Coupled Extensional-Torsional Vibration Frequency of Hoisting Rope in Tower-Type Friction Drive Hoist System
In order to avoid resonance, and to enhance safety of hoisting system and monitoring reliability, an impact mechanical model of mine hoisting rope for friction drive hoist system was built. According to Hamilton principle and considering the effect of oriented pulley and hoisting rope string, coupled extensional-torsional and extensional only mathematical models of hoisting rope were deduced. Mode shape and transcendental equation of angular frequency were obtained based on the hypothesis that the wave of vibration propagated with sine shape. With numerical calculation, results show that the frequency considering the effect of oriented pulley and hoisting rope string was slightly lower comparing with the frequency ignoring the effect at the bottom of shaft, but much different at the mouth; and there is significant difference between coupled frequency and extensional vibration only. Thereby, to make the design and monitoring of mine hoisting much more reliably, it is suggested that the extensional-torsional coupled vibration of hoisting rope, oriented pulley and hoisting rope string should be considered.
EFFECTS OF COUPLED EXTENSIONAL-TORSIONAL OSCILLATIONS IN WIRE ROPE DURING OCEAN SALVAGE AND CONSTRUCTION OPERATIONS
It is well established, and intuitively clear from the geometry of a wire rope, that a tensile load produces not only an extension but also a rotation of the rope (or a torque if both ends of the rope are prevented from rotating). This property of a wire rope leads, in a dynamic situation, to coupling of the extensional and rotational waves propagating through the rope. Classically, this coupling has been neglected, and only extensional waves treated, when analyzing the dynamic behavior of wire ropes used as lifting lines. Here, the effects of including the coupled oscillations in the dynamic analysis of lifting lines are considered, and the results are compared to those generated by the classical technique. Significant differences in the predicted dynamic response of the lifting line are found. A comparison of the predictions with experimental data also shows the importance of considering coupled extensional-torsional oscillations for obtaining an accurate description of lifting line dynamics.
On non-linear free vibrations of an elastic cable
Abstract The effect of non-linear terms in the equations of motion on the first normal modes of the oscillations of an elastic flexible cable under the action of gravity is studied. The non-linear equations are derived and approximate solutions are found by the Ritz-Galerkin method. A numerical example is given and the significance of the results is discussed with regard to the galloping oscillations of overhead transmission lines.