Directional Control of Rayleigh Wave Propagation in an Elastic Lattice by Gyroscopic Effects

We discuss the propagation of Rayleigh waves at the boundary of a semi-infinite elastic lattice connected to a system of gyroscopic spinners. We present the derivation of the analytical solution of the equations governing the system when the lattice is subjected to a force acting on the boundary. We show that the analytical results are in excellent agreement with the outcomes of independent finite element simulations. In addition, we investigate the influence of the load direction, frequency and gyroscopic properties of the model on the dynamic behavior of the micro-structured medium. The main result is that the response of the forced discrete system is not symmetric with respect to the point of application of the force when the effect of the gyroscopic spinners is taken into account. Accordingly, the gyroscopic lattice represents an important example of a non-reciprocal medium. Hence, it can be used in practical applications to split the energy coming from an external source into different contributions, propagating in different directions.