Phononic Band Structures and Transmission Coefficients: Methods and Approaches

Vasseur, J. O.; Deymier, Pierre A.; Sukhovich, Alexey; Merheb, B.; Hladky‐Hennion, Anne‐Christine; Hussein, Mahmoud I.

doi:10.1007/978-3-642-31232-8_10

Cited by 12 publications

(4 citation statements)

References 28 publications

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“…For a periodic medium, this equation can be derived by applying the Bloch expansion theorem [5] to a representative unit cell and subsequently solving an eigenvalue problem for ω at specified values of k or for k at specified frequencies ω. These two solution techniques are known as ω(k)-or k(ω)-approaches, respectively [54,2,23]. Thus, by analyzing the dynamics of only a single unit cell, both approaches allow constructing a complete band/dispersion diagram including propagating and evanescent waves for an entire infinite periodic medium.…”

Section: Introductionmentioning

confidence: 99%

Visco-elastic effects on wave dispersion in three-phase acoustic metamaterials

Krushynska

Kouznetsova

Geers

2016

Journal of the Mechanics and Physics of Solids

131

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Section: Introductionmentioning

confidence: 99%

Visco-elastic effects on wave dispersion in three-phase acoustic metamaterials

Krushynska

Kouznetsova

Geers

2016

Journal of the Mechanics and Physics of Solids

131

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“…The derived dispersion equation establishes a relationship between the frequency ω and the Bloch parameter q, allowing us to construct a complete band/dispersion diagram including all possible propagating and evanescent wave modes. As will be seen in the next section, two different approaches exist: ω(q), obtaining ω for a given real value of q, and q(ω), giving q for specified real values of ω [35][36][37]. It should be noted that, in general, the in-plane elastic wave propagation involves a complicated coupling between P-waves (compressional waves) and SV-waves (vertically polarized shear waves).…”

Section: Wave Propagation In Layered Media With Suture Joints: Basic ...mentioning

confidence: 99%

“…The derived dispersion equation establishes a relationship between the frequency ω and the Bloch parameter q, allowing us to construct a complete band/dispersion diagram including all possible propagating and evanescent wave modes. As will be seen in the next section, two different approaches exist: ωfalse(qfalse), obtaining ω for a given real value of q, and qfalse(ωfalse), giving q for specified real values of ω [35–37].…”

Section: Wave Propagation In Layered Media With Suture Joints: Basic ...mentioning

confidence: 99%

Elastic wave dispersion in layered media with suture joints: influence of structural hierarchy and viscoelasticity

2023

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Suture joints contribute to the exceptional combination of stiffness, strength, toughness and efficient load bearing and transmission of many biological structures like the cranium or ammonite fossil shells. However, their role in the attenuation of vibrations and effect on dynamic loads is less clear. Moreover, the self-similar hierarchical geometry often associated with suture joints renders its treatment with standard numerical approaches computationally prohibitive. To address this problem, this paper investigates the dynamic response of periodic layered media with suture joints using an analytical approach based on material homogenization. A general trapezoidal suture geometry is considered together with the fundamental ingredients of hierarchy and viscoelasticity. The Spectral Element Method and Bloch theorem are used to derive the dispersion relation and band diagram of the system, including propagating and evanescent dispersion modes. A strong influence of the suture morphology and material properties emerges, and the analysis reveals an important advantage of adding hierarchy, i.e. the possibility of simultaneously obtaining wider bandgaps and their shift to higher frequencies. A synergy between hierarchy and structure is also observed, providing superior levels of wave attenuation. These findings suggest a possible design concept for bioinspired devices with efficient and tailorable wave attenuation properties.

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“…The calculation of vibrational properties -in particular phonon band structures -started with the very first papers on phononic crystals [20,21]. Several computational methods are available to study the phonon properties of phononic crystals [22]. Most of these methods are based on linear elasticity theory.…”

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confidence: 99%

Vibrational band structure of nanoscale phononic crystals

Meyer

2016

Physica Status Solidi (a)

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The vibrational properties of two-dimensional phononic crystals are studied with large-scale molecular dynamics simulations and finite element method calculation. The vibrational band structure derived from the molecular dynamics simulations shows the existence of partial acoustic band gaps along the $\Gamma$-M direction. The band structure is in excellent agreement with the results from the finite element model, proving that molecular dynamics simulations can be used to study the vibrational properties of such complex systems. An analysis of the structure of the vibrational modes reveals how the acoustic modes deviate from the homogeneous bulk behaviour for shorter wavelengths and hints towards a decoupling of vibrations in the phononic crystal.Comment: 9 pages, 6 figures. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archivin

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Phononic Band Structures and Transmission Coefficients: Methods and Approaches

Cited by 12 publications

References 28 publications

Visco-elastic effects on wave dispersion in three-phase acoustic metamaterials

Visco-elastic effects on wave dispersion in three-phase acoustic metamaterials

Elastic wave dispersion in layered media with suture joints: influence of structural hierarchy and viscoelasticity

Vibrational band structure of nanoscale phononic crystals

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