Evolution of nonlinear Rayleigh waves in a coated substrate

Nonlinear Rayleigh waves propagating in a substrate coated with a thin elastic film are studied numerically. The evolution model consists of the nonlinear spectral equations of Zabolotskaya [J. Acoust. Soc. Am. 91, 2569-2575 (1992)] augmented ad hoc to include film dispersion. The dispersion relation is obtained from linear theory but is otherwise exact. Both loading and stiffening films are considered. Computations are performed for nonlinear evolution of an initially sinusoidal Rayleigh wave under three distinct dispersion regimes corresponding to different film thicknesses. The validity of the evolution model is also examined.