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math.DS2025
On bandgap sensitivity to three-to-one internal resonances between acoustic and optical waves in metamaterials
Laura Di Gregorio, Walter Lacarbonara
We investigate the nonlinear equations governing wave propagation across a metamaterial consisting of a cellular periodic structure hosting resonators with linear and cubic springs…
math.DS2024★ 1 cited
Three-to-one internal resonances in coupled harmonic oscillators with cubic nonlinearity
Laura Di Gregorio, Walter Lacarbonara
We investigate a general system of two coupled harmonic oscillators with cubic nonlinearity. Without damping, the system is Hamiltonian, with the origin as an elliptic equilibrium…