### Numerical simulation of a guitar [chapter]

E. Bécache, A. Chaigne, G. Derveaux, P. Joly
2003 Computational Fluid and Solid Mechanics 2003
The purpose of this study is to present a time-domain numerical modeling of the guitar. The model involves the transverse displacement of the string excited by a force pulse, the flexural motion of the soundboard and the sound radiation in the air. We use a specific spectral method for solving the Kirchhoff-Love's dynamic plate model for orthotropic material, a fictitious domain method for solving the fluid-structure interaction and a conservative scheme for the time discretization. One of the
more » ... zation. One of the originality of the proposed scheme is a stable coupling method between a continuous time resolution and a discrete one. 2. The model. 2.1. Description of the guitar. The body of guitar is made up of the soundboard, the sides, the back and the neck. The 6 string are attached on one side to the neck and on the other side to the bridge. The soundboard itself is a thin wooden layer containing a sound hole and reinforced by struts (pieces of hard wood glued on its internal face which have a great influence on the shape of the structural modes of the soundboard and on the radiation efficiency of the guitar [39, 35] ). The sound produced by a string is appreciated since antiquity for its natural harmonic properties. Unfortunately, this sound is practically inaudible because of its very small diameter. The vibrations of the string are thus transmitted to the soundboard, which large area 2 ensures efficient coupling to the air. In addition, the soundboard is itself coupled to an acoustic cavity pierced by a hole in order to reinforce the sound power in the low frequency range, by the help of the Helmholtz resonance frequency [40, 23] . The following assumptions were made in order to propose a physical modeling of the instrument: • the amplitudes of vibration are small, which justify a linear model, • the body has no thickness and the neck is neglected, • only the soundboard vibrate (the rest of the body is supposed perfectly rigid), • the soundboard is modeled using a Kirchhoff-Love flexural plate equation (the motion parallel to the medium plan is neglected). The struts and the bridge are considered as heterogeneities, • only the transverse polarization of the string is considered: the in-plane displacement of the string (parallel to the soundboard) is neglected, • the string is excited with an idealized plucking force,