Guitar analysis with Finite elements

Simulating a guitar:

The top plate's orthotropy was taken into account for and the material properties were taken from a book entitled "The Acoustics Of Wood". The lower string support was assumed completely rigid. Rigidity was also assumed for the rest of the guitar body and were modeled as "sound hard" boundaries. I did not take into account any damping effects.

The effect of the cross-like support structure under the bottom plate were not taken into account. It is a typical small displacement fluid-structure interaction problem. There is not a very good agreement with published results probably due to the aforementioned crude simplification. The picture including the top tone-wood plate is from an analysis taking into account the string excitation. The string excitation was simulated as a constant frequency acceleration parallel to the neck (the neck not depicted and not modeled). The analysis takes into account only the dominant eigenmode of the string, that is closer to a simulation of the string being plucked exactly at the center (Fret 12). The color scale is different in the various model result snapshots. The zero displacement obviously corresponds to the plate edge.

String displacements induced modulations:

Open bass E string:

Open A string:

Open D string:

At first I conducted a modal analysis of the air mass inside the guitar body for different frequencies to gain insight to the way the sound waves get excited by the top plate. However, the fluid-structure model, has significantly different eigenfrequencies. Below I present the modulating pressure distribution of the fluid structure eigenmodes

We can see easily see that the eigenmodes for the eigenfrequencies around the open string frequencies are the ones mostly taking part to the guitar body entraped air modulation. The fact that some of the the first eigenfrequencies (dominant - more energy) of the guitar body - enclosure system are close to the eigenfrequencies of the strings justifies the guitar body shape.

With computations and robust determination of the top plate tone-wood properties there may be room for signifficant improvements in the guitar design and resulting lowdness.

The unaccounted for supporting structure effect may be the reason for the difference between other published results. (see for instance http://dx.doi.org/10.1016/j.bbr.2011.03.031 )

A measure for energy - plate modulation energy for different notes

In the following chart, I present for the top plate an improvised measure of modulation energy and calculate the top plate energy for the 6 open string modulations. The measure is the logarithm of the squared absolute displacement multiplied by 20. That is for more accurate depiction of the human detectable acoustic energy transmitted away from the top plate.

There seems to be a nice uniform distribution of modulation energy along the six frequencies. However the arbitrariness of reference energy might lead to wrong insterpretation of the results.

To be done:

• Take into account the top plate truss support - compare with published results for verification,
• Calculate sound pressure induced outside the guitar and give a db response curve for all tones playable with the guitar,
• Experimentaly verify with the real guitar.

E-mail me or leave comments for questions and suggestions. I will give away the model as it currently is beyond request!