Vibration analysis of a bowed string involving dynamics of a soundbox and neck and its application to a Chinese traditional bowed string instrument "Erhu"

Abstract

In this paper, the author extends existing analysis methods for bowed string vibration to that involving the dynamics of a soundbox and neck of a bowed string instrument. Almost all the components of the instrument such as strings, nut, tuning pegs, neck, soundbox, and bridge are physically modeled and numerically analyzed by the finite element method, thereby yielding an equation of motion of the total multi-degree-of-freedom (MDOF) system. Then, the MDOF system is introduced into an existing equivalent circuit representation of the vibrations of a bowed string. The developed method is applied to the physical modeling sound synthesis of the erhu, a Chinese traditional bowed string instrument. Trial numerical calculations demonstrate that the developed method is effective in the sound synthesis of the erhu and also has the potential to analyze the three-dimensional spatial vibration of a bowed string and the effect of the interaction between the string and soundbox vibrations.