Parametric-resonance-induced cable vibrations in network cable-stayed bridges. A continuum approach

There is a wealth of evidence to suggest that the bearing cables of cable-stayed bridges may experience large-amplitude oscillations, attributed in general to parametric resonance with the girder vibrations. A common coutermeasure consists of connecting the principal stays together with secondary cables to form a network and, here, optimal cable arrangments will be discussed when such a network is uniform and triangular meshed. The present approach is qualitative, and basically consists of homogenizing the cable net to an orthotropic elastic membrane, and then considering an auxiliary structure where the bridge girder, instead of being supported by the cable network, is supported by wedge-shaped membranes. The elastic solution under uniformly distributed loads, found using Lekhnitskii's approach, is the starting point for the discussion of the system in dynamic equilibrium. Having established a correspondence between the cable-net size and shape and the elastic moduli of the homogenized membrane, simple formulas are obtained to describe the global bridge vibration, as well as the local oscillations of the cables. It is then possible to estimate the girder and cable-net characteristic frequencies, to evaluate those conditions possibly leading to parametric resonance and, with respect to these variables, to determine optimal cable arrangements. This method is finally applied to the paradigmatic example of the Normandy Bridge.