Wave propagation in stress-driven nonlocal Rayleigh beam lattices. (1st February 2022) - Russillo, Andrea Francesco; Failla, Giuseppe
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. Graphical abstract: Highlights: Small-size 2D beam lattice modelled by stress-driven nonlocal Rayleigh beam theory. Elastic wave propagation analysis by dynamic-stiffness or finite-element approaches. Dynamic-stiffness approach: Unique beam element for lattice member. Finite-element approach: Nonlocally interacting beam elements for lattice member. Finite-element results converge to dynamic-stiffness ones for refined meshes.