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Abstract

SENSITIVITY ANALYSIS OF THE NATURAL FREQUENCY AND MODAL EFFECTIVE WEIGHT OF MODE (0, 0) OF THE TOP AND BACK

PLATE OF AN ACOUSTIC STEEL-STRING GUITAR

USING FEM

Paul Michael Shaheen

December 2004

Tuning the top and back plate mode (0, 0) to a predetermined frequency has been established as a means to control sound quality of a guitar. Also, controlling the modal effective weight of mode (0, 0) of the top plate has been determined in recent research to have a possible influence on loudness and tonal balance. Understanding the factors that influence these parameters is important in the ability of the luthier to make sound decisions during the design process. In an effort to quantify the influences features and parameters have on the frequency and modal effective weight of mode (0, 0) of both the top and back plate, a FEM was created of a Martin D-28 folk guitar and a sensitivity analysis was performed. The influences for all iterations were reported as a percent change for each successive model as the features are added or the parameters changed.

Initially, the FEM was correlated to existing mode shape and frequency data. The frequency of mode (0, 0) of the top plate for the test case and FEM case was 163 Hz and 162 Hz respectively. The frequencies of mode (0, 0) of the back plate for the test case and FEM case were both 165 Hz. Both these results gave confidence to the model. The x-braces had the most affect on the top plate mode (0, 0) frequency with a +39.5% adjustment when added to the FEM. The back support braces had the most affect on the back plate mode (0, 0) frequency with a 68.8% adjustment when added to the FEM. The bass bars had the most affect on the top plate mode (0, 0) modal effective weight with a +750.5% adjustment when added to the FEM. The back support braces had the most affect on the back plate mode (0, 0) modal effective weight with an 84.4% adjustment when added to the FEM.