Investigation of the Helmholtz Motion of a Violin String: A Finite Element Approach

Abstract

In the context of this work, a violin string motion is examined using a finite element approach. The string is formulated via ideal string elements and is bowed at one point on the string; hence, there is a nodal contact between the bow and the string. The bow movement induces the stick-slip effect, which is the cause for the violin string sound. The present paper aims at the investigation of the stick-slip phenomenon of bowed strings, considering well-known bowed string effects like the Helmholtz corner modulation, the Schelleng ripples, and the flattening effect. One key element that is used in this work is the Schelleng diagram, which indicates the “perfect” bow force depending on the bowing position. Within these parameters, the Helmholtz motion is carried out. Additionally, different friction characteristic curves are applied in order to study the impact of the rosin on the string motion.