ON THE VIOLIN FAMILY STRING/BODY DYNAMICAL COUPLING
O INÁCIO J ANTUNES MCM WRIGHT, José V. Antunes, MCM WRIGHT · 2023
paper 1 was a landmark pioneer effort on the dynamics of bowed strings.Since then, a plethora of research papers has been published on bowed-string instruments, including enlightening work by Friedlander 2 , Schelleng 3 , McIntyre, Schumacher and Woodhouse 4 , to name just a few classics among many other significant papers (see Cremer's book 5 , for an extensive account of the field).In previous work we developed a modal method to deal with plucked and bowed strings 6-9, enabling an effective simulation of such systems, even when dispersive effects are significant.As in most other published work, our simulations assume a string pinned at the bridge and the nut, and therefore decoupled from the instrument body.Such approach proved adequate to obtain the typical motion patterns displayed by bowed-strings.However, because the bridge is assumed motionless, computations are obviously unable to cope with more subtle phenomena related to the coupling of string and body motions.A crude approach to incorporate body effects, when simulating string sounds, is to start by computing the vibratory response of an "isolated" (bowed or plucked) string, and then use the resulting string/bridge interaction force to drive a given body vibro-acoustic transfer function.However, this simple approach is quite limited and cannot account for any energy feedback from the body into the string -such as found for instance in "wolf notes" -because no true string/body coupling has been modelled.To our best knowledge, only a few authors have attempted to address the string/body coupling problem.Schumacher, McIntyre and Woodhouse 4 incorporated in their wave-propagation computational algorithm a bridge-reflexion function which encapsulates the dynamical behaviour of a given body resonance, enabling them to simulate the coupled dynamics between the string and the chosen body resonance.In the same vein, Puaud et al.10 used in their work (connected with a so-called "numerical bow") a mass-stiffness bridge-resonator, therefore also emulating a chosen body-resonance coupled to the string dynamics.Recently, a different approach has been pursued by several authors to simulate instrument bodies and cavities -see Huang et al. 11