Topological Elastic Edge Modes

Kirchhoff plate lattice — mechanical analogue of topological insulators

Topological edge modes in mechanical lattices arise when the Zak phase (Berry phase across the Brillouin zone) is π. A 1D SSH-like dimerized chain of resonators supports interface modes protected by inversion symmetry.
ω²edge ≈ √(κ·(1/m + 1/M)) — within the bulk bandgap
The bulk-boundary correspondence guarantees a localized mode at the interface between topologically distinct phases. The left panel shows displacement amplitude; right shows the band structure with the edge mode (green dot) in the gap. Driving at the edge frequency shows exponential localization.