dispersion relation

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.

For the first time, a design of a “deflecting elastic prism” is proposed and implemented for waves in a chiral medium. A novel model of an elastic lattice connected to a non-uniform system of gyroscopic spinners is designed to create a unidirectional wave pattern, which can be diverted by modifying the arrangement of the spinners within the medium. This important feature of the gyro-system is exploited to send a wave from a point of the lattice to any other point in the lattice plane, in such a way that the wave amplitude is not significantly reduced along the path.