Periodicity effects of axial waves in elastic compound rods

Nielsen, Rasmus Hjorth; Sorokin, Sergey

doi:10.1016/j.jsv.2015.05.013

Cited by 23 publications

(20 citation statements)

References 24 publications

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“…at /2 xl  , involve many frequencies, by contrast to the cases of a moving uniform, and a non-moving non-uniform string, cf. (30) and (34).…”

Section: Solution By the Methods Of Varying Amplitudesmentioning

confidence: 96%

“…This is in contrast to the case of non-moving periodic structures, for which all components of the compound wave feature the same frequency, cf. [24][25][26]30]. Indeed, for…”

Section: Solution By the Methods Of Varying Amplitudesmentioning

confidence: 99%

“…For non-moving spatially periodic structures the corresponding compound wave comprises many components with different wavenumbers, but the same frequency, cf. [24][25][26] and (29), (30). The dispersion relation of such a wave can be properly represented by the relation between the frequency and one of the wavenumbers [24], in some papers called the phase constant, cf.…”

Section: Dispersion Relation and Frequency Band-gaps 41 Non-moving mentioning

confidence: 99%

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Wave propagation in axially moving periodic strings

Sorokin

Thomsen

2017

Journal of Sound and Vibration

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“…at /2 xl  , involve many frequencies, by contrast to the cases of a moving uniform, and a non-moving non-uniform string, cf. (30) and (34).…”

Section: Solution By the Methods Of Varying Amplitudesmentioning

confidence: 96%

“…This is in contrast to the case of non-moving periodic structures, for which all components of the compound wave feature the same frequency, cf. [24][25][26]30]. Indeed, for…”

Section: Solution By the Methods Of Varying Amplitudesmentioning

confidence: 99%

Section: Dispersion Relation and Frequency Band-gaps 41 Non-moving mentioning

confidence: 99%

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Wave propagation in axially moving periodic strings

Sorokin

Thomsen

2017

Journal of Sound and Vibration

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“…The occurrence of band gaps in these infinite structures has been explained in light of gaps in the unit cell's dispersion curve (band diagram) and/or the negative effective mass density concept [29,30]. Discrepancies in the response of actual metamaterials motivated several efforts to understand band gap realizations in finite structures and the effect of imposed boundary conditions [31][32][33]. Significant among those is the investigation of the relationship between the borders of Bragg-effect band gaps in phononic (periodic) structures and the corresponding eigenfrequencies, explained using the phase-closure principle [32,33].…”

Section: Introductionmentioning

confidence: 99%

Formation of local resonance band gaps in finite acoustic metamaterials: A closed-form transfer function model

Ba’ba’a

Nouh

Singh

2017

Journal of Sound and Vibration

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The objective of this paper is to use transfer functions to comprehend the formation of band gaps in locally resonant acoustic metamaterials. Identifying a recursive approach for any number of serially arranged locally resonant mass in mass cells, a closed form expression for the transfer function is derived. Analysis of the end-to-end transfer function helps identify the fundamental mechanism for the band gap formation in a finite metamaterial. This mechanism includes (a) repeated complex conjugate zeros located at the natural frequency of the individual local resonators, (b) the presence of two poles which flank the band gap, and (c) the absence of poles in the band-gap. Analysis of the finite cell dynamics are compared to the Bloch-wave analysis of infinitely long metamaterials to confirm the theoretical limits of the band gap estimated by the transfer function modeling. The analysis also explains how the band gap evolves as the number of cells in the metamaterial chain increases and highlights how the response varies depending on the chosen sensing location along the length of the metamaterial. The proposed transfer function approach to compute and evaluate band gaps in locally resonant structures provides a framework for the exploitation of control techniques to modify and tune band gaps in finite metamaterial realizations.

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“…20 Huang, et al investigated the relation between bandgap properties and structures of periodic waveguides. 21 And, in 2015, Nielsen and Sorokin 22 demonstrated the relationship between the stopband patterns and two parameters of the corrugated waveguide, which are the impedance mismatch and the ratio of propagation times. Later in 2016, Sorokin 23 explored into the relationship between the amplitudes of the harmonics of the corrugation series and widths of the frequency band-gaps using the method of varying amplitudes.…”

Section: Introductionmentioning

confidence: 99%

Interactions between the first mode and the second Bragg gap in a cylindrical waveguide with undulated walls

Xue

Liu

et al. 2017

AIP Advances

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Interactions between the first mode and the second Bragg gap in a cylindrical waveguide with undulated walls Bragg resonances caused by the same transverse modes can always play a major role in periodic waveguides when the period is larger than the average radius. Because of higher-order mode cutoffs, the related Bragg gaps can be identified as interactions between different spatial harmonics of the fundamental mode, and the first Bragg gaps are more intensive than the higher ones. When we alter the parameters of the periodic waveguide, especially, decrease the period, the first transverse mode can be involved in Bragg gaps. Here, we demonstrate a direct mode-stopband interaction between the first mode and the second Bragg gap, that an extraordinary passband arises in the original second Bragg gap and splits the bandgap into two. Furthermore, the extraordinary passband is mainly composed of a pure first mode, which effectively suppresses the transmission of the fundamental one. We have also investigated the influence of wall profiles on the transmission and mode purity, and have found that the defined shape factor of wall profiles is proportionally related to the width of both pass and stop bands. The results could benefit not only the understanding of wave phenomena but also the applications in mode generators, filters, and so on.

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Periodicity effects of axial waves in elastic compound rods

Cited by 23 publications

References 24 publications

Wave propagation in axially moving periodic strings

Wave propagation in axially moving periodic strings

Formation of local resonance band gaps in finite acoustic metamaterials: A closed-form transfer function model

Interactions between the first mode and the second Bragg gap in a cylindrical waveguide with undulated walls

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