Mode-coupled infinite topological edge state in bulk-lattice-merged mechanical Su–Schrieffer–Heeger chain

Abstract

Band topology has emerged as a powerful tool for designing mechanical engineering systems, from phononic crystals to metamaterials. Various design principles — whether bulk-based or lattice-based — have been proposed and successfully implemented according to unit cell structures. Here, we present a bulk-lattice merged Su–Schrieffer–Heeger (SSH) chain constructed from single-column woodpile metamaterials. This system consists of a lattice array of cylindrical particles, where each particle's bulk dynamics exhibits local resonance-mode coupling with wave propagation. We demonstrate that topological edge states emerge in direct correspondence with these local resonance modes, manifesting as mode-coupled topological states. Experimentally, we observe the initial emergence of these mode-coupled topological edge states, with their frequencies accurately predicted by nonlinear characteristic equations rooted in continuum dynamics and topological symmetry. Additionally, the system's weak nonlinearity enables simultaneous frequency shifts, allowing multivariate tunability in its topological states. © 2025 Elsevier Ltd