Whole-body finite-difference formulation of the violin
Rolf Bader · The Journal of the Acoustical Society of America · 2006
The whole body of a violin was modeled with the finite-difference method in terms of a transient calculation. The model, like a previous guitar body model, takes bending or transversal and longitudinal or in-plane motion of the wooden body into consideration and couples these two kinds of vibrations. Here, the curvature of the violin body also enhances this coupling according to the amount of curvature. The string/bow mechanism was modeled in terms of sticking/slipping, depending on the displacement difference of the bowing point to a point next to this bowing point. The different parts of the violin show different behavior within the steady state of one bowing cycle. Most noticeable, the ribs showed a chaotic motion, causing it to be quite small and greatly influenced by the surrounding parts. As this is practically the only part with noisy components, we can say the violin bowing noise comes from the ribs. Additionally, initial transients were modeled by changing the bowing pressure and velocity over the intial transient phase for a soft and a hard attack, resulting in reasonable descriptions of the violin playing attack.