Dynamic stiffness matrix of an inclined cable

The free vibration analysis and a dynamic stiffness matrix for an inclined cable are presented. The cable is assumed to have an elastic catenary profile, and its chord-wise component of the self-weight and damping are considered. After linearization of the equations of motion, closed-form solutions of free vibration are derived. Based on the solution of free vibration of a cable with displaceable boundaries, the dynamic stiffness for each degree of freedom is derived by applying each harmonically varying boundary displacement and the dynamic stiffness matrix is assembled. The dynamic stiffness coefficient derived in this study is compared with other closed-form solutions. The characteristics of the dynamic stiffness coefficient and the effects of damping are investigated. The dynamic stiffness matrix for an inclined cable can be usefully applied to the dynamic analysis of cable-supported structures such as cable-stayed bridges or guyed masts.