Vibration modes and natural frequencies of saddle form cable nets

The objective of this paper is to investigate the dynamic behaviour of cable networks, in terms of their natural frequencies and the corresponding vibration modes. A multi-degree-of-freedom cable net model is assumed, having circular plan view and the shape of a hyperbolic paraboloid surface. The cable supports are considered either rigid or flexible, thus accounting for the deformability of the edge ring. On the basis of numerical analyses, empirical formulae are proposed for the estimation of the linear natural frequencies, taking into account the mechanical and geometrical characteristics of the cable net and the ring, expressed in the form of appropriate non-dimensional parameters. The sequence of the symmetric and antisymmetric modes of the network and the occurrence of modal transition can be predicted in relation to one of these parameters, in analogy to single cables. The differences between a network with rigid cable supports and one with boundary ring, concerning the eigenmodes and the corresponding eigenfrequencies are identified.