Partial and Lamb waves in non-local elasticity with kernel modification

We study dispersion of Rayleigh-Lamb (R-L) waves in an infinite isotropic strip within the theory of non-local elasticity with kernel modification. Within this approach, the set of constitutive boundary conditions (CBCs) embedded in the attenuation functions contain the set of natural boundary conditions (BCs) of the problem and this feature, besides avoiding nonphysical BCs, warrants that the problem is well-posed. We show that, contrast to local elasticity, the dispersion equation emerges from imposing the equations of motion, given that the BCs are automatically satisfied by the very choice of the attenuation functions. Similarly to local elasticity, the problem naturally decouples into symmetric and anti-symmetric partial modes, although this feature is not obvious here and crucially depends on certain symmetry properties of the kernels. We prove that symmetric and anti-symmetric kernels may be constructed directly, to avoid solving the full problem, and we show how these kernels relate to the original. Explicit dispersion relations for symmetric and anti-symmetric partial waves are obtained, that reveal the size-dependent deviation from the classical predictions. Overall, results reproduce the general features already observed in local elasticity, such as the convergence of the fundamental modes the Rayleigh speed and of the higher modes to the bulk wave speeds, although these are no longer constants. Yet, both fundamental modes, and especially the symmetric one, significantly depart from the local theory, which fact has important consequences on the corresponding asymptotic model for non-local beams.