This paper deals with the free propagation problem of resonant and close-to-resonance waves in onedimensional lattice metamaterials endowed with nonlinearly viscoelastic resonators. The resonators’ constitutive and geometric nonlinearities imply a cubic coupling with the lattice. The analytical treatment of the nonlinear wave propagation equations is carried out via a perturbation approach. In particular, after a suitable reformulation of the problem in the Hamiltonian setting, the approach relies on the well-known resonant normal form techniques from Hamiltonian perturbation theory. It is shown how the constructive features of the Lie Series formalism can be exploited in the explicit computation of the approximations of the invariant manifolds. A discussion of the metamaterial dynamic stability, either in the general or in the weak dissipation case, is presented.

Free propagation of resonant waves in nonlinear dissipative metamaterials / Fortunati, A.; Arena, A.; Lepidi, M.; Bacigalupo, A.; Lacarbonara, W.. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A. - ISSN 1364-5021. - 480:2287(2024). [10.1098/rspa.2023.0759]

Free propagation of resonant waves in nonlinear dissipative metamaterials

Arena A.;Lepidi M.;Lacarbonara W.
2024

Abstract

This paper deals with the free propagation problem of resonant and close-to-resonance waves in onedimensional lattice metamaterials endowed with nonlinearly viscoelastic resonators. The resonators’ constitutive and geometric nonlinearities imply a cubic coupling with the lattice. The analytical treatment of the nonlinear wave propagation equations is carried out via a perturbation approach. In particular, after a suitable reformulation of the problem in the Hamiltonian setting, the approach relies on the well-known resonant normal form techniques from Hamiltonian perturbation theory. It is shown how the constructive features of the Lie Series formalism can be exploited in the explicit computation of the approximations of the invariant manifolds. A discussion of the metamaterial dynamic stability, either in the general or in the weak dissipation case, is presented.
2024
mechanical metamaterials; nonlinear damping; internal resonances; resonant normal forms; nonlinear waves
01 Pubblicazione su rivista::01a Articolo in rivista
Free propagation of resonant waves in nonlinear dissipative metamaterials / Fortunati, A.; Arena, A.; Lepidi, M.; Bacigalupo, A.; Lacarbonara, W.. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A. - ISSN 1364-5021. - 480:2287(2024). [10.1098/rspa.2023.0759]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1708712
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