Topological dynamics of continuum lattice structures

Continuum lattice structures which consist of joined elastic beams subject to flexural deformations are ubiquitous in nature and engineering. Here, first, we reveal the topological dynamics of continuous beam structures by rigorously proving the existence of infinitely many topological edge states within the bandgaps. Then, we obtain the analytical expressions for the topological phases of bulk bands, and propose a topological index related to the Zak phase that determines the existence of the edge states. The theoretical approach is directly applicable to general continuum lattice structures. We demonstrate the topological edge states of bridge-like frames, plates, and continuous beams on elastic foundations and springs, and the topological corner states of kagome frames. The continuum lattice structures serve as excellent platforms for exploring various kinds of topological phases and demonstrating the topologically protected states at multifrequencies, and their topological dynamics has significant implications in safety assessment, structural health monitoring, and energy harvesting.