random response analysis

8/2/2019 Random Response Analysis

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Performing a Random Response Analysis

1. Introduction

In this example problem you will learn how to perform a random response analysis. The model shown inFigure 1 is a 1in. by 10in. plate with a thickness of 0.1in.

Figure 1: Beam Model

You will first need to build or import the geometry. Follow the steps provided in Performing a ModalAnalysis, to do so. If the model is imported be sure to delete the loads, rigid elements and masselements before beginning.

A number of functions must be entered for use in this type of analysis. The first function is the inputfunction; this function is versus frequency. From the FEMAP main menu select Model then Function.In the Function Definition dialog box type in PSD Input into the Title field. In the Type pull downwindow select 3..vs. Frequency. Click the Single Value radio button and enter 0 into the X field and0.01 into the Y field.


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Figure 2. Function Definition

Click More. Now enter 10 into the X field and 1 into the Y field. Click More. Enter 500 into the X fieldand 1 into the Y field. Click More. Enter 510 into the X field and 0.01 into the Y field. Click More.Finally, enter 5000 into the X field and 0.01 into the Y field and Click More. Your dialog box should looklike the one below.


Click OK. Click Cancel. The input function has now been created. To look at the function youve justcreated press F5. In the View Select dialog box click on the XY of Function radio button and click theModel Data button. In the Function field in the Select pull down menu select 1..PSD Input. Click


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OK. Click OK. Your plot should now look like the one below.

Figure 4. Plot of PSD Input

To return to your model press F5 and click on the Draw Model radio button under the Model Style field.Click OK. Your model should now appear on the screen.

The second function that we will now define is the table of frequencies of interest. This function is againversus frequency. From the FEMAP main menu select Model Function. In the FunctionDefinition dialog box type in Analysis Frequencies into the Title field. In the Type pull down windowselect 3..vs. Frequency. Click the Linear Ramp radio button and enter 50 into the DeltaX field, 1 intothe X field, 5001 into the To X field, and 1 into the Y and To Y fields.


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Click More. Click OK. You can view this function as a plot in the same manner as done before.

Figure 6. Plot of Analysis Frequencies

The next function is the load function, again versus frequency. From the FEMAP main menu selectModel Function. In the Function Definition dialog box type in Load Function into the Title field.In the Type pull down window select 3..vs. Frequency. Click the Single Value radio button and enter 0


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into the X and 1 into the Y field.


Click More. Now enter 100 into the X and 1 into the Y field. Click More. Your dialog box should looklike the one below.


Click OK. Click Cancel. You can view this function as a plot in the same manner as done before.


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Figure 9. Plot of the Load Function

The final function is the damping function. This function is a Critical Damping versus Frequency function.From the FEMAP main menu select Model Function. In the Function Definition dialog box type inDamping Function into the Title field. In the Type pull down window select 7..Critical Damp vs. Freq.Click the Single Value radio button and enter 0 into the X and 0.05 into the Y field.


Click More. Enter 5000 into the X field and 0.05 into the Y field. Click More. Your dialog box shouldlook like the one below.


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Figure 11. Function Definition (cont.)

Click OK. Click Cancel. You can view this function as a plot in the same manner as done before.

Figure 12. Plot of the Damping Function


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2. Setting up the Dynamic Analysis

We will now set up a random analysis. From the FEMAP main menu click on Model Load DynamicAnalysis. In the Title field enter Dynamic Load and Click OK. Click the Modal Frequency radiobutton for the Solution Method from the Load Set Options for Dynamic Analysis dialog box. Fromthe three pull down menus select 4..Damping Function, 2..Analysis Frequencies and 1..PSD Input asshown below.

Figure 13. Load Set Options for Dynamic Analysis

Click the Advanced button. The Advanced Load Set Options for Dynamic Analysis dialog boxnow appears. Select 2..Cluster around Modes for the Input Type. Select a Min Frequency (Hz) of 1,a Max Frequency (Hz) of 5000 a Frequencies/Subrange of 20 and a Cluster Value of 0.5. Changethe NASTRAN PSD Interpolation to 1..Linear. Your dialog box should look like the one below.


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Figure 14. Advanced Load Set Options for Dynamic Analysis

Click OK. From the Load Set Options for Dynamic Analysis dialog box, click the Enforced Motionbutton. From the Locate Enter Coordinates for Base Mass enter 0 for X, 0.5 for Y, and 0 for Z. ClickOK. In the Entity Selection Select Nodes on Base dialog box, click on the three nodes that make upthe left side of the model. Click OK. In the Create Loads on Nodes (Node 65) or (Node 64) dependingon if the model was imported, make sure that Acceleration is highlighted; then click on the AY buttonand enter 50 into the field. From the Function Dependence pull down menu select 3..Load Function.

Figure 15. Create Loads on Nodes


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Click OK. Click OK in the Mass/Accel Scale Factor. Click OK. The model and load should appear onthe screen as shown below.

Figure 16. Loaded Model

3. Setting up the Constraints

The final step in setting up the model is to set up the appropriate constraints. For this model the largemass will be fixed except in the Y direction. All other nodes will be fixed in the TZ, RX and RY DOFs toforce a 2-D condition. If the constraints were imported with the model and are correct, this step can beignored.

From the FEMAP main menu click Model Constraint Nodal. From the Create or ActivateConstraint Set dialog box, type in Constraints for the Title.

Figure 17. Create or Activate Constraint Set


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Click OK. The Entity Selection Enter Node(s) to Select dialog box appears. Type 64 or 65,whichever contains the loading, into the ID field and click More. Click OK. Click on all DOFs except forthe TY and Click OK. Click the Pick^ button and select Box. Using the left mouse button twice, createa box that surrounds all the nodes except for the three left edge nodes of the plate. Click once to startone corner of the box and click again when the box surrounds the proper nodes. Click OK. In theCreate Nodal Constraints/DOF dialog box, click the TZ, RX and RY boxes. This will allow motion in the

XY-Plane only.

Figure 18. Create Nodal Constraints/DOF

Click OK. Click Cancel. The constraints should now appear on the plate. This would be a good time tosave the model. From the FEMAP main menu select File Save. Browse to your working directory andsave the model.

Figure 19. Constrained and Loaded Model


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4. Running a Random Response Analysis

First we will need to group the concentrated mass and the node on the center of the right edge of thebeam. From the FEMAP main menu select Group Set. Give it a title (Output Set) and click OK.Select GroupNode then ID. Type in the node number of which the load is connected in the ID fieldand click More. Select the far right center node on the 1in. vertical curve and click OK.

We will now run a random response analysis. From the FEMAP main menu select Model Analysis.Click New and type in Random Response for the Title and select 31..NEiNastran for the AnalysisProgram and 6..Random Response for the Analysis Type. Click Next. Click Next. Check the AllPlates as QUADR/TRIAR box. Click Next. In the From (Hz) field enter 1 and in the To (Hz) fieldenter 5000. Click Next. Click Next. Click the Power Spectral Density Functions radio buttons forboth the Nodal Output Requests and Elemental Output Requests. Click Next five times. Selectonly Displacement, Applied Load, and Acceleration for the Nodal Output Requests. For each outputrequest select 1..Output Set from the pull down menu. Click OK. Click Analyze to start the Analysis.Browse to your working directory, type in Random Response for the File name and click Write.

5. Viewing the Results

The results of a random response analysis are best viewed with XY plots. Figure 20 shows the XY plotsettings for the PSD output at node 24 (on the response end). The output sets are shown from the firstPSD to the last PSD set. The output set is chosen in the middle of the PSD because with certain inputfunctions it is possible to get zero values for the initial outputs; in these cases, FEMAP will not permitpicking of the desired output vector. The view options menu can be used to set appropriate bounds forthe plot axis.

Press F5. Pick the XY vs Set Value radio button and click XY Data. From the Output Vector pulldown menu select 23..T2 ACCELERATION. In the Output Location field in the Node box enter 24, thisis the center node on the right side vertical curve of the beam. In the ShowOutput Sets (Blank = All)field enter 178 for From and 354 for To. Your dialog box should look like the one below.


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Figure 20. Select XY Curve Data

This will display the PSD Output at the response end of the beam. Click OK. Click OK. The graphshould appear like the one below.

Figure 21. PSD Output at the Response End of the Beam


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We can now look at the PSD Output at node 64, or 65, the node containing the load. Press F5 andfollow the above steps, except this time enter 64, or 65, into the Output Location field in the Node box.Click OK. Click OK. Your plot should appear like the one below. As we suspected it looks similar to thePSD Input function.

Figure 22. PSD Output at the Input End of the Beam

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