NATURAL FREQUENCIES OF TWISTED CABLES: A NUMERICAL AND EXPERIMENTAL STUDY

Abstract

As the uses of cables have increased in different engineering applications, a better understating of their mechanical and dynamical behavior becomes more critical. Over the past several decades, many analytical, experimental, and finite element models have been developed to investigate vibrations of the cable structure. This attention explains the importance of such a structure, where it is more challenging than many ordinary structures because of the nonlinearity of the geometry and other combined effects. In addition, the twist along cable length leads to coupling behavior on the various kinematic variables of the cable system. This work is aimed at predicting and investigating the natural frequencies and the translations and rotations mode shapes occurring stimulatingly for both horizontal and inclined sagged cables, using both numerical and experimental methods An efficient numerical procedure using elasticity-based finite elements is presented to generate the primary elastic stiffness coefficients of single-layered six-wire strands where the cables are subjected to axial and torsional loads in three-dimensional space. Cable models with lay angles varying from 5 to 30 degrees are then compared to eight different one-dimensional analytical models for the same range of angles. The finite element model gives stiffness coefficients that are in good agreement with the analytical models for angles below the maximum angle of the cable. The free vibration behavior of untwisted and twisted cables is then analyzed using the derived stiffness and mass matrices. When discretized over the horizontal span, the sagged cable is represented using transformed axial, coupling, and torsional characteristics where the resulting two-node cable element has three translational and three rotational degrees of freedom. A similar computational approach is used for inclined cables using inclination angles from 10 to 60 degrees. The natural frequencies and modal shapes are found to be in very good agreement in comparison with the results obtained using extensive experimental tests for identical cable geometries and materials. Where a harmonically time-varying support motion is employed, undergo different conditions. The acceleration and angular velocity time histories are then collected by sensors mounted on the mid and quarter span of the cables. In addition to the experimental results, the frequency spectrum and the translational and rotational mode shapes are analyzed and compared with the limited analytical model available from the literature and the computer finite element software ABAQUS. Practical examples are used to demonstrate the validity and applicability of the finite element model for untwisted and twisted cables. Then, the influence of the principal and microstructural parameters variation on the dynamics of the cable is investigated. This study shows that the elasticity, twist coupling, initial sag, inclination angle, and self-weight of the cable play a considerable role in the frequency and modal coupling behavior. It further suggests that some of the simple models available may not be adequate to fully understand the significant levels of modal coupling in the cable's dynamic behavior. The methods used in this study are finally extended to experimentally find the internal damping ratios and the reduction in the in-plane peak motions when a damper is used.