Amplitude-dependent group velocity transformations in nonlinear lattices with nonlocal coupling

Mass-spring lattices with weak stiffness nonlinearity undergo shifts in their band structure as a function of wave amplitude. Prior studies have characterized these shifts using perturbation techniques to derive small corrections to linear band structures. While lattice systems with nearest neighbor interactions are typically studied, growing attention is surrounding the effect of non-local elastic coupling. In this work, we report dramatic amplitude-dependentdispersion shifting in nonlinear lattices with nonlocal coupling. We demonstrate that nonlocal interactions with weak cubic stiffness have a profound impact on the amplitude-dependent group velocity of plane waves. Using a multiple scales perturbation technique, we obtain closed-form corrections to band structures that exhibit significant changes in sign and magnitude of group velocity compared to their linear counterparts. Analytical results are validated through direct numerical integration of the lattice equations of motion. [Work supported by the Office of Naval Research.]