Existence and uniqueness of subsonic surface-wave speed in generalized Cosserat continua

Establish the existence and uniqueness of a subsonic surface-wave speed for Love-wave propagation in Cosserat solids within generalized continuum theories beyond the isotropic linear Cosserat half-space, by proving that the corresponding secular equation admits an admissible solution ensuring exponential decay with depth and ruling out spurious roots.

Background

The paper develops a matrix-analysis method based on an algebraic Riccati equation to determine wave amplitudes and speeds for Love waves in an isotropic linear Cosserat half-space. A key contribution is a rigorous proof of existence and uniqueness of the subsonic wave speed, which validates the secular equation and avoids spurious roots without relying on Stroh formalism.

The authors note that, although Love waves in Cosserat materials have been studied, the proof that the secular equation admits an admissible solution ensuring decay with depth has often been missing. While their approach resolves this issue for isotropic Cosserat materials, they explicitly state that the broader problem remains unresolved in most Cosserat solids generalized continuum theories.