Transfer matrix for a weakly nonlocal elastic layer and Lamb waves in layered nonlocal composite plates

Abstract

In this paper, we establish the transfer matrix for an orthotropic elastic layer made of nanomaterial that is modeled by the weakly nonlocal elasticity model. This model is proposed recently and different from other existing nonlocal models of elasticity it has been proved to be well-posed for any problem of plane waves. Since the established transfer matrix is totally explicit, it is a convenient tool in investigating various problems of plane waves propagating in layered nonlocal elastic media. To prove this point, we use it to derive the dispersion equation of Lamb waves propagating in a composite plate consisting of two weakly nonlocal orthotropic layers. The dispersion equation in explicit form of Lamb waves has been derived, and it is shown that the derivation of this equation is much more simple than the one using the traditional technique. The obtained explicit dispersion equation will be used to establish techniques monitoring the health of layered nanostructures.