|
Chapter 5 |
|
CHAPTER 5 PROCEDURES
Overview The following section outlines the procedures followed in the analysis of the finite element model of the Martin D-28 guitar. All analysis was conducted using the Normal Modes Analysis in the Simulation module in I-DEAS 10. First, a normal modes analysis was performed on the top plate and the back plate in order to determine how closely the frequencies of the major modes of the FEM correlated to the actual tests results published by Rossing [9] on the same guitar model. Next, a sensitivity analysis was conducted to determine the following: influence of feature inclusion, parameter change, and arching on the frequency and modal effective weight on mode (0, 0) of the top plate and back plate. A step by step procedure for performing a normal modes analysis in I-DEAS can be seen in Appendix B.
Procedure for Normal Modes Analysis Top Plate A normal modes analysis was run for the top plate. The boundary conditions used were BC1 as described in Chapter 4. The first 20 modes were extracted. The following mode shapes were selected based on visual similarity comparison to the mode shapes published by Rossing [9]: (0, 0), (0, 1), (1, 0), (0, 2), (1, 1), (0, 3), and (2, 0). Figure 27 shows the mode shapes for the top plate from test results by Rossing [9].
FIGURE 27. Top plate mode shapes for actual Martin D-28 folk guitar [9].
Back Plate A normal modes analysis was run for the back plate. The boundary conditions used were BC2 as described in Chapter 4. The first 20 modes were extracted. The following mode shapes were selected based on visual similarity comparison to the mode shapes published by Rossing [9]: (0, 0), (0, 1), (0, 2), (1, 0), (0, 3), (1, 1), (0, 4), (2, 1), and (1, 2). Figure 28 shows the mode shapes for the back plate from test results by Rossing [9].
FIGURE 28. Back plate mode shapes for actual Martin D-28 folk guitar [9].
Procedure for Sensitivity Analysis Top Plate Influence of feature inclusion on frequency of mode (0, 0). Multiple FE models were created in I-DEAS with each model representing the successive feature inclusion to the top plate. For each model, a normal modes analysis was run and the frequency of mode (0, 0) was extracted. The boundary conditions used were BC1 as described in Chapter 4. Table 1 shows the model number and the feature added. Appendix D shows pictures of each model.
TABLE 1. Top Plate FE Models for Feature Inclusion
Influence of parameter change on frequency of mode (0, 0). Multiple FE models were created in I-DEAS with each model representing a parameter change to the top plate. For each model, a normal modes analysis was run and the frequency of mode (0, 0) was extracted. The boundary conditions used were BC1 as described in Chapter 4. Table 2 shows the model number and the parameter change.
TABLE 2. Top Plate FE Models for Parameter Change
Influence of arching on frequency of mode (0, 0). Multiple FE models were created in I-DEAS with each model representing a maximum top plate arch displacement of 0.00”, 0.050”, and 0.100”. The procedure used to create the arch was outlined in Chapter 3. For each model, a normal modes analysis was run and the frequency of mode (0, 0) was extracted. The boundary conditions used were BC3 as described in Chapter 4. Table 3 shows the model number corresponding to the maximum top plate arch displacement.
TABLE 3. Top Plate FE Models for Arching
Influence of feature inclusion on MEW of mode (0, 0). Modal effective mass extracted for mode (0, 0) from results of Chapter 5 and multiplied by 386.4 to convert modal effective mass (lbm) to modal effective weight (lbf).
Influence of parameter change on MEW of mode (0, 0). Modal effective mass extracted for mode (0, 0) from results of Chapter 5 and multiplied by 386.4 to convert modal effective mass (lbm) to modal effective weight (lbf).
Influence of arching on MEW of mode (0, 0). Modal effective mass extracted for mode (0, 0) from results of Chapter 5 and multiplied by 386.4 to convert modal effective mass (lbm) to modal effective weight (lbf).
Back Plate Influence of feature inclusion on frequency of mode (0, 0). Multiple FE models were created in I-DEAS with each model representing the successive feature inclusion to the back plate. For each model, a normal modes analysis was run and the frequency of mode (0, 0) was extracted. The boundary conditions used were BC2 as described in Chapter 4. Table 4 shows the model number and the feature added. Appendix D shows pictures of each model.
TABLE 4. Back Plate FE Models for Feature Inclusion
Influence of parameter change on frequency of mode (0, 0). Multiple FE models were created in I-DEAS with each model representing a parameter change to the back plate. For each model, a normal modes analysis was run and the frequency of mode (0, 0) was extracted. The boundary conditions used were BC2 as described in Chapter 4. Table 5 shows the model number and the parameter change.
TABLE 5. Back Plate FE Models for Parameter Change
Influence of arching on frequency of mode (0, 0). Multiple FE models were created in I-DEAS with each model representing a maximum back plate arch displacement of 0.00”, 0.100”, and 0.200”. The procedure used to create the arch was outlined in Chapter 3. For each model, a normal modes analysis was run and the frequency of mode (0, 0) was extracted. The boundary conditions used were BC3 as described in Chapter 4. Table 6 shows the model number corresponding to the maximum back plate arch displacement.
|
|
GuitarEngineer.com |
|
Front View of Vacuum System |
|
Technical information on classical and steel-string guitar research, design, manufacturing. |
|
Model |
Description |
|
1 |
Attached to Body |
|
2 |
+ Kerfing |
|
3 |
+ X-Braces |
|
4 |
+ Bass Bars |
|
5 |
+ Tone Bars |
|
6 |
+ Soundhole Bars |
|
7 |
+ Upper Bars |
|
8 |
+ Bridge Plate |
|
9 |
+ Bridge |
|
11 |
+ Arching 0.050" |
|
12 |
+ Arching 0.100" |
|
Model |
Description |
|
11 |
Baseline |
|
11.1 |
Sitka 1, EX, +15% |
|
11.2 |
Sitka 1, EX, -15% |
|
11.3 |
Sitka 1, density, +15% |
|
11.4 |
Sitka 1, density, -15% |
|
11.5 |
Top Plate, thick, +15% |
|
11.6 |
Top Plate, thick, -15% |
|
Model |
Description |
|
9 |
Arch 0.000" |
|
11 |
Arch 0.050" |
|
12 |
Arch 0.100" |
|
Model |
Description |
|
1 |
Attached to Body |
|
2 |
+ Kerfing |
|
3 |
+ Braces |
|
4 |
+ Reinforce Strip |
|
10 |
+ Arching 0.100" |
|
11 |
+ Arching 0.200" |
|
Model |
Description |
|
11 |
Baseline |
|
11.1 |
Rose 1, EX, +15% |
|
11.3 |
Rose 1, density, +15% |
|
11.4 |
Rose 1, density, -15% |
|
11.5 |
Back Plate, thick, +15% |
|
11.6 |
Back Plate, thick, -15% |