Weakly nonlocal Rayleigh waves with impedance boundary conditions

In this paper, we study the propagation of Rayleigh waves in a nonlocal orthotropic elastic half-space subject to impedance boundary conditions using the weakly nonlocal elasticity model which is introduced recently by the first two authors of the paper. The half-space may be compressible or incompressible. Our main aim is to derive explicit secular equations of Rayleigh waves and based on them examine the effect of nonlocality, impedance boundary conditions and incompressibility on the Rayleigh wave characteristics, such as the velocity and the displacement components at the half-space surface. The secular equation for the compressible half-space is derived using the surface impedance matrix method. The secular equation for the incompressible half-space is then obtained by employing the incompressible limit method. It is shown numerically that: (i) While the Rayleigh wave velocity decreases when increasing the nonlocal and impedance parameters, the incompressibility makes it increasing. (ii) The nonlocality affects very strongly the displacement amplitudes at the half-space’s surface, the incompressibility and the impedance boundary conditions affect them considerably.