Wave propagation in fractionally damped nonlinear phononic crystals

Sepehri, Soroush; Mashhadi, Mahmoud Mosavi; Fakhrabadi, Mir Masoud Seyyed

doi:10.1007/s11071-022-07704-z

Cited by 5 publications

(1 citation statement)

References 92 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the intertwined effect of nonlinearity and damping is shown to be of great value in modelling and tuning the wave propagation behavior of PCs. Previous studies have investigated the effect of viscous and quadratic damping on monoatomic chains [41] as well as the effect of fractional damping on the wave propagation in nonlinear 1D and 2D monoatomic lattices [42]. Additionally, the analytical study of 1D diatomic nonlinear damped PC is another major contribution to the field [43].…”

Section: Introductionmentioning

confidence: 99%

Influence of coulomb damping on wave propagation behaviors of nonlinear nonconservative phononic chains/lattices

Sepehri

Bodaghi

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

Fascinating nonlinearity-induced behavior of phononic crystals (PCs) has recently become a hot research topic in the community. However, due to the limitations in the analytical modelling of damping in dynamic systems, the study of damped PCs has not received proper attention. In this paper, the influence of Coulomb damping on the wave propagation behavior of cubically nonlinear monoatomic phononic chains is investigated. To do so, the nonlinear dispersion relation is obtained analytically using the well-established multiple scales method and the band structure of the damped nonlinear chains is compared to the ones corresponding to the linear and nonlinear undamped chains. Due to the coupling between the amplitude and the frequency, stemmed from the nonlinear nature of the chain, Coulomb damping can lead to lower dispersion frequencies in the chain. The formulation and results are then expanded to 2D nonlinear lattices. The present manuscript is the first attempt to capture the effect of Coulomb damping on the wave propagation behavior of nonlinear lattices and the results put us one step closer to developing a comprehensive analytical model for the behavior of damped PCs which can in turn lead to invaluable design concepts for nonlinear nonconservative wave-manipulation devices.

show abstract

Section: Introductionmentioning

confidence: 99%

Influence of coulomb damping on wave propagation behaviors of nonlinear nonconservative phononic chains/lattices

Sepehri

Bodaghi

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

show abstract

Research on new wave behavior and mechanisms in nonlinear diatomic acoustic metamaterials with linear damping

Liu,

Xia

2023

Nonlinear Dyn

View full text Add to dashboard Cite

Elastic metamaterials with fractional-order resonators

Kaczmarek,

HosseinNia

2023

Fract Calc Appl Anal

View full text Add to dashboard Cite

Elastic metamaterials incorporating locally resonating unit cells can create bandgap regions with lower vibration transmissibility at longer wavelengths than the lattice size and offer a promising solution for vibration isolation and attenuation. However, when resonators are applied to a finite host structure, not only the bandgap but also additional resonance peaks in its close vicinity are created. Increasing the damping of the resonator, which is a conventional approach for removing the undesired resonance peaks, results in shallowing of the bandgap region. To alleviate this problem, we introduce an elastic metamaterial with resonators of fractional order. We study a one-dimensional structure with lumped elements, which allows us to isolate the underlying phenomena from irrelevant system complexities. Through analysis of a single unit cell, we present the working principle of the metamaterial and the benefits it provides. We then derive the dispersion characteristics of an infinite structure. For a finite metastructure, we demonstrate that the use of fractional-order elements reduces undesired resonances accompanying the bandgap, without sacrificing its depth.

show abstract

Wave propagation in fractionally damped nonlinear phononic crystals

Cited by 5 publications

References 92 publications

Influence of coulomb damping on wave propagation behaviors of nonlinear nonconservative phononic chains/lattices

Influence of coulomb damping on wave propagation behaviors of nonlinear nonconservative phononic chains/lattices

Research on new wave behavior and mechanisms in nonlinear diatomic acoustic metamaterials with linear damping

Elastic metamaterials with fractional-order resonators

Contact Info

Product

Resources

About