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.