Natural vibrations of suspended cables with flexible supports

A finite difference algorithm is applied to the study of in-plane natural vibrations of an inextensible cable with symmetric movable supports. Attention is given mainly to the analysis of the influence of support flexibility on the dynamic phenomenon. Several parametric studies are carried out and the analogy between the two cable models with lumped or distributed flexibility is shown. The main results regarding the influence of the elastic cable parameters, reported by earlier investigators, are obtained by lumping the cable flexibility at the supports. The algorithm can thus be applied over the whole sag/span ratio range and appears as a possible alternative to finite element models. Finally, the relative importance of cable and real support flexibilities in the dynamic behaviour of the system is examined. Besides numerical results, reference is made for the description of the transition phenomenon to a synthetic mechanical descriptipn based on Irvine's theory.