On the existence of surface waves in an elastic half-space with impedance boundary conditions

In this work, the problem of surface waves in an isotropic elastic half-space with impedance boundary conditions is investigated. It is assumed that the boundary is free of normal traction and the shear traction varies linearly with the tangential component of displacement multiplied by the frequency, where the impedance corresponds to the constant of proportionality. The standard traction-free boundary conditions are then retrieved for zero impedance. The secular equation for surface waves with impedance boundary conditions is derived in explicit form. The existence and uniqueness of the Rayleigh wave is properly established, and it is found that its velocity varies with the impedance. Moreover, we prove that an additional surface wave exists in a particular case, whose velocity lies between those of the longitudinal and the transverse waves. Numerical examples are presented to illustrate the obtained results.

► We consider an elastic isotropic half-space with impedance boundary conditions.
► We study the existence of surface waves for these boundary conditions.
► We prove that the Rayleigh wave exists for all values of the impedance.
► We show the existence of an additional surface wave for a particular case.