Some Properties of Nonlinear Lateral Oscillations of Flexible Elements under Parametric Excitation

Lateral oscillations of flexible elements (belts, cables, guy ropes, strings, etc.) in machines and devices under parametric excitation are studied. Mathematically the problem is presented as a partial differential equation describing parametric oscillations of flexible element with due account of its geometrical, static and physical nonlinearities. Two different methods of analysis have been used: mathematical simulation on analogue-digital computer system and numerical solution with computer programme MATLAB. It is shown that under some conditions resonant parametric oscillations of flexible element occur within wide continuous frequency zones. 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