– Fix all nodes of the block in all dofs.

– Apply an acceleration of 386 in/sec2

In Solution Control menu,

– Set analysis to “large displacement transient”.

– Set time=0.001.

– 2 substeps

– Request output of all results for all substeps on the results file

– Static solution (time integration effects off) with Step applied load.

– Set beta damping of .0003183.

• SOLVE


… Bouncing Block

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Load Step 2 ( transient):

Go back to solution control menu and

– Time=1.5

– Automatic time stepping on, with starting ITS = 0.02, minimum ITS =

its (from step 4) and maximum ITS = 0.02

– Transient solution (time integration effects “on”)

– Release the block

– SOLVE


… Bouncing Block

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… Bouncing Block

6. Review results:

– Plot the UY displacements of the beam mid-point and the block versus time.

– Plot the FY reaction force at one of the constraints versus time.

– Animate results over time. Note: To store all the frames needed for animation, you

may need to reduce the size of the graphics window.

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… Bouncing Block

8. Do not exit ANSYS:

– You will continue this workshop with a restart later on.

7. Animate results over time.

Note: To store all the frames

needed for animation, you

may need to reduce the size of

the graphics window.

/post1

/focus,,50,50

/dist,,70

/dsca,,1

/eshape,0

inres,nsol

set,first

pldisp

/noerase

*do,t,0.001,1.5,3/50

set,near,,,,t

pldisp

*enddo

/erase

Restarting a Transient

Workshop

Bouncing Block

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… Bouncing Block

Description:

• Continue the bouncing block analysis from

the previous exercise. That analysis was

stopped at time=1.5. In this exercise we

will continue to follow the block‟s motion

up to time=3.0.

• The restart files needed (.r001 /.ldhi /.rdb )

are available from the previous workshop.

• The results file from the previous transient

analysis is also available. ANSYS will

append the new results to this RST file as

load step 3.

Time = 1.5

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Instructions:

1. Continue the ANSYS session from the previous workshop.

2. Solution > Analysis Type > Restart

This will bring up a lister window showing a summary of the

restart files available. Choose the load step and substep number

from this summary.

3. In Solution Control menu under the Time Control section: change

TIME to 3.0 and select “Time increment”.

4. Solve.


… Bouncing Block

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… Bouncing Block

• In Time History postprocessor graph the UY displacement of a

node on the block and a node on the beam again.

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… Bouncing Block

• In the general postprocessor animate the bouncing of the block

again.

– Animate results over time. Note: To store all the frames needed for

animation, you may need to reduce the size of the graphics window.

Time = 1.5 to 3

Response Spectrum

Workshop

Workbench Table

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Description:

Determine the displacements

and stresses in a workbench

table due to the acceleration

spectrum shown below.

Accele

ration

Frequency

20 80 200 300

217 217

79.5

150.2


… Workbench Table

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… Workbench Table

Instructions

1. Clear the database and read input

from table.inp to create the model

geometry and mesh.

2. Obtain a modal solution (15

modes) and view the first few

mode shapes. Be sure to request

element stress calculations.

Mode 1 Mode 2

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… Workbench Table

3. Do a spectrum analysis for the

given acceleration spectrum

applied in the global X direction.

Use the SRSS method of mode

combination.

4. Review displacements and table

top stresses for each load step. pldisp,2

plns,u,x plns,s,1

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5. If time permits, repeat the analysis with the spectrum applied in the Y

direction, then in the Z direction.


… Workbench Table

Random Vibration (PSD)

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Model Airplane Wing

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Random Vibrations Workshop


Description:

Determine the displacements and stresses of the model airplane

wing due to an acceleration PSD applied to the base of the wing in

Y direction. Assume the wing to be fully fixed at Z=0.

Accele

ration

(G2/H

z)

Frequency (Hz)

20 100 400 600

0.1 0.1

0.025

0.075

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Instructions

1. Clear the database and read input from wing.inp to create the model geometry and mesh.

2. Define material properties.

Young‟s modulus = 38000 psi

Poisson‟s ratio = 0.3

Density = 1.033E-3/12 lbf-sec2/in4

3. Apply boundary conditions. Hint: Choose Apply Displacements on Areas, pick the Z=0 area, and fix it in all DOF.

4. Extract (and expand) the first 15 natural frequencies using the Block Lanczos method.

5. Review mode shapes.

Mode 1

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6. Perform a PSD Spectrum analysis using the acceleration PSD

shown.

Hint: Be sure to use G2/Hz as the units of the PSD.

7. Specify excitation in the Y direction (by applying unit

displacements in the Y direction at the base nodes).

8. Compute Participation factors.

9. Use PSD mode combination method and SOLVE.



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10. In the general postprocessor look at the relative displacements/ stresses (

Load step 3).

– Can you directly use stress contours for, say SZ, to compare to yield stress?

– What is in load step 1?

– Are equivalent/principal stresses derived from 1 sigma component stresses valid?

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11. In Time History Postprocessor create the response PSD for UY at one of

the nodes of the wingtip. Plot on log-log scale.

– Hint: When you get into time history postprocessor first issue „Store Data‟ and

accept the default. This is required for computing Response PSD.

NODE 182

Pre-stressed Modal

Workshop

Pre-Stressed Disc

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… Pre-stressed Disc

Description:

• Determine the first ten natural frequencies and mode shapes of the

perforated aluminum disc shown. The disc is constrained at the central

hole both in the radial and out-of-plane directions. A pre-stress exists due

to a radial pressure load of -20 lbs/inch at the perimeter. Properties of the

disc are as follows:

– Young‟s modulus = 1.0 x 107 psi



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Instructions

1. Clear the database and read input from disc.inp to create the model

geometry and mesh.

2. Apply displacement constraints: UZ=0 and symmetry b.c. (for radial

constraints) at the central hole. Hint: You will need to use two

menus:

Solution > Define Loads >Apply > Structural > Displacement > On Lines for the UZ

constraint

Solution > Define Loads > Apply > Structural > Displacement > Symmetry B.C. > On Lines

for symmetry b.c.

To pick the lines easily, switch to front view and use Circle picking.



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3. Apply the radial load as pressure on

the lines at the perimeter : -20

pounds/inch on the outer edges of the

disc.

Hint: Stay with the front view, use

Circle picking to pick the entire disc,

then use Circle unpicking to unpick all

except the outer edges.

4. Activate pre-stress effects (using the

Analysis Options dialog box), obtain a

static solution, and review results.

plns,s,1

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5. Switch to modal analysis,

activate pre-stress effects

(again), and extract the first 10

modes of the pre-stressed disc

using the Block Lanczos method.

6. Review the mode shapes.

7. If time permits, do a second,

stress-free modal analysis (with

pre-stress effects off) and

compare results. Shown to the

right is the first mode shape for

each case. Can you guess which

one is pre-stressed?

FREQ = 73.484

FREQ = 1.582

Modal Cyclic Symmetry

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Spiral Bevel Gear

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Description:

• Determine the first two natural frequencies

of nodal diameter 2 for the spiral bevel

gear shown. Assume a free-free condition

(i.e., no displacement constraints).

Material properties of the gear are as

follows:

– Young‟s modulus = 2.9 x 107 psi




… Spiral Bevel Gear

Courtesy: Sikorsky Aircraft

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Instructions

1. Clear the database and read input from

bevel.inp to create the basic sector and define

material properties.

2. Issue the CYCLIC command to automatically

detect the low and high edge components using

“BEVEL” as the Root name for the components

( Preprocessor > Modeling > Cyclic Sector > Cyclic

Model > Auto Defined )



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3. Display the current cyclic status:

Preprocessor > Modeling > Cyclic Sector > Cyclic Model > Status



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4. Define a modal analysis with the following options:

– Block Lanczos method

– Extract two modes in the frequency range 100 to 10,000

– Expand 2 modes

5. Solve for nodal diameter range 2 to 2:

1. Solution > Solve > Cyclic Options

2. Solution > Solve > Current LS



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6. Expand results to all 53 sectors ( General Postproc > Cyclic Analysis > Cyc Expansion ). Then read in the results of the first mode shape (General Postproc > Read Results > First set ). Plot the nodal solution for UZ displacements.

NOTE: The /CYCEXPAND command actually creates new elements and

nodes for all 53 sectors.



/gline,1,-1

plns,u,z

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7. Plot the vector sum displacement.



plns,u,sum

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8. Execute the ANCYC traveling wave animation:

• Utility Menu > PlotCtrls > Animate > Cyc Traveling Wave

• No. of frames to create = 25

• Time delay = 0.1

• Animation Mode = Forward-Reset-Forward

• Nodal Solution Data

– DOF solution

– USUM

• [OK]



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Documents

transient workshop

harmonic analysis workshop

transient analysis workshop

modal analysis workshop

gertie dynamics

galloping gertie

static analysis

typical dynamic analysis