Wave and vibration analysis of elastic metamaterial and phononic crystal beams with slowly varying properties

Fabro, Adriano T.; Beli, Danilo; Ferguson, N.S.; Arruda, José Roberto de França; Mace, Brian

doi:10.1016/j.wavemoti.2021.102728

Cited by 22 publications

(10 citation statements)

References 95 publications

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“…In addition, the zero-point energy should be included in the phonon occupation number when the temperature is above onethird of T D . [249] At low temperature, other methods, such as Monte Carlo simulations [213,[250][251][252][253][254][255][256] and ab initio calculations [257][258][259] mainly based on the discussion in Section 3.2.1, are more applicable to obtain κ and have been largely applied in recent literature on PnCs and MMs. Other methods, such as the Allen-Feldman theory for disordered harmonic solids [260] and atomistic Green's function method, [261] have also been widely used to study phonon transport, however, with constraints, including the negligence of anharmonicity, which requires further adaptations in their applications.…”

Section: Molecular Dynamics Simulation Of Phonon Transportmentioning

confidence: 99%

Phonon Engineering of Micro‐ and Nanophononic Crystals and Acoustic Metamaterials: A Review

2022

Small Science

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Figure 2. a,e) Experimental specimens of a regular Kagome lattice (a) and a topological Kagome lattice (e). b,f ) Isofrequency contours (first phaseconstant surface in the first Brillouin zone) of regular (b) and topological (f ) Kagome lattices calculated from FEA. c,g) Group velocity isofrequency contours (frequency increasing from dark red to bright yellow) highlighting symmetric or asymmetric directivity of regular (c) and topological (g) lattices. d,h) Snapshots of experimentally acquired wave fields in regular (d) and topological (h) lattices, confirming symmetric or asymmetric propagation. Colors denotes the magnitude of the scan point velocities, normalized by the largest value at the considered instants. a-h) Reproduced with permission. [40]

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Section: Molecular Dynamics Simulation Of Phonon Transportmentioning

confidence: 99%

Phonon Engineering of Micro‐ and Nanophononic Crystals and Acoustic Metamaterials: A Review

2022

Small Science

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“…Elastic/mechanical/acoustic metamaterial structures [ 1 , 2 , 3 ], generally composed of periodically arranged substructures in the form of sandwich structures [ 4 , 5 , 6 ], have special mechanical properties. It is a research hotspot in the fields of mechanics, materials, physics and engineering in recent years [ 7 , 8 , 9 , 10 ].…”

Section: Introductionmentioning

confidence: 99%

A Finite/Spectral Element Hybrid Method for Modeling and Band-Gap Characterization of Metamaterial Sandwich Plates

Linzhongyang

et al. 2023

Materials

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In this study, elastic metamaterial sandwich plates with axially deformed Timoshenko beam cores, considering both the out-of-plane and in-plane deformations of the face plates, are designed and the vibration band-gap properties are explored. The beam cores act as local resonators that can bear axial force, bending moment and shearing force. The finite element method (FEM) and the spectral element method (SEM) are combined to create the finite/spectral element hybrid method (FE-SEHM) for establishing the dynamic model and calculating the frequency response functions (FRFs) of the elastic metamaterial sandwich plate with axially deformed beam cores. It is observed that the metamaterial sandwich plate possesses both the axial and transverse vibration band-gaps of the beams, and the two kinds of band-gaps are independent. Compared with the metamaterial sandwich plates with rod cores, those with axially deformed beam cores have more extensive application ranges for vibration reduction.

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“…It was shown that band gaps can be simultaneously tuned by the axial force and the active electrical control actions for an actively controllable locally resonant beam [41]. A parametric investigation showed that a slowly varying spatial profile plays a role on the band gap performance and that the presence of a critical section can significantly affect the band gap width and the amplitude of vibration attenuation [42]. Inspired by above studies, a frequency response function based optimization scheme was presented for a locally resonant metamaterial beam that considers both the resonant frequencies and distribution locations of the resonators to achieve three optimization objectives involving broadband, multi-band, and high-attenuation characteristics [43].…”

Section: Introductionmentioning

confidence: 99%

Multiple resonances, fragmented propagation and homogenized attenuation of the beam model coupled with bi-periodic resonators

Tang

Ran

Zhang

et al. 2023

Preprint

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Wave propagation and attenuation behaviours of beam-resonators coupling model are dominated by the local resonators and the periodicity. Inspired by bi-periodic structures in engineering practice and based on a previous study, beam models coupled with bi-periodic resonators are proposed by introducing a parametric variant resonator into the periodic model. Wavenumber spectrum relation of the bi-periodic coupling system with a parametric variant resonator and several regular resonators is obtained by means of the method of reverberation-ray matrix and solved by numerical techniques. Effects of various parameters of the parametric variant resonator on the wavenumber spectrum characteristics of the bi-periodic models are investigated in numerical examples, which show that the parametric variant resonator results in an additional resonant peak and extra non-local resonant attenuation bands. Bandwidth of the local resonant attenuation band can be broadened by either increasing the translational stiffness or decreasing the mass of the parametric variant resonator. Compared to wavenumber spectrum curves of the beam model coupled with periodic resonators, the introduction of the parametric variant resonator makes the wavenumber spectrum curves of the real part divided into more curved and straight segments in an alternating presentation. The appearance of extra non-local resonant attenuation bands and the decrease of attenuation performance of the original non-local resonant attenuation bands indicates that the attenuation capability of the non-local resonant attenuation bands is homogenized in the frequency domain for the bi-periodic coupling system. The innovative findings and practical suggestions in the whole frequency range could provide potential references for the researchers and engineers in vibration reduction design of bi-periodic structures in engineering practice.

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Wave and vibration analysis of elastic metamaterial and phononic crystal beams with slowly varying properties

Cited by 22 publications

References 95 publications

Phonon Engineering of Micro‐ and Nanophononic Crystals and Acoustic Metamaterials: A Review

Phonon Engineering of Micro‐ and Nanophononic Crystals and Acoustic Metamaterials: A Review

A Finite/Spectral Element Hybrid Method for Modeling and Band-Gap Characterization of Metamaterial Sandwich Plates

Multiple resonances, fragmented propagation and homogenized attenuation of the beam model coupled with bi-periodic resonators

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