NASTRAN EXAMPLE
SPRING 2009
ME443
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 can
determine how the natural frequencies depend on E , ρ , A , and L . However, with NASTRAN, we need to
specify these quantities to determine the solution. To obtain information about how the natural frequencies
depend on these quantities, we’d need to changed them, one at a time, and rerun NASTRAN -> a much
more time consuming process. Here, the solution is obtained for an aluminum ( E =72*109 Pa, ρ =2800
kg/m3 ) rod of length L =1 m and radius r=1 cm. ( ρAL =0.88 kg, EA / L =2.26*107 N/m).
u2
u1
a)
u2
k2
b)
m2
k1
u1
m1
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 result
Set
Action = Create
Object = Node
Method = Edit
Node 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 between
point does not effect the results, so choose a distance =1.
In the Right Menu called Finite Elements
Set
Action = Create
Object = Element
Method = Edit
Shape = 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 result
Set
Action = Create
Object = Displacement
Type = 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 result
Set
Action = Create
Object = 0D
Type = Mass
Options = 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 Properties
Set
Action = Create
Object = 1D
Type = 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 window
Also use the pull-down menus to pick “UX” for Dof at Node 1 and for Dof at
Node 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 result
Set
Action = Analyze
Object = Entire Model
Type = Analysis Deck
Pick Solution Type
Choose NORMAL MODES for Solution 103.
Pick Subcases
In the Subcases pop-up menu
Set Action = Create
Choose a Subcase Name, e.g., subcase.1.
Pick Subcase Parameters
In the Subcase Parameters poop-up menu
Set
Extraction Method = Lanczos
Lower (Frequency Range of Interest) = 0
Number of Desired Roots = 2
Normalization Method = Maximum
Click OK
Click Apply. And Click Cancel.
Pick Subcase Select
In the Subcase Select pop-up menu
Select the subcase you created
Click OK
Click Apply to write the data deck.
5. Run Nastran
Add a grdset,,,,,,,23456 card to the bulk data deck first.
Then run NASTRAN
Check the frequencies and mode shapes in the .f06 file.
Attach the .xdb file to the Patran model
6. Display and Animate the Mode Shapes
From the Top Menu, choose Results.
A Right Menu called Results will result
Set
Object = Quick Plot
Choose (highlight) a mode under Select Result Cases, e.g., Mode 1.
Choose (highlight) Eigenvectors, Translational under Select Deformation Result
Check Animate box to see an animation of the mode.
In the Right Menu called Results
Set
Object = Graph
Set
Method = Y vs X
Choose (highlight) a mode under Select Result Cases, e.g., Mode 1.
Set
Y = Result
Set
X = Coordinate
Set
Select Coordinate Axis = Coord 0.1
Click on the Target Entities button, the second in the set of 4 buttons with graphics.
Set Target Entity = Nodes
Drag 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 choose
a different mode shape.