Flexural wave band gaps in a multi-resonator elastic metamaterial plate using Kirchhoff-Love theory

Miranda, Edson Jansen Pedrosa de; Nóbrega, Edilson Dantas; Ferreira, Anderson; Santos, José Maria Campos dos

doi:10.1016/j.ymssp.2018.06.059

Cited by 160 publications

(38 citation statements)

References 48 publications

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“…Nouh et al [39] Chen et al [41] created two resonator mass-in-mass lattice structures that had multiple bandgaps. Pai et al [42], Peng et al [43], Xiao et al [44], and Miranda Jr et al [45] proposed multi stopband metamaterials by replacing single mass-spring resonators with two integrated mass-spring subsystems.…”

Section: Introductionmentioning

confidence: 99%

Rainbow metamaterials for broadband multi-frequency vibration attenuation: Numerical analysis and experimental validation

Meng

Chronopoulos

Fabro

et al. 2020

Journal of Sound and Vibration

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In this study, we propose a 'rainbow' metamaterial to achieve broadband multifrequency vibration attenuation. The rainbow metamaterial is constituted of a Π-shaped beam partitioned into substructures by parallel plates insertions with two attached cantilever-mass acting as local resonators. Both resonators inside each substructure can be non-symmetric such that the metamaterial can have multi-frequency bandgaps. Furthermore, these cantilever-mass resonators have a progressively variant design along the beam, namely rainbow-shaped, for the purpose of achieving broader energy stop bands. Π-shaped beams partitioned by parallel plate insertions can be extended to honeycomb sandwich composites, hence the proposed rainbow metamaterial can serve as a precursor for future honeycomb composites with superior vibration attenuation for more industrial applications. A mathematical model is first developed to estimate the frequency response functions of the metamaterial. Interaction forces between resonators and the backbone structure are calculated by solving the displacement of the cantilever-mass resonators. The plate insertions are modeled as attached masses with both their translational and rotational motion considered. Subsequently, the mathematical model is verified by comparison with experimental results. Metamaterials fabricated through an additive manufacturing technique are tested with a laser doppler receptance measuring system. After the validation of the mathematical model, a numerical study is conducted to explore the influences of the resonator spatial

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Section: Introductionmentioning

confidence: 99%

Rainbow metamaterials for broadband multi-frequency vibration attenuation: Numerical analysis and experimental validation

Meng

Chronopoulos

Fabro

et al. 2020

Journal of Sound and Vibration

View full text Add to dashboard Cite

show abstract

“…For this, some scholars have proposed multidegree of freedom local resonance beam structures, namely, the LRPCs beam attached with multiple local resonators. And these LRPCs beams are always composed of the local resonators attached in series [29,30] or in parallel [25,[31][32][33], so as to obtain the multifrequency band gaps. Nevertheless, both the series type and parallel type might induce mass concentration of local resonators at connection point of the beam, which may adversely affect the structure.…”

Section: Introductionmentioning

confidence: 99%

Vibration Attenuation Investigations on a Distributed Phononic Crystals Beam for Rubber Concrete Structures

Zhang

Gao³

et al. 2021

Mathematical Problems in Engineering

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Locally resonant phononic crystals (LRPCs) beam is characterized by the band gaps; some frequency ranges within which flexural waves cannot propagate freely. So, the LRPCs beam can be used for noise or vibration isolation. In this paper, a LRPCs beam with distributed oscillators is proposed, and the general formula of band gaps and transmission spectrum are derived by the transfer matrix method (TMM) and spectrum element method (SEM). Subsequently, the parameter effects on band gaps are investigated in detail. Finally, a rubber concrete beam is designed to demonstrate the application of distributed LRPCs beam in civil engineering. Results reveal that the distributed LRPCs beam has multifrequency band gaps and the number of the band gaps is equal to that of the oscillators. Compared with others, the distributed LRPCs beam can reduce the stress concentration when subjected to vibration. The oscillator interval has no effect on the band gaps, which makes it more convenient to design structures. Individual changes of oscillator mass or stiffness affect the band gap location and width. When the resonance frequency of oscillator is fixed, the starting frequency of the band gap remains constant, and increasing oscillator mass of high-frequency band gap widens the high-frequency band gap, while increasing oscillator mass of low-frequency gap widens both high-frequency and low-frequency band gaps. External loads, such as the common uniform spring force provided by foundation in civil engineering, are conducive to the band gap, and when the spring force increases, all the band gaps are widened. Taken together, a configuration of LRPCs rubber concrete beam is designed, and it shows good isolation on the vibration induced by the railway. By the presented design flow chart, the research can serve as a reference for vibration isolation of LRPCs beams in civil engineering.

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“…In [15], resonating beams arranged in concentric circles were connected to a plate to create a directional cloak. Time-harmonic waves produced by an external force in a thin plate with attached masses were studied in [16]. The band structures of thin and thick plates incorporating periodic arrays of spring-mass resonators were discussed in [17,18].…”

Section: Introductionmentioning

confidence: 99%

Scattering Reduction and Resonant Trapping of Flexural Waves: Two Rings to Rule Them

2021

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In this paper, we discuss two problems concerning scattering and localisation of flexural waves in structured elastic plates. Firstly, we compare the scattering amplitudes of waves in a thin plate, generated by a point source, due to a single mass and to a large number of smaller masses, having the same equivalent mass and located around a circle. We show that in the second case, the scattering can be reduced, in particular in the medium- and high-frequency regimes. Secondly, we develop a homogenised model for a double-ring cluster of spring-mass resonators, connected to an elastic thin plate. We determine the conditions for which the plate exhibits vibration modes trapped between the two rings. Further, we show that the frequencies of the localised modes can be tuned by varying the geometry of the two rings and the characteristics of the resonators. The analytical results are corroborated by numerical simulations performed with independent finite element models.

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Flexural wave band gaps in a multi-resonator elastic metamaterial plate using Kirchhoff-Love theory

Cited by 160 publications

References 48 publications

Rainbow metamaterials for broadband multi-frequency vibration attenuation: Numerical analysis and experimental validation

Rainbow metamaterials for broadband multi-frequency vibration attenuation: Numerical analysis and experimental validation

Vibration Attenuation Investigations on a Distributed Phononic Crystals Beam for Rubber Concrete Structures

Scattering Reduction and Resonant Trapping of Flexural Waves: Two Rings to Rule Them

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