A coupled 3D finite element model of the sound production by mallet percussion instruments

The sound production in mallet percussion instruments involves mechanical vibrations, acoustical resonance, and radiation inherently coupled. The source of energy is the mallet that excites mechanical oscillations in the sound bar when the player hits one of the notes. The sound bar in itself is an inefficient radiator, therefore acoustical resonators are applied in order to reinforce the radiated sound. There are various challenges in modeling tuned idiophone instruments, including the nonlinear interaction of the mallet and the sound bar, the orthotropic behavior of the material of the bars, and the sound radiation into the half-open acoustical space. In this contribution the coupled finite element model of a xylophone is examined in detail. The three-dimensional model consists of mechanical and acoustical finite elements, and infinite acoustical elements that emulate free field radiation conditions. The coupled system is solved in the time domain with exploiting the benefits of the modal basis for reducing the size of the system of equations. The paper demonstrates the capabilities of the model, emphasizing the effect of two-way vibroacoustic coupling between the sound bar and the resonator. By analyzing the energy balance of the mechanical and acoustical subsystems the effect of tuning the resonator is investigated. The three-dimensional sound bar model is further exploited by studying the effect of the excitation of the torsional modes of the bar. Finally, synthesized sound samples illustrate the applicability of the model for physics-based sound synthesis