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Chapter 6 |
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CHAPTER 6 RESULTS
Normal Modes Analysis The results of the normal modes analysis are presented in Chapter 6 in 2 sections. The section headings are Normal Modes Analysis Results of Top Plate and Normal Modes Analysis Results of Back Plate. Both sections compare the results against the test results presented by Rossing [9].
Normal Modes Analysis Results of Top Plate Table 7 shows the frequency of each mode shape as reported by Rossing [9], and compares the findings versus the results found by normal modes analysis of the FEM. The last column reports the percentage difference of the tested frequencies of the modes versus the FEM results. To note, mode (0, 0) correlated well and the frequencies show less than 1% difference.
TABLE 7. Normal Modes Analysis Results for Top Plate
Figure 29 depicts the mode shapes of top plate mode (I0, 0) of the guitar found during the normal modes analysis and compares it to a graphical representation, shown in bottom right corner, of the same mode shape as observed during testing by Rossing [9]. Similar figures for all the modes listed in Table 7 are located in Appendix E.
FIGURE 29. Top plate mode (0, 0) [9].
Normal Modes Analysis Results of Back Plate Table 8 shows the frequency of each mode shape of the back plate as reported by Rossing [9] and compares the findings versus the results found by normal modes analysis of the FEM. The last column reports the percentage difference of the tested frequencies of the modes versus the FEM results. To note, mode shape (0, 0) correlates well and the frequencies show no difference.
TABLE 8. Normal Modes Analysis Results for Back Plate
Figure 29 depicts the mode (0, 0) of the back plate of the guitar found during the normal modes analysis and compares it to a graphical representation, shown in top right corner, of the same mode shape as observed during testing by Rossing [9]. Similar figures for all the modes listed in Table 8 are located in Appendix E.
FIGURE 30. Back plate mode (0, 0) [9].
Sensitivity Analysis The results of the sensitivity analysis are presented in Chapter 6. A first section shows the results for sensitivity analysis of the top plate related to the frequency of mode (0, 0). Another section presents the results for the sensitivity analysis of the back plate related to the frequency of mode (0, 0). A third section shows the results for sensitivity analysis of the top plate related to the modal effective weight of mode (0, 0). A fourth section presents the results for the sensitivity analysis of the back plate related to the modal effective weight of mode (0, 0).
Frequency of Mode (0, 0) for Top Plate The influence by feature inclusion. Table 9 and Figures 31 and 32 show the results of the successive addition of each feature of the top plate and the individual influence by feature on the frequency of mode (0, 0). To note, the features with the greatest influence were observed to be the x-braces with a 39.5% influence on the frequency of mode (0, 0), followed by the bass bars, 24.3%, and then the bridge with an 11.5% influence.
TABLE 9. Influence by Feature on Top Plate Mode (0, 0) Frequency
Figure 31 is a column chart showing the influence on the mode (0, 0) of the top plate in percentage form for each feature as it was added to the FEM.
FIGURE 31. Influence by feature inclusion on top plate mode (0, 0) frequency. Figure 32 is a line graph showing the natural frequency of mode (0, 0) of the top plate as each feature was added successively to the FEM.
FIGURE 32. Frequency of top plate mode (0, 0) by feature inclusion.
The influence by parameter change. Table 10 and Figures 33 and 34 show the results of changing various parameters of the top plate and the individual influence of each parameter change on the frequency of mode (0, 0). To note, the parameter change of greatest influence are observed to be the changing the thickness of the top plate by ±15%, which results in a +4.6% and -4.7% change respectively.
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Mode |
Frequency Test (Hz) |
Frequency FEM (Hz) |
∆ (%) |
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(0, 0) |
163 |
162 |
-0.6% |
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(0, 1) |
276 |
309 |
10.7% |
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(1, 0) |
390 |
404 |
3.5% |
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(0, 2) |
431 |
503 |
14.3% |
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(1, 1) |
643 |
474 |
-35.7% |
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(0, 3) |
733 |
649 |
-12.9% |
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(2, 0) |
756 |
815 |
7.2% |
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Mode |
Frequency Test (Hz) |
Frequency FEM (Hz) |
∆ (%) |
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(0, 0) |
165 |
165 |
0.0% |
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(0, 1) |
257 |
201 |
-27.9% |
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(0, 2) |
337 |
237 |
-42.2% |
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(1, 0) |
369 |
266 |
-38.7% |
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(0, 3) |
480 |
282 |
-70.2% |
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(1, 1) |
509 |
273 |
-86.4% |
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(0, 4) |
602 |
288 |
-109.0% |
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(2, 1) |
678 |
442 |
-53.4% |
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(1, 2) |
693 |
419 |
-65.4% |
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Model |
Description |
Mode (0,0) (Hz) |
∆ (%) |
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1 |
Attached to Body |
102.2 |
- |
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2 |
+ Kerfing |
104.5 |
2.3% |
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3 |
+ X-Braces |
145.8 |
39.5% |
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4 |
+ Bass Bars |
181.3 |
24.3% |
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5 |
+ Tone Bars |
183.8 |
1.4% |
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6 |
+ Soundhole Bars |
184.7 |
0.5% |
|
7 |
+ Upper Bars |
185.1 |
0.2% |
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8 |
+ Bridge Plate |
178.5 |
-3.6% |
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9 |
+ Bridge |
158.0 |
-11.5% |
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11 |
+ Arching 0.050" |
162.5 |
2.8% |
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12 |
+ Arching 0.100" |
171.5 |
5.5% |