A phononic band gap model for long bridges. The 'Brabau' bridge case

In this paper, we study the dynamic flexural behaviour of a long bridge, modelled as an infinite periodic structure. The analysis is applied to the 'Brabau' bridge across the river Tirso in Italy. The approach reduces to a spectral problem leading to the analytical expression of the dispersion relation, which provides the ranges of frequencies for which waves do and do not propagate. The contributions of the bridge structural elements on the dispersive properties of the structure are investigated in detail. The direct link between frequency intervals determined by the proposed approach and distribution of eigenfrequencies of the full three-dimensional structure is demonstrated. The analysis of the unit cell allows to avoid the tedious computations required when using a finite element code, at least at a preliminary stage of the design. Finally, we demonstrate that a more precise prediction of the eigenfrequency ranges of the bridge can be obtained by studying a single repetitive cell numerically and imposing Floquet-Bloch conditions at its ends. The proposed approach can be implemented as a simple procedure to design structures with repetitive units, with the advantage of simplifying numerical simulations and reducing the computational cost.