Nonlinear Lateral Oscillations of Flexible Elements in Machines: Characteristic Features and Practical Applications

Abstract

Lateral oscillations of flexible elements (belts, cables, strings, etc.) in machines under simultaneous action of kinematical and parametric excitations are studied. Mathematically the problem is presented as a partial differential equation describing interaction of forced and parametric oscillations of flexible element with due account of its geometrical, static and physical nonlinearities. By the mathematical simulation the influence of additional pulsation of axial tension force of flexible element on parameters of its forced resonant oscillations has been analyzed. New approach to the suppression of unfavorable nonlinear resonant oscillations of flexible element based on application to the system of additional parametric excitation is proposed. This method makes it possible to prevent nonlinear pulling of resonant oscillations and thanks to this extends the allowable operating frequency range of machine. The results of theoretical study are confirmed by experiments.