The flexural SSH-type model: Topology and edge states in elastic beam systems

We study the topological properties of slender flexural waveguides subject to kinematic constraints that selectively suppress rotations or transverse displacements. By deriving the 2 × 2 Bloch Hamiltonian, which possesses sublattice symmetry, we map the continuous flexural system onto the discrete Su-Schrieffer-Heeger (SSH) model and characterize its band topology. The emergence of topological edge states is also predicted by the quantized values of the Zak phase. In addition, we examine finite configurations with different boundary conditions to demonstrate bulk-boundary correspondence, revealing edge modes localized at either end depending on the termination and the coupling parameters. We further introduce elastic boundary springs as tunable elements to continuously control the existence and localization of edge modes. The present framework lays the groundwork for future extensions to more general flexural models, incorporating all kinematic variables, more elaborate boundary conditions, and additional physical effects.