Cable Vibration Considering Internal Friction

Abstract

The cable consists of an assemblage of wires laid helically around a core. The cable is widely used as an efficient structure for use in cable-stayed structures, for signal transmission and for power transmission. For overhead power transmission cables, both strength and dynamic characteristics are critical design parameters. Due to the inherently low damping characteristics of long span cables, vibration can result in damage to transmission cables and shorten their useful life. Moreover, for cable-stayed structures, vibrations can lead to a decrease in the cable load-carrying capacity. In addition, agreement on helical cable designs is difficult. Cable design choices include jacket materials, water blocking techniques, and the number of fibers to place within the cable. The cable design chosen depends on the cable's intended application. Each different application may require a slightly different cable design. The cable must meet minimal levels of performance in safety and durability (able to withstand shock, vibration, etc.). These current design concerns suggest that the dynamic behavior of cables need to be better understood. Determination of various mechanical characteristics of helical cables has never been an easy task. Substantial work has been accomplished over the past twenty years to model the structural behavior of such cables. The most important dynamical property of cables is wire slippage that creates large variations in flexural rigidity. Various flexural rigidities have been predicted by a number of previously developed models. In addition, the static and dynamic behavior of cables also have been predicted by previously reported models. The main focus of recent research has been the response of the cable under dynamic loading conditions. The primary dynamic response of cables includes free vibration and forced vibration. Gutzer, Seemann and Hagedorn (1995) applied a MASING model for a steel cable damping vibration system, in which the cable was analyzed as a collection of discrete and continuous systems of bonded layers. Each of the different layers consists of one or more parallel JENKIN or PRANDTL elements. The stick-slip behavior between the structural parts was simulated as a special case of static hysteresis. The slowly varying amplitude method and the phase method were used in the simulation to identify the damping parameters of the physical cable. Gatti-Bono and Perkins (2003) conducted an analysis of a two-dimensional towed cable in an attempt to cover all aspects of cable under tension, torsion, and two-axis bending. A numerical algorithm based on separate finite differencing in time and in space is described. Seabed contact forces are added by modeling the seabed as an elastic foundation with a prescribed profile. In deriving the motion of the cable, the cable was treated as a one-dimensional dynamic elastic inextensible continuum. An alternative approach of cable analysis was suggested by Zhong (2003). The cable is modeled as a one-dimensional continuum with varying flexural rigidity. A simplified cable vibration model, the frictional bending model (FBM), was developed to estimate cable damping due to internal friction. Her study showed that the numerical solution can be derived by directly integrating the equation of motion of the cable. The results of her study showed some agreement with experimental data. All of these investigations address the improvements of dynamic analyses of the cable, and that the effects of internal dry friction between helical wire layers of a cable playa significant role in the dynamic behavior of the cable. Although these research studies illustrate different applications of the cable, the major focus has been the dynamic response of these cables to external load and internal frictions. Their results provide methods for cable dynamic analyses, and are very helpful for the design of cable systems. Some of these analyses have resulted in rather complex stiffness matrixes, while others have focused on individual wires of cable layers, which may not be easily applied to other types of cables. The objective of this study is to develop a mathematical cable model to predict cable vibration and the attendant reduction in vibration amplitude due to internal friction caused by relative wire slippage, which allows a faster identification of the vibration nature of the cable. In addition, a computer program is to be developed to investigate cable free vibration cases using the mathematical cable model. Finally, the validity of this model is to be verified by experimental data for forced vibration.