Vibrations of cables with bending stiffness by an asymptotic approach

摘要

Vibrations of cables with a small bending stiffness concerns many engineering applications suchrnas the fatigue assessment of stay cables. With the Finite Element (FE) method, the analysis can be performedrnwith nonlinear truss elements, but bending effects are not taken into account. Otherwise, beam elements canrnbe used, but the smallness of the bending stiffness may lead to numerical instability and mediocre results inrnboundary regions.rnIn this context, the paper presents an alternative method to calculate the time evolution of the profile of bendingrnmoments in boundary layers of cables, avoiding heavy FE analysis. The developments combine the theory ofrnvibrations of extensible rods with asymptotic methods. The equations are decoupled between the slow dynamicsrnof the boundary regions and the fast dynamics of the span. Then, a composite solution is constructed by meansrnof a matched asymptotic procedure.