The bufferness phenomenon in distributed mechanical system

✍ Scribed by A.Yu. Kolesov; N.Kh. Rozov

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 764 KB
• Volume: 65
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(01)00022-3

✦ Synopsis

Self-excited oscillations of weakly non-linear systems with distributed parameters are investigated. From the unified standpoints of the Lyapunov-Poincar6 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 mechanical objects, namely, a model of the transverse vibrations of a rotating thin shaft of circular cross-section, taking into account small internal and 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 oscillating circuit (an oscillator) of the Van der Pol type. In both models a "buffemess phenomenon" is established: the systems may have several stable limit cycles, depending on the values of the parameters (the angular velocity of rotation of the shaft or tension forces in the string) and corresponding to different oscillatory modes of distributed systems.