Time history theoretical analysis for stick-slip vibration of violin strings

Abstract

The stick-slip vibration of violin string was completely formulated by using CA (Cellular Automaton) method in time history analysis. The local neighborhood rule of the CA method was derived for the travelling wave along the string, both ends of string, and the bow point. The key in success is that the bow point is to be fixed point and also to be velocity excited point at the same time. This means that reflected wave velocity is equal to the incidental wave velocity plus bow velocity. Displacement of arbitrary point of string is calculated and is compared with measured one. Excellent agreement of displacement suggests that CA method can simulate the stick-slip vibration of violin string. Acceleration time of the bow until it reaches a certain speed is also studied to form a complete Helmholtz waves. Step input and acceleration time within fundamental period is not valid to form Helmholtz wave. Acceleration time of more than four times of the fundamental period can substantially form Helmholtz waves.