Non-Reciprocal Behaviour of a Gyroscopic Elastic Continuum

We study an elastic continuous half-plane endowed with distributed gyricity, which is capable of breaking the reciprocity of wave propagation. First, we determine analytically the dispersion properties of the system, and we observe a clear non-symmetry in the eigensolutions for positive and negative values of the wavenumber. Successively, we demonstrate the non-reciprocal behaviour of the gyroscopic continuum by performing an independent finite element computation, which shows a non-symmetric response of the medium to an external excitation. The results of this work can be employed in the design of mechanical splitters, that can channel wave propagation into predefined directions.