Propagation of Love waves in linear elastic isotropic Cosserat materials

We investigate the propagation of Love waves in an isotropic half-space modelled as a linear elastic isotropic Cosserat material. To this aim, we show that a method commonly used to study Rayleigh wave propagation is also applicable to the analysis of Love wave propagation. This approach is based on the explicit solution of an algebraic Riccati equation, which operates independently of the traditional Stroh formalism. The method provides a straightforward numerical algorithm to determine the wave amplitudes and speeds. Beyond its numerical simplicity, the method guarantees the existence and uniqueness of a subsonic wave speed, addressing a problem that remains unresolved in most Cosserat solid generalized continua theories. Although often overlooked, proving the existence of an admissible solution is, in fact, the key point that validates or invalidates the entire analytical approach used to derive the equation determining the wave speed. Interestingly, it is confirmed that the Love waves do not need the artificial introduction of a surface layer, as indicated in the literature.