Some Characteristic Features of Nonlinear Parametric Oscillations of Flexible Elements

The aim of the paper is a study of nonlinear parametric oscillations of flexible elements in machines using three different methods of analysis: mathematical simulation on analogue-digital computer system, numerical solution with computer programme MATLAB, experimental investigations. Mathematically the problem is presented as a partial differential equation describing for lateral oscillations of flexible element under the periodic pulsation of its tension force with due account of geometrical, static and physical nonlinearities. It is shown that spectrum of resonance lateral oscillations of flexible elements may be sufficiently dense (simple parametric resonances of different orders, combination resonances). The evaluation of danger extent of different resonant regimes which can occur in the system is made. Under some conditions continuous resonant zones occur in wide frequency range, which defines the scientific novelty of these investigations. Besides, abrupt changes of amplitudes and modes of oscillations become possible within these zones. In such conditions system’s tuning away from dangerous resonant regimes remains problematic. The possible ways for practical application of these nonlinear effects are considered