Dispersion of Rayleigh waves in an elastic layer imperfectly attached to a microcontinuum substrate
Shikha Deep, Richa Goyal, Vikas Sharma
Abstract
The problem of Rayleigh waves is investigated in an isotropic elastic layer imperfectly bonded to a size-dependent substrate. The substrate is modeled using size-dependent consistent couple stress theory which involves an additional length-scale parameter called characteristic length (l), besides the Lame’s parameters of classical theory. The role of internal microstructures in defining the behavior of material at macroscopic level is captured through characteristic length parameter (l). Dispersion equation for the propagation of Rayleigh waves in considered geometry is obtained by using appropriate boundary conditions. Dispersion relation for the propagation of Rayleigh waves, when layer and substrate are in perfect contact has been established, as a special case. The dispersion equation of Rayleigh waves in a consistent couple stress substrate using stress-free conditions is also obtained. The role of imperfectness parameters, thickness of the layer and microstructural parameter of the substrate has been depicted on the dispersion behavior of Rayleigh waves.