The dynamical properties of a unit cell model for a CFRP is considered [2]. We -- joint work with S. Yoshikawa (Oita) - are interested in the asymptotic properties, e.g. damping of oscillations, as time increases, depending on the properties of the two different materials. Mathematically being a transmission problem [2], we investigate wave equations in an infinite two-dimensional waveguide. We prove that oscillations polynomially decay to zero as time tends to infinity. The presentation focuses on giving a suggestion how mathematics from PDE transmission dynamics might further enter the treatment of CFRPs. [1] J.E. Munoz Rivera and R. Racke, Transmission problems in (thermo)viscoelasticity with Kelvin-Voigt damping: nonexponential, strong, and polynomial stability, SIAM J. Math. Anal., \textbf{49} (5) (2017), pp. 3741-3765. [2] A. Oechsner, Mechanics of classical sandwich structures, Springer, 2023.