Elastic wave propagation in weakly nonlinear media and metamaterials: a review of recent developments

Fronk, Matthew D.; Fang, Lezheng; Paćko, Paweł; Leamy, Michael J.

doi:10.1007/s11071-023-08399-6

Cited by 22 publications

(2 citation statements)

References 112 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the theoretical point of view, considering the distinctive contribution of different nonlinear sources in physical-mathematical models can substantially enrich the nature and multiplicity of stable solutions resulting from the governing equations of motion. From a methodological and technical point of view, harnessing the complexity of the nonlinear dynamic phenomena is progressively generating a paradigm shift in the conception and design of new-generation materials [5]. This revolutionary approach opens a wealth of opportunities for an entirely novel realm of functionalities, in which the oscillation amplitude regime is exploited as an extra design variable to trigger and govern hardening/softening behaviours, dispersion modulations, inertial amplifications, superharmonic frequency generations, enhanced dissipation mechanisms, non-reciprocal energy transfers, supertransmission channels, solitary waves propagations and wave interactions [6].…”

Section: Introductionmentioning

confidence: 99%

Free propagation of resonant waves in nonlinear dissipative metamaterials

Fortunati,

Arena,

Lepidi

et al. 2024

Proc. R. Soc. A.

View full text Add to dashboard Cite

This paper deals with the free propagation problem of resonant and close-to-resonance waves in one-dimensional 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.

show abstract

Section: Introductionmentioning

confidence: 99%

Free propagation of resonant waves in nonlinear dissipative metamaterials

Fortunati,

Arena,

Lepidi

et al. 2024

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…[4][5][6] Nonlinear wave propagation has attracted the attention of physicists and engineers because of its technological applications, such as shock damper and mechanical logic elements. [7][8][9][10][11][12][13] A thorough understanding of nonlinear wave propagation dynamics in the ordered granular chain(GC) is often considered as the groundwork.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric scattering effect of solitary wave in a two-section composite granular chain

Liu,

Jiao,

Zhang

et al. 2024

Nonlinear Dyn

View full text Add to dashboard Cite

This study presents numerical simulations on the asymmetric scattering effect of solitary waves in a two−section composite granular chain. On the basis of Nesterenko's work on solitary waves in monodisperse granular chains and continuous acoustic wave theory in linear medium, we argue that the mismatches of acoustic velocity and acoustic impedance, because of the differences of mass density and elastic coefficient, dominate the asymmetric scattering effect at the mismatched interface. The simulation results confirm the occurrence of a multipusle structure for the transmitted solitary waves when the solitary wave passes through the mismatched interface with a small−large wave velocity. The overshooting effect occurs for the reflected solitary waves because of the mismatched interface with high−low acoustic impedance. The phase diagram in the space of the mass density and the elastic coefficient ratio of the right−section granular chain to the left−section granular chain further validates the predictions. The results are crucial for the fundamental understanding of the dynamic behavior of solitary waves in granular chains.

show abstract

Elastic Wave Propagation in 2D Carbon Nano‐Onion Lattices

Lashani,

Ghavanloo

2024

Advcd Theory and Sims

View full text Add to dashboard Cite

This study presents a simple analytical model to investigate wave propagation in 2D carbon nano‐onions (CNOs) and nitrogen‐doped carbon nano‐onions (N‐CNOs) lattices. Furthermore, the dispersion relationships of the waves and bandgaps in these lattices are derived based on Bloch's theorem. The CNOs and N‐CNOs lattices are modeled as infinite 2D mass‐in‐mass structures accurately assembled using linear springs. The Lennard–Jones potential energy is employed to obtain equivalent spring constants. A key finding of this research is the identification of bandgaps within all lattice structures, signifying regions where wave propagation is prohibited. The existence of these bandgaps offers potential for the advancement of adjustable nano‐scale metamaterials.

show abstract

Elastic wave propagation in weakly nonlinear media and metamaterials: a review of recent developments

Cited by 22 publications

References 112 publications

Free propagation of resonant waves in nonlinear dissipative metamaterials

Free propagation of resonant waves in nonlinear dissipative metamaterials

Asymmetric scattering effect of solitary wave in a two-section composite granular chain

Elastic Wave Propagation in 2D Carbon Nano‐Onion Lattices

Contact Info

Product

Resources

About