Mode conversions for elastic waves transmitted and reflected by ultrathin elastic metamaterial plates with anisotropic resonances

In this work, we study the conversions between longitudinal and transverse modes by one layer of oblique anisotropic dipolar resonators, whose size can be orders smaller than the wavelength. Mode conversions are found for both transmitted and reflected waves by such small resonators with a normal incidence. A mass-spring model is proposed to depict analytically the mode conversion, giving simplified analytical expressions for the conversion rates. The reflected conversion will gradually increase to the maximum while the solid material behind the resonators becomes soft, or vice versa. This work may provide theoretical guidance for practical applications.