Self-induced vibrations in a string-bow system

Abstract

The vibrations of a thin stretched string is studied in the case when a bow slides on it with a constant velocity orthogonal to the string. The interaction between the bow and the string is governed by a smooth nonlinear law of friction with a falling segment of the characteristic. The motion of this mechanical system is described by an infinite coupled system of nonlinear ordinary differential equations. Some averaged equations of motion are derived in terms of the action-angle variables. The stationary points corresponding to self-vibration modes are found. The stability of these modes is analyzed.