Analysis of a Bowed String by the Method of Averaging

This experiment using a relatively simple apparatus shows how the method of averaging can be used to calculate different self-excited vibrations of a bowed string, if a certain number of modes and a special restriction in the phase differences for each mode are taken into account. First, the coefficient of friction as a function of the relative velocity is incorporated into a nonlinear analysis of the self-excited vibrations of a bowed string. Next, using Galerkin's procedure, the equation of motion for the bowed string is reduced to the nonlinear ordinary differential equations. Finally, the solutions for these equations, which are determined using the method of averaging, are compared with the computed results using the Runge-Kutta-Gill method and the experimental results.