Dynamic Stiffness Matrix of Sagging Cable

Abstract

The dynamic behavior of an extensible sagging cable is investigated. A dynamic stiffness matrix is presented whose coefficients are functions of the frequency of motion, and that is suitable for dynamic direct‐stiffness analysis of composed systems such as cable‐stayed bridges and guyed masts. The study is restricted to small displacements (linear theory) and considers motion within the vertical cable plane only. Viscous damping due to external fluid is taken into account. Trigonometrical solution functions with complex arguments are utilized, which implies a substantial simplification in the analysis of damped vibrations. By means of example calculations, stiffness functions are discussed and compared to the results of other authors. For tightly stretched inclined cables, utilization of the more accurate theory presented in this paper is indispensable.