Unified finite difference formulation for free vibration of cables

In this paper, a finite difference formulation for vibration analysis of structural cables is introduced. This formulation incorporates into a unified solution the effects of the bending stiffness of cable and its sag-extensibility characteristics and provides a tool for accurate determination of vibration mode shapes and frequencies. Various cable-end conditions, variable cross sections, and intermediate springs and/or dampers are taken into account. Using a nondimensional form of this formulation, a parametric study was conducted an the effects of sag-extensibility and bending stiffness. The formulation is verified with available theoretical solutions and compared with finite-element analyses. Capabilities of this formulation are demonstrated through examples. A simple relationship among nondimensional cable parameters is also introduced for the range of parameters applicable to stay cables in cable-stayed bridges. This simple relationship provides an accurate tool for measurement of tension forces in stay cables using the vibration method.