Expressions of nonlocal quantities and application to Stoneley waves in weakly nonlocal orthotropic elastic half-spaces

Abstract

In this paper, we introduce a novel model of nonlocal elasticity, called the weakly nonlocal elasticity, and provide explicit expressions of nonlocal quantities for harmonic plane waves propagating in the weakly nonlocal elastic solids. Then, we apply these expressions to investigate the propagation of Stoneley waves along the interface between two weakly nonlocal orthotropic elastic half-spaces. The half-spaces may be compressible or incompressible, and they are in welded contact. Our main aim is to derive explicit dispersion equations of Stoneley waves. First, we derive the explicit dispersion equation for the compressible case (when two half-spaces are compressible) using the surface impedance matrices of half-spaces. Then, the explicit dispersion equations for the incompressible cases (at least one half-space is incompressible) are obtained using the incompressible limit method. The simple and immediate derivation of these equations proves the convenience of the incompressible limit method. Some numerical examples are carried out to examine the effect of nonlocality and incompressibility on the Stoneley wave velocity.

On the well-posedness of Eringen’s non-local elasticity for harmonic plane wave problems

“…It is seen from figure 1 that: (i) the non-locality strongly decreases the Rayleigh wave velocity. (ii) The non-locality of Eringen's model decreases the Rayleigh wave velocity more strongly than the one of the weakly non-local model [46].…”

Wave propagation in context of Moore–Gibson–Thompson thermoelasticity with Klein–Gordon nonlocality

“…Recently, the solution to the differential model in context to Eringen's theory of nonlocal elasticity has been challenged by some researchers like Romano [39] and Kaplunov et al [40,41] by giving some counter examples. Anh and Vinh [42] introduced a novel model of weakly nonlocal elasticity in space and studied harmonic plane waves and Stoneley waves at an interface between two weakly nonlocal half-spaces. Anh et al [43] also studied the Rayleigh wave with impedance boundary conditions in context of weakly nonlocal elasticity.…”