Investigation of String Motions of Bowed String Instruments: A Finite Element Approach

Abstract

The bowed string motion of violin strings is examined using finite element analysis. The string is modeled as a bar with a finite number of elements, whereas the bow is one single node. The cause of the sound is the stick-slip effect, which occurs at steady bowing of a string. The contact area between the bow node and one string node is modeled as nodal contact. This work aims at investigating the Schelleng Diagram as well as the Guettler diagram. The Schelleng diagram shows bow force over bowing position and identifies the area of normal sound, i.e. the Helmholtz motion (von Helmholtz, Von den Tonempfindungen als physiologische Grundlage fur die Theorie der Musik. Vieweg, Braunschweig, 1863), overtone sound and raucous sound, the latter depicts bow force over bow acceleration in order to find a proper parameter configuration for “perfect bowing starts”. The influence of different friction curves of the rosin are modeled and simulated as well, which has been tested and investigated extensively in the literature mainly experimentally, see e.g (Smith, Woodhouse, J Mech Phys Solids 48(8):1633–1681, 2000).