Enhanced modelling of cable-stayed bridge dynamics

The present review summarizes recent research results obtained in understanding and correctly modelling cable-deck dynamic interactions in cable-stayed bridges. With this aim, nonlinear analytical and finite element models are presented, in order to capture the main dynamic phenomena implying large amplitude cable vibrations due to possible mechanical energy transfer between deck and cables. A continuous model of a cable-stayed cantilever is formulated by means of the Hamiltonian Principle, in order to synthetically reproduce single-cable-deck interaction, while a sectional model is used to highlight the role played by different internal resonance conditions in the description of multi-cable-deck interactions. These simple models are used to interpret the main dynamics behaviors due to linear and nonlinear coupling both in the response of large finite element bridge models and in on-site measured response of the cable-stayed bridge. On the one hand, the spectral properties, obtained from the closed form solution of the linearized eigenproblems, exhibit strong localization of the eigenfunctions within a large range of the system parameters. However, particular combinations of the parameters are found to realize 1:1 internal resonance conditions between a global and a local mode. In these cases both the eigenfunctions undergo a hybridization process, due to a veering phenomenon which avoids the perfect coalescence of the related frequencies. The effect of this condition on the bridge dynamic response is then summarized. The phenomenon complexity is enriched by the description through a sectional model of the presence of several cables with close local frequencies tuned with a global frequency. On the other hand, the nonlinear phenomena responsible of high amplitude cable vibrations are effectively described by a two degrees of freedom model, obtained expressing the system displacement field as the linear combination of a global and a local mode. The resulting dynamic systems in the modal amplitudes, which presents a complete set of quadratic and cubic nonlinearities, is used to describe the relevant response of subharmonic 2:1 and superharmonic 1:2 global-local resonant systems. The analytical findings are verified by laboratory tests on an experimental specimen and the better understanding of the role played by internal resonances has been used to describe evident cable-deck interaction experienced on a cable-stayed bridges.