Closed-Form Vibration Analysis of Sagged Cable/Mass Suspensions

A theoretical model is presented which describes the three-dimensional nonlinear motion of a sagged cable that supports an array of discrete masses. An asymptotic form of this general model is derived for the linear response of a cable/mass suspension having small equilibrium curvature and horizontal supports. While the asymptotic model remains rich enough to capture dominant sagged cable effects, it is simple enough to permit closed-form analysis. A free vibration analysis is pursued that leads to closed-form solutions for problems which, heretofore, were analyzed using purely numerical methods. Among the advantages of the present method is its ability to pro vide results for: (1) complex mass arrays, (2) high-order modes, and (3) dynamic cable tension. Examples highlight the key role played by mass array symmetry and lead to new conclusions regarding free vibration.