Since a few years, in the field of computer music, researchers have designed efficient and realistic sound synthesis models to represent such physical phenomena. These so-called "waveguide" models represent in terms of linear filters (in the signal processing sense) the most important features of the propagation of waves between the two ends of the medium which are the propagation time, the dissipation and the dispersion phenomena. These filters can be deduced from the classical stress or flexural wave propagation equations, but more importantly, they can also be estimated from the analysis of real sounds, allowing a characterization of the propagation medium.

In many cases, the representation of the resonator of a musical instrument using a single waveguide is not sufficient. For example, in the case of a piano, around two hundred strings are mechanically coupled together at the bridge level. This complexity brought up the researchers to design coupled waveguide models which are able to represent the interactions between several elementary resonators. In a phenomenological point of view, a defective wood beam can be considered as a set of elementary resonators coupled by the defects, which makes the coupled waveguides models approach attractive for this problem. To validate this approach, we have built a set of wood beams with a defect artificially created, the position of which was varying. We have resynthesized in an accurate way the sound produced by their natural mechanical vibrations using a model involving two coupled elementary waveguides whose parameters have been adapted using a-priori knowledge on the beam. This synthesis model naturally takes into account the characteristics of the defect (position, reflection and transmission coefficients) as well as the propagation characteristics of the two parts without defects.

At this point of our study, we are convinced that this approach is relevant for the direct problem, which is the simulation of the vibrations of a defective wood beam, since such models are very easy to implement and fast to compute. Nevertheless, the most challenging point is the inverse problem which consists in estimating the parameters of the model from the analysis of the free vibrations of a defective wood beam. This part of the work is in progress.