The bufferness phenomenon in distributed mechanical system

Self-excited oscillations of weakly non-linear systems with distributed par ameters are investigated. From the unified standpoints of the Lyapunov-Poin care perturbation method, the limit cycles are determined in a constructive manner and conditions are found for the existence and stability of "quasi- linear" self-excited oscillatory modes of behaviour for two classes of mech anical objects, namely, a model of the transverse vibrations of a rotating thin shaft of circular cross-section, taking into account small internal an d non-linear external viscous friction, and a two-dimensional model of the linear vibrations of a string connected at its midpoint to a self-excited o scillating circuit (an oscillator) of the Van der Pol type. In both models a "bufferness phenomenon" is established: the systems may have several stab le limit cycles, depending on the values of the parameters (the angular vel ocity of rotation of the shaft or tension forces in the string) and corresp onding to different oscillatory modes of distributed systems. (C) 2001 Else vier Science Ltd. All rights reserved.