Model-predicted geometry variations to compensate material variability in the design of classical guitars.

Musical instrument making is often considered a mysterious form of art, its secrets still escaping scientific quantification. There is not yet a formula to make a good instrument, so historical examples are regarded as the pinnacle of the craft. This is the case of Stradivari's violins or Torres guitars that serve as both models and examples to follow. Geometric copies of these instruments are still the preferred way of building new ones, yet reliably making acoustic copies of them remains elusive. One reason for this is that the variability of the wood used for instruments makes for a significant source of uncertainty-no two pieces of wood are the same. In this article, using state-of-the-art methodologies, we show a method for matching the vibrational response of two guitar top plates made with slightly different materials. To validate our method, we build two guitar soundboards: one serving as a reference and the second acting as a copy to which we apply model-predicted geometry variations. The results are twofold. Firstly, we can experimentally validate the predictive capabilities of our numerical model regarding geometry changes. Secondly, we can significantly reduce the deviation between the two plates by these precisely predicted geometry variations. Although applied to guitars here, the methodology can be extended to other instruments, e.g. violins, in a similar fashion. The implications of such a methodology for the craft could be far-reaching by turning instrument-making more into a science than artistic craftsmanship and paving the way to accurately copy historical instruments of a high value.

An entirely reverse-engineered finite element model of a classical guitar in comparison with experimental data.

The classical guitar is a popular string instrument in which the sound results from a coupled mechanical process. The oscillation of the plucked strings is transferred through the bridge to the body, which acts as an amplifier to radiate the sound. In this contribution, a procedure to create a numerical finite element (FE) model of a classical guitar with the help of experimental data is presented. The geometry of the guitar is reverse-engineered from computed tomography scans to a very high level of detail, and care is taken in including all necessary physical influences. All of the five different types of wood used in the guitar are modeled with their corresponding orthotropic material characteristics, and the fluid-structure interaction between the guitar body and the enclosed air is taken into account by discretizing the air volume inside the guitar with FEs in addition to the discretization of the structural parts. Besides the numerical model, an experimental setup is proposed to identify the modal parameters of a guitar. The procedure concludes with determining reasonable material properties for the numerical model using experimental data. The quality of the resulting model is demonstrated by comparing the numerically calculated and experimentally identified modal parameters.