Model of influence of a rope defect on the spectrum of its free transverse vibrations

Abstract

In earlier work the possibility of diagnosing a defect of a steel wire rope by spectral composition of its free transverse vibrations was substantiated. In the present work, an analytical model of transverse vibrations of a steel wire rope with local damage is proposed. The presence of the defect in the model is taken into account only in the form of a loss of bending stiffness of the corresponding section without changing the specific mass along the length. The model represents three homogeneous rope sections “stitched” together, where the middle one represents a defective section with a lower value of bending stiffness. According to the model calculations, it is shown that the character of the dependence of the natural frequencies of oscillations on their number practically does not change in the presence of a defect. However, its presence and location affects the ratio of vibration amplitudes of undamaged sections, which can be used to monitor the condition of the rope.