Wave propagation in stress-driven nonlocal Rayleigh beam lattices

Abstract

This paper focuses on small-size planar beam lattices, where size effects are modelled by the stress-driven nonlocal elasticity theory in conjunction with the Rayleigh beam theory. The purpose is to propose two novel computational approaches for elastic wave propagation analysis. In a first dynamic-stiffness approach, every lattice member is modelled by a unique two-node beam element, the exact dynamic-stiffness matrix of which is built solving, in concise analytical form, the stress-driven differential equations of motion. In a second finite-element approach, every lattice member is discretized by an increasingly refined mesh of two-node beam elements; in this case, the stiffness and mass matrices of the lattice member are obtained from shape functions built based on the exact solutions of the stress-driven differential equations for static equilibrium. Advantages of the two approaches are compared and discussed. Dispersion curves are calculated for a typical planar lattice, highlighting the role of nonlocality.