Edge States and Topological Pumping in Spatially Modulated Elastic Lattices

Abstract

One-dimensional elastic lattices with spatial modulations of stiffness defined by the sampling of a two-dimensional surface exhibit non-trivial topological properties measured by integer valued Chern numbers. We show that non-trivial gaps in the spectrum are spanned by edge modes for finite lattices whose location is determined by the stiffness phase. These principles are applied for the implementation of a topological pump in an array of continuous elastic beams coupled elastically through a distributed stiffness. Adiabatic modulation of the coupling stiffness along the length of the beams drives a mode transition from a localized state at one boundary, to a bulk state and, finally, to another localized state at the opposite boundary.