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Joint Applied Math and Probability Seminar
Numerical Simulation of the Acoustic Guitar
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The purpose of this study is the time-domain numerical modelisation of the acoustic guitar. The method consists in the modeling of the vibratory and acoustical phenomena from the initial pluck to the 3-D radiation. An idealized plucking force is acting on a 1-D damped string model. The string is coupled to the soundboard via the bridge. The soundboard is modeled as an orthotropic heterogeneous damped Kirchhoff-Love plate, with a soundhole, clamped at its boundaries. The other parts of the body (back, neck, sides...) are assumed to be perfectly rigid. The plate radiates both inside the cavity and in the external free field. The modeling of the complete 3D sound field is a new approach comparing to almost all previous works on the guitar, where the cavity is taken into account as a simple oscillator. We obtain a system of partial differential equations which are solved numerically in the time-domain. The space discretization of the equations relies on a mixed variational formulation of the complete system. The Kirchhoff-Love's dynamic plate equation is solved with a specific spectral method. For the string equation and the sound radiation, a standard mixed method for the space discretization and centered finite differences in time are used. The fluid-structure interaction is solved by the help of the fictitious domain method which allows to take into account the geometry of the guitar inside a uniform cubic mesh for the calculation of the 3D sound radiation. To simulate the free space, the actual computations are restricted to a box of finite size with the help of high order absorbing boundary conditions. The originality of the proposed scheme is a stable coupling method between a continuous time resolution and a discrete one. Number of numerical simulations are realized, which show the validity of the method and its application for acoustical purpose. |