Vibrations of cables with bending stiffness by an asymptotic approach

摘要

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