Novel Enriched Kinetic Energy continuum model for the enhanced prediction of a 1D lattice with next-nearest interactions

Abstract

In this paper, a novel Enriched Kinetic Energy model is proposed for an enhanced prediction of the dynamic behaviour of a one-dimensional lattice with next-nearest interactions playing an important role. The lattice system here considered is made up of a chain formed by particles equally spaced and connected with nearest and next-nearest neighbours, through linear springs with different stiffness. The ability of the novel model proposed in this work in capturing the dynamic behaviour of the lattice system is compared with that of others presented in the literature, concluding that it is the one that shows the best performance around the limit of the Irreducible Brillouin Zone (small wavelengths) when next-nearest interactions are relevant. For this purpose, natural frequencies provided by the continuum models for the finite solid are compared with those provided by the discrete system, considered as a reference. Moreover, the novel Enriched Kinetic Energy model does not present physical inconsistencies, nor higher-order spatial derivatives in its governing equation, so it does not need non-classical boundary conditions to be solved when finite solids are treated.