Finite-element simulation of the acoustic guitar

Abstract

The purpose of this work is a 3-D time-domain numerical modeling of the acoustic 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. A specific spectral method is used for solving the Kirchhoff-Love’s dynamic plate model for a damped, heterogeneous orthotropic material. The airplate interaction is solved with a fictitious domain method, which allows for making a good approximation of the geometry of the instrument while using a regular mesh for the calculation of the 3-D sound radiation. A conservative scheme is used for the time discretization. Frequency analysis is performed on the simulated sound pressure and plate velocity waveforms in order to evaluate quantitatively the transfer of energy through the components of the coupled system. The effects of structural changes in soundboard thickness and cavity volume on the produced sounds are presented. Simulations of the same guitar in three different cases are also performed: ‘‘in vacuo,’’ in air with a perfectly rigid top plate, and in air with an lastic top plate. This allows comparisons between structural, acoustic, and structural acoustic modes of the instrument.