Nonlinear dispersion relation in anharmonic periodic mass-spring and mass-in-mass systems

摘要: Abstract The study of wave propagation in chains anharmonic periodic systems is fundamental importance to understand the response dynamical absorbers vibrations and acoustic metamaterials working nonlinear regime. Here, we derive an analytical dispersion relation for mass-spring mass-in-mass resulting from considering hypothesis factorization spatial temporal parts solution a distribution function as ansatz general part equations motion. A comparison with numerical simulations shows range validity this expression. This work provides tool design dynamics some classes seismic such composite foundations, perturbative metamaterials, metasurfaces.