Demonstrating an In Situ Topological Band Transition in Cylindrical Granular Chains

We numerically investigate and experimentally demonstrate an in situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its interparticle stiffness in a controllable way, simply by changing the contact angles between the cylinders. The spatial variation of particles' stiffness results in an in situ transition of the system's topology. This manifests as the emergence of a boundary mode in the finite system, which we observe experimentally via laser Doppler vibrometry. When two topologically different systems are placed adjacently, we analytically predict and computationally and experimentally demonstrate the existence of a finite-frequency topologically protected mode at their interface.