Non-reciprocity and refraction of elastic waves in a solid with aligned parallel gaps

Abstract

Non-reciprocal and refractive devices for elastic waves are designed using a solid with aligned parallel gaps. The gaps are assumed to be thin so that they can be considered as parallel rectangular cracks separating effective thin plates. To formulate the transmission and reflection coefficients for SV- and P-wave, an analytical model is established using thin plate theory with displacement and force continuous at the junction between plate and exterior body. The analytical model compares well with full FEM simulations. The non-reciprocity effect for P-waves is achieved by sending an incident P-wave at a critical angle, at which total conversion to SV-wave happens, with respect to the normal of a free boundary. An array of parallel gaps perpendicular to the propagation direction of the reflected waves stop the SV-wave but let P-wave travel through. Thus, the energy transmission is high from one side to another and is low from the opposite direction. The refractive effect for SV-waves is achieved by choosing the slope of the edge of plate array, and plate members for |T| = 1 at the same frequency with the ratio between plate length and flexural wavelength fixed. Examples of elastic non-reciprocal and wave steering devices will be discussed.