On different modes of Rayleigh wave fields in a micropolar nonlocal viscoelastic medium

This paper explores the propagation of Rayleigh wave fields in a viscoelastic medium under the framework of small-scale theories such as nonlocal elasticity and micropolar elasticity. Leading-order nonlocal corrected dispersion relations are derived by applying appropriate refined nonlocal traction-free boundary conditions. One of the dispersion relations is entirely due to the micropolarity and, therefore, vanishes in its absence. The other dispersion relation corresponding to its elastic counterpart gives rise to quasi-elastic and viscoelastic modes. Nonlocal elastic effects in viscoelastic solids also generate distinct nonlocal quasi-elastic modes that vanish without them. Two special viscoelastic solids, namely (a) an incompressible solid and (b) a Poisson solid, are numerically examined. An example with small viscous terms is considered, and conditions for the existence of various modes are derived. It further confirms the dependence of nonlocal and material parameters on the propagation of Rayleigh wave fields in different modes. Moreover, the equation for the path traversed by the Rayleigh wave field particles at the surface is evaluated, and the nature of the path (prograde or retrograde) is investigated for every possible mode of Rayleigh wave fields. Moreover, graphs are plotted using MATLAB software, specifically to comprehend the conditions imposed on the material and nonlocal parameters, as well as to observe the phase velocity behavior for all possible multiple modes.