The guitar is a widely used musical instrument which has evolved in many forms in order to accommodate the diversity of musical styles brought by different cultures. Of particular interest in this work, descendant from the European cittern, the Portuguese guitar is closely associated with the traditional music called "Fado" and, since recently, also plays a considerable role among urban Portuguese musicians. Contrary to conventional acoustic guitars, this guitar has a pear-shaped body with six pairs of metal strings tuned to octave and unison and supported by a "violin-like" floating bridge. From the dynamical point of view, if the bridge transmits the strings vibrations to the top plate of the instrument to maximize the radiated energy, it also couples all the strings together so that their dynamics influence the sound decay of the instrument by adding a subtle amount of beats, as well as an"aural sound" due to sympathetic string vibrations. Furthermore, contrary to the classical guitar, the strings extend beyond the floating bridge leading to additional dynamics. Following our recent work on the Portuguese guitar, we extend in this paper our developed linear physical-based model to account for nonlinear string effects and assert their significance on the string polarization and coupling of the string motions, as well as on the features of the instrument sound. Based on a modal approach, we propose a fully coupled string/body time-domain model comprising the nonlinear coupled dynamics of the twelve strings, the interaction between the bridge and the set of strings, as well as a realistic finite-element representation of a typical Portuguese guitar soundboard. Among other features stemming from our simulations, the nonlinear behavior is clearly audible similarly to what happens in real-life instruments.
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