Non-Reciprocity in the Elastic Chain

We consider a microstructural lattice model consisting of two springs of different stiffness and identical mass. The dynamic behavior of the elastic system is investigated analytically and compared with numerical solutions. The results for the dispersion relation of the model have demonstrated obvious advantages associated with the manipulation of elastic wave propagation. Based on the model, a non-reciprocal device design is introduced by incorporating a gyroscopic spinner into one of the isolated masses. A particular non-reciprocal effect for transmitted waves due to the coupling effect is verified based on the theoretical concept supported by the computation of two mutual work between the applied forces.