Empirical Validation of Free Vibration of Sagging Cables

Abstract

Sagging cables lack unique natural state, but possess unique equilibrium state under sustained loads. However, for the purpose of predicting their dynamic response, the static equilibrium state of heavy cables under self-weight is assumed to be their initial state. The theory of sagging elastic cables presented earlier by the Authors pertains to weightless cables carrying nodal masses apart from static and inertial forces. For applying the proposed theory for sagging heavy cables, the cable is divided into ten segments of equal length. The initial equilibrium configuration of the cable fixed at both the ends is determined by the weights of these lumped nodal masses applied at ten nodes with one end fixed. The stiffness matrix of the cable is determined from tangent configurational flexibility matrix and tangent elastic flexibility matrix of twenty degree of freedom system. The cable tied at both the ends in an equilibrium state is set into motion by releasing it at one end. The theoretically predicted response of the cable is compared with the experimental data from the two investigations. The first experimental investigation by Fried pertains to the planar undamped vibrations of a sagging elastic cable, in which cable is released from its right end and its configurations are plotted at regular time intervals of 0.001s. In the second investigation by Koh, Zhang and Quek, the configurations of a different cable at regular time intervals of 0.125s during half the vibration cycle is measured. The dynamic tensile force at the fixed end has also been predicted in the latter case. The theoretical prediction of the evolving cable configuration have been found to be compatible with experimental data.