Using the J L Analyzer
for Finite Element Analysis
of Wooden Plates - Part I
Free Plate Vibration
I have finished writing my book "Left-Brain Lutherie: Using Physics and Engineering Concepts for Building Guitar Family Instruments: An Introductory Guide to Their Practical Application". Details can be found here.
For the past month or two (Fall 2002), I've been trying out the J L Analyzer FEA software demo (500 nodes) available from www.autofea.com
Not being a math whiz or experienced with FEA, I have been heartened (after a continuing steep learning curve) by the simple things that the 500 node free demo model can do. Enough so that I've upgraded to the 3000 node model.
What am I trying out? Well, the first thing was just to do free plate frequency distributions and see the extent to which the model related to my measurements and the math model that Graham Caldersmith created.
Using the data in the
spreadsheet [ CalderPlateModes.xls
(to download double-click or option-click) ] I entered Lx, Ly, h, Ex, Ey, Exy, est. Gxy, est. nuxy and nuyx and density (lbm/in^3) and it took less than a minute for the program to generate modal frequency distributions (up to 50 can be calculated). All the modal frequency estimates were within 2-3 Hz of my actual measurements. There are many different display possibilities but the animated color ones with exaggerated vertical movement give me the most insight. The instructions below (modified from the JL Analyzer tutorial) give step-by-step instructions for repeating this experiment.
The procedures in the PROCESS menu (upper right screen) include:
1. Geometry modeling
2. Mesh generation
3. Material and geometry properties
4. Boundary condition and loads
Following the building of the model, we then proceed to:
B. Analysis, on the top menu bar
C. Examine results, in the PROCESS menu
Step A: Modeling
SPECIICATION OF THE PROJECT
The purpose of this lesson is to determine the modal frequencies of a wooden plate, 14 x 10.75 x .102 inches. The plate is free from any constraints.
Step 1: Geometry Modeling
1. Select the Geometry command in the PROCESS menu that is on the right and top corner of the screen
2. Select the Sketch command in the GEOMETRY menu
Note: Input a new project name if itís not available now.
3. Select the Rectangle command in the SKETCH menu
4. Move the cursor to the position (0, 0) then click the left button
Note: The cursor coordinates are shown at the bottom left corner of the graphics window.
5. Move the cursor to the position (14, 10.75), then click the left button (The rectangle is done.) If you can't get 10.75 exactly, 10.8 will be close enough.
6. Select the Done command in the SKETCH menu to finish sketch procedure and save the drawing to the database. The sketch grids will disappear and drawing is shown on the top view. Select the Return command in the GEOMETRY menu to return to the PROCESS menu
Step 2: Mesh Generation
Since this example has 3D geometry, we will mesh it as a shell element.
1. Select the Mesh command in the PROCESS menu
2. Select the Generate command in the MESH menu
3. Select the Shell command in the MESH Plate menu
4. Select the Accept commands in the Plate ELEM
Note: The commands Quad4 and Whole part are the default selections. If no highlighted on it, then click on it.
5. Input mesh length 1.0 in the dialog box
6. Click OK. The mesh creation procedure is finished and shown on the screen. Select the Return command in the MESH menu to return to the PROCESS menu.
Step 3: Assign Properties
The model must have a set of material properties. In this example we select the wood plate properties from the spreadsheet provided above.
1. Select the Property command in the PROCESS menu
2. Select the Material Property command in the PROPERTY menu
3. Select the Define command in the MATERIAL menu
4. Select Orthotropic from the M Type box, then fill in the properties from the spreadsheet using English units: Ex, Ey, Exy, nuxy, nuyz, Gxy and mass density.
5. Select the Whole part command in the M ASSIGN menu to assign the wood properties to the entire model. Click the Return command in the MATERIAL menu to return to the PROPERTY men.
The model must also have a third dimension. This step defines the plate thickness necessary for the plane stress element.
1. Select the Geometry Property command in the PROPERTY menu
2. Select the Thickness command in the GPROP menu
3. Select the Whole part command in the G SHELL menu
4. Input a value 0.102 in the dialog box for plate thickness, then click OK. Click the Return command in the GPROP menu, then click the Return in the PROPERTY menu to back to the PROCESS menu
Step 4: Define Boundary Conditions and Loads
There are no constraints or loads on this plate so this section will not be used.
The modeling is completed.
Click Analysis on the top menu, then select Frequency to perform frequency analysis.
In the Frequency menu, choose 20 for Eigen Values, 15 for max iterations, .001 for tolerance, check the box for frequency shift and put a value of -100 and check the box for modes. These calculations take about 12 seconds on my computer.
By choosing List in the top menu, then Results, then Frequency and Frequency again, you can see a list of the modes generated. In this case the first 6 modes are not relevant and should be ignored.
By going to the Process Menu and choosing Exam Results, then Frequency, then Animate, then Accept (allowing the default values) then choosing any mode value of 7 or above, you can then be treated to an animated view of the plate flexing. Very spiffy! Here are some stills of the Ex, Ey and Exy modes. The blue areas are the nodes...
If you have problems creating the file but want to see what the animations look like anyway, please download the following file and store it in the AutoFea folder:
Then open up the JL Analyzer and in the File menu choose Open Metafile. Choose PlateFlex1.ses from the listing. Now you can go directly to the Process Exam Results section, choose Frequency, Animate, etc. and off you go.
Now go back to the spreadsheet and look up the value of Lx/Ly for which the frequencies of the 2,0 and 0,2 modes are the same and then alter either Lx or Ly to attain that ratio. Repeat the above procedure and be treated to the "ring" mode!
The next procedure will show a wooden plate with two opposing edges flexibly fixed.
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