Propagation of Stoneley wave along wavy interfaces between two half-spaces

We put forward the characteristic equation of Stoneley waves along wavy interfaces, and calculate the dispersion curves, wave structures and cutoff frequencies. After confirming the existence of Stoneley waves at flat interfaces, by incorporating wavy boundary conditions, we derive the governing equation and reveal unique propagation behaviors, specifically a velocity reduction followed by an increase at high frequencies. Furthermore, the cutoff frequency is directly proportional to the Stoneley wave velocity and inversely proportional to the wavy period. The results indicate that the stable Stoneley wave propagation is confined to frequencies below the cutoff limit and to interfaces with a relatively low steepness. Finite element simulations are performed, and four different experimental samples are employed to verify the existence and characteristics of Stoneley waves such as dispersion curves and cutoff frequencies. The findings significantly advance the understanding of Stoneley wave propagation characteristics in wavy interfaces and establish a robust theoretical foundation for nondestructive evaluation in structures with wavy interfaces.