Topologically Insulated Modes in Strongly Nonlinear Mechanical Chains

The adaption of topological band theory in classical mechanics is unlocking topologically protected waves in acoustic and elastic media. The theoretical underpinnings of insulator theory rely on the application of the Bloch theorem. However, this is not applicable in the strongly nonlinear regime. To address this, we consider a mechanical analog of the Su-Schrieffer-Heeger interface model with the addition of a strong cubic nonlinearity. Numerical continuation of the systems nonlinear normal modes (NNMs) reveals the frequency-energy evolution of the topological mode and bulk-spectra. Then, the nontrivial half-lattice is numerically simulated at the high-symmetry points of the Brillouin Zone to recover empirical estimates of the systems Zak Phase to define a critical energy level. The critical energy level is confirmed by numerically simulating the full system at various energy-frequency combinations to uncover at which energies the topological mode can be excited. Interestingly, this energy level is found to coincide nearly perfectly with the energy level at which the topological NNM intersects the linear bulk-spectrum.