Using the J L Analyzer
for Finite Element Analysis
of Wooden Plates - Part III
Fixed Disk 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.
In Part I, we modeled free plate frequency distributions and saw the extent to which the model related to my measurements and the math model that Graham Caldersmith created.
We used the data in the
spreadsheet [ CalderPlateModes.xls
(to download double-click or option-click) ] and 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 gave me the most insight.
We'll now use the same data from the above spreadsheet and do a simple fixed disk model. The simple operations we'll do in this and the next tutorial will lead us to making an instrument top. The instructions below (modified from the JL Analyzer tutorial) give step-by-step instructions for repeating this experiment. Many of these steps are the same as in Parts I and II.
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 disk, 14 inches in diameter and 0.102 inches thick. The disk edges will be fixed.
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 Circle command in the SKETCH menu
4. Move the cursor to the position (7, 7) 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, 7), then click the left button (The circle is done.)
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 0.5 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
1. Select the BC/Load command in the PROCESS menu
2. Select the Constraint command in the BC/Load menu
3. Select the Define command in the CONSTRAINT menu
4. Select the Edge and Rigid Joint commands in the CNST DEFINE menu
Note: The commands Edge and Rigid joint are the default selections. If Edge and Rigid Joint are not highlighted, then click on it.
5. Pick the 2 opposing edges of the plate and a rim of blue colored triangles will appear.
6. Click the right button or click the left button on the empty place in the graphics window to finish the command. Click the Return command in the CONSTRAINT menu to back to the BC/Load menu.
Now Return to the Process Menu
The modeling is completed.
Click Analysis on the top menu, then select Frequency to perform the frequency analysis.
In the Frequency menu, choose 20 for Eigen Values, 15 for max iterations, and .001 for tolerance. Because the edges are rigid in this instance it's not necessary to 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 Displacement, you can see a list of the displacements generated.
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 1 or above, you can then be treated to an animated view of the disk flexing. Here are some stills of the 0,0 1,0 2,0 and 0,1 modes. The blue areas are the nodes...
Many other display options exist for the reader to explore on their own.
The next procedure will show alterations to a wooden disk with a fixed boundary (as time allows me to create the instructions).
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