Self-oscillations in the system string-bow / V. G. Vil'ke, I. L. Shapovalov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 1. P. 34-40 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 1-7].

The oscillations 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-oscillation regimes are found. The stability of these regimes is analyzed.

Key words: self-oscillations of a string, nonlinear viscous friction, averaging method, stability.

№ 1/2015