Nonreciprocal Transmission of Non-collinear Mixing Wave in Nonlinear Elastic Wave Metamaterial

This investigation is focused on the nonreciprocal transmission of the non-collinear mixing wave in a nonlinear elastic wave metamaterial. The nonlinear elastic wave metamaterial with asymmetric structure is used to break the traditional reciprocal transmission, which is composed of a nonlinear material and a linear phononic crystal. When two non-collinear shear waves following the resonant condition interact with each other, the sum frequency longitudinal wave can be generated and propagate together with fundamental and second harmonics. Based on the transfer and stiffness matrices, band gaps and transmission coefficients are derived. The changing of band structures results in manipulating elastic waves with different frequencies. In the nonreciprocal frequency region, elastic waves can propagate along the positive direction while the reverse case is prohibited. The mixing of two incident SV waves in the nonlinear elastic wave metamaterial is verified by experiments and the results can support the theoretical analysis and numerical calculations. Because of material nonlinearity and asymmetric structure, the nonlinear elastic wave metamaterial can behave as a mechanical diode. The present work shows the possibility to design nonreciprocal elastic wave device by nonlinear wave mixing methods.