NASTRAN EXAMPLE ME443SPRING 2009 Applied Vibrations

NASTRAN solution to the 2 degree-of-freedom lumped parameter model of longitudinal beam vibration.The beam and lumped parameter models are shown in Figure 1a) and 1b), respectively.It can be shown that k1 = k2 = 2EA / L and m2 = 2m1 = ρAL / 2 . Using the analytical solution we candetermine how the natural frequencies depend on E , ρ , A , and L . However, with NASTRAN, we need tospecify these quantities to determine the solution. To obtain information about how the natural frequenciesdepend on these quantities, we’d need to changed them, one at a time, and rerun NASTRAN -> a muchmore time consuming process. Here, the solution is obtained for an aluminum (E=72*109 Pa, ρ=2800kg/m3) rod of length L=1 m and radius r=1 cm. ( ρAL=0.88 kg, EA / L=2.26*107 N/m).

Figure 1. a) Longitudinal vibration of a beam and b) lumped parameter model.

PATRAN INSTRUCTIONS:

1.) Create nodal points. The length of the springs does not affect the solution. I put nodes 1, 2, and 3 at x =2, 1, and 0, respectively.

1. Create three, two point elements, and two bar elements.Concentrated masses will be point elements and springs will be bar elements.From the Top Menu, choose Elements.

A Right Menu called Finite Elements will resultSet Action = Create

Object = NodeMethod = EditNode ID = 100

Use the default Reference and Analysis Coordinate Frames of Coord 0.Turn off Associate with Geometry.Enter the Node Location List in the format [0,0,0].Click Apply.On the tool bar below the top menu, click node size button to see node locations.Repeat to create nodes with ID 1 and 2 along a line in the x direction. Distance betweenpoint does not effect the results, so choose a distance =1.

u1u2

m2 m1

k2k1

u1u2

a)

b)

In the Right Menu called Finite ElementsSet Action = Create

Object = ElementMethod = EditShape = Point

Note the Element ID automatically increments to the next integer.Use the mouse to pick Node 1 and create Element 1.Use the mouse to pick Node 2 and create Element 2.

Set Shape = Bar and use default for Topology and Pattern.Use the mouse to pick Node 1, then Node 2 and create a 2D element.Use the mouse to pick Node 2, then Node 2 and create a 2D element.

2. Specify the Boundary Condition at the fixed end.From the Top Menu, choose Loads/BCs.

A Right Menu called Load/Boundary Conditions will resultSet Action = Create

Object = DisplacementType = Nodal

Choose a New Set Name, e.g., spc.1.Select Input Data button.

Input <0,,> for the translational degrees of freedom. Click OK.Select the Select Application Region button.

Set the Geometry Filter to FEM and use the mouse to pick Node 3.Add Node 3 to the Application Region. Click OK.

Click Apply.

3. Specify 0D elements are CONM2 and input mass values.Specify 1D elements are springs and input spring constant and direction of application.From the Top Menu, choose Properties.

A Right Menu called Element Properties will resultSet Action = Create

Object = 0DType = MassOptions = Lumped

Choose a Property Set Name, e.g., mass.1.Select Input Properties button.

Input the value for m1 for mass in the pop-up window and click OK.Use the mouse to pick Element 1. Point Element needs to be selected in Pic menu.Add Element 1 to the Application Region. Click OK.Repeat to create the second concentrated mass element.

In the Right Menu called Element PropertiesSet Action = Create

Object = 1DType = Spring

Choose a Property Set Name, e.g., spring.1.Select Input Properties button.

Input the value for k1=k2 for stiffness in the pop-up windowAlso use the pull-down menus to pick “UX” for Dof at Node 1 and for Dof atNode 2. Click OK.

Use the mouse to pick Elements 3 and 4. Bar Element needs to be selected in Pic menu.Add Elements 3 and 4 to the Application Region. Click Apply.

4. Write a NASTRAN data deck.From the Top Menu, choose Analysis.

A Right Menu called Analysis will resultSet Action = Analyze

Object = Entire ModelType = Analysis Deck

Pick Solution TypeChoose NORMAL MODES for Solution 103.

Pick SubcasesIn the Subcases pop-up menuSet Action = CreateChoose a Subcase Name, e.g., subcase.1.Pick Subcase Parameters

In the Subcase Parameters poop-up menuSet Extraction Method = Lanczos

Lower (Frequency Range of Interest) = 0Number of Desired Roots = 2Normalization Method = MaximumClick OK

Click Apply. And Click Cancel.Pick Subcase Select

In the Subcase Select pop-up menuSelect the subcase you createdClick OK

Click Apply to write the data deck.

5. Run NastranAdd a grdset,,,,,,,23456 card to the bulk data deck first.Then run NASTRANCheck the frequencies and mode shapes in the .f06 file.Attach the .xdb file to the Patran model

6. Display and Animate the Mode ShapesFrom the Top Menu, choose Results.

A Right Menu called Results will resultSet Object = Quick PlotChoose (highlight) a mode under Select Result Cases, e.g., Mode 1.Choose (highlight) Eigenvectors, Translational under Select Deformation ResultCheck Animate box to see an animation of the mode.

In the Right Menu called ResultsSet Object = GraphSet Method = Y vs XChoose (highlight) a mode under Select Result Cases, e.g., Mode 1.Set Y = ResultSet X = CoordinateSet Select Coordinate Axis = Coord 0.1Click on the Target Entities button, the second in the set of 4 buttons with graphics.

Set Target Entity = NodesDrag the mouse to create a rectangle to select all nodes in the Select Nodes box.Click Apply

Click on the Select Results button, the first in the set of 4 buttons with graphics, to choosea different mode shape.