From the ship sails to the suspension bridges, tensile structures have conquered the field of structural engineering, triggering also the interest of architects with their lightness and elegancy. Prestressed membranes or cable roofs, air-supported, inflated or tensegrity structures, suspension or cable-stayed bridges, antennae or guyed masts, sea-based applications, smaller structures such as snow avalanche nets, rock fall barriers, cranes, sailboats, mooring lines, trawl lines and nets, floating or submerged breakwaters, aerostats, or even simpler creations, such as the umbrellas or the rope we use to dry the laundry, belong to the family of tensile structures.

They consist of members that operate in pure tension. Their final shape depends on the loads and the initial pretension. They present large deformations with respect to the unloaded geometry, which influences also their stiffness. The analysis of such structures should be nonlinear for each load combination, considering large deformations, while the principle of superposition does not apply.

Cable nets, forming the surface of a hyperbolic paraboloid belong to this family of tensile structures. They have the capacity to cover large spans without intermediate supports and to carry loads much heavier than their own weight. They are attractive solutions for covering hangars, stadia, swimming pools, ice rinks, exhibition halls, theatres, concert halls, churches and other long-span areas.

This is an advanced course in dynamics, which requires a good knowledge of the theory of linear dynamics of structures. It constitutes a window to the extraordinary world of cable nonlinear dynamics. Although engineers are familiar with the science of linear dynamics, the nonlinear dynamic behaviour of tensile structures hides several new and different resonant phenomena, difficult to be detected. Let us discover them together.