Studies of band gaps in flexural vibrations of a locally resonant beam with novel multi-oscillator configuration

Zuo, Shuguang; Tianxin, Ni; Wu, Xudong; Jialu, Fan

doi:10.1177/1077546315598032

Cited by 32 publications

(13 citation statements)

References 40 publications

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“…Substituting Eqs. (15) into the differential df f0 = dX 2 √X obtained from the definition X = ω 2 /ω 2 0 easily leads to . The roots provides the eigen frequencies and so the band gap limits for C = 0 (full line), C = 0.6 (dashed line), C = 0.9 (dotted line).…”

Section: Dispersion Curves and Analytical Derivation Of The First Banmentioning

confidence: 99%

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On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

Pelat

Gallot

Gautier

2019

Journal of Sound and Vibration

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This work aims to provide better physical understanding of Bragg band gap effects in continuously periodic corrugated beams for flexural waves. The main outcome is the establishement of original algebraic formulas for the band gap width and central frequency. It is shown that the band gap width and central frequency only depend on a thickness contrast parameter. To do so, a so called two-skins geometry is proposed to approximate the usual solid beam cross section, in order to greatly simplify analytical derivations following the Plane Wave Expansion (PWE) method applied to Euler-Bernoulli theory. Theoretical predictions in the two-skins geometry successfully match the results in the practical case of a solid geometry obtained from both experiments on a beam demonstrator and numerical simulations done by classical PWE (1D Euler and Timoshenko theories) or finite element (3D elasticity theory) methods. The complete set of results is benchmarked in details so that the geometrical approximation is validated and the algebraic formulas are usable as design tools of such notch filters. Moreover, flexural and longitudinal motion coupling due to the non-symetrical thickness profile of the demonstrators leads to an additional band gap that is experimentally identified. A numerical study illustrates the resulting double filtering effect. Potential applications of the background provided by this work can concern Noise,Vibration and Harshness (NVH) engineering, for which meta-materials can be very relevant especially when structure lightening is required.

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Section: Dispersion Curves and Analytical Derivation Of The First Banmentioning

confidence: 99%

“…The insertion of local resonances also leads to many architected layouts leading to structures that efficiently open band gaps [9,10,11,12,13,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

Pelat

Gallot

Gautier

2019

Journal of Sound and Vibration

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“…Theoretical results were validated by experimentally measured FRF on a finite periodic beam specimen, with special attention on the material damping in the rubber. Zuo et al [66] investigated the band gaps by TMM with the results validated by FEM, and observed the effects of band-gap coupling, the intervals, and oscillator parameters. In the case of attached resonators with more finite DOF, Xiao et al [67] extended the PWE method to study the complex band structures of locally resonant beams attached with multiple periodic arrays of spring-mass resonators based on EBT, which were validated by the FRF obtained with commercial FEM software.…”

Section: Introductionmentioning

confidence: 99%

Reverberation-Ray Matrix Analysis and Interpretation of Bending Waves in Bi-Coupled Periodic Multi-Component Beams

Guo

2018

Applied Sciences

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Featured Application: The method of reverberation-ray matrix (MRRM) and the interpretation of bending waves proposed in this paper provide respectively analysis method and profound knowledge for bending waves in bi-coupled periodic multi-component beams. These achievements will push forward the applications of bi-coupled periodic multi-component beams in wave filtering and vibration isolation.Abstract: Most existing research on periodic beams concerns bending waves in mono-coupled and bi-coupled periodic mono-component beams with the unit cell containing only one beam segment, and very few works on bi-coupled periodic multi-component beams with the unit cell containing more than one beam segments study the bending waves in structures with only binary unit cells. This paper presents the method of reverberation-ray matrix (MRRM) as an alternative theoretical method for analyzing the dispersion characteristics of bending waves with the wavelength greater than the size of the cross-sections of all components in bi-coupled periodic multi-component beams. The formulation of MRRM is proposed in detail with its numerically well-conditioned property being emphasized, which is validated through comparison of the results obtained with the counterpart results by other methods for exemplified bi-coupled periodic beams. Numerical examples are also provided to illustrate the comprehensive dispersion curves represented as the relations between any two among three in frequency, wavenumber (wavelength) and phase-velocity for summarizing the general features of the dispersion characteristics of bending waves in bi-coupled periodic multi-component beams. The effects of the geometrical and material parameters of constituent beams and the unit-cell configuration on the band structures are also demonstrated by numerical examples. The most innovative finding indicated from the dispersion curves is that the frequencies corresponding to the Brillouin zone boundary may not be the demarcation between the pass-band and stop-band for bending waves in bi-coupled periodic multi-component beams.

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“…Various methods have been developed for band structure calculation. Transfer Matrix (TM) method is widely used 5,[13][14][15][16][17][18] in 1D periodic beams and multi-layered structure. However, the TM method usually can only be applied in one direction.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, as the main medium for 1D propagation with attached resonators, Timoshenko beam theory has been used by Yu et al 13,26 to study the band structures of metamaterial beams with the transfer matrix method. Extensive studies 14,16,21,27,28 have been done on locally resonant structures based on Euler-Bernoulli and Timoshenko beam theories.…”

Section: Introductionmentioning

confidence: 99%

Reduced order derivation of the two-dimensional band structure of a mixed-mode resonator array

Amirkhizi

Wang

2018

Journal of Applied Physics

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In this paper, the 2D band structure of a mixed-mode metamaterial resonator array for in-plane waves is investigated. The band structure in the interior and on the boundary of the irreducible Brillouin zone as well as 1D dispersion diagrams for different propagation angles are calculated numerically and presented. Additionally, a reduced order analytical method is established to compare and approximate the band structure. The studied metamaterial, with a T-shaped cantilever beam as resonator in its square array repeating unit cells, exhibits branches with mixed P and SV waves except at exactly one angle of propagation. This paper also reports on the occurrence of avoided level crossings, which are related to the existence of exceptional points in the complex domain. A reduced order analytical approach is used that can generate partial (low branches) band structure with relatively little computational effort. The reduced order model agrees well with the numerical results for these low branches and can provide support in mode identification and band sorting. With proper adjustments in parameters, this analytical method will be applicable for other metamaterials that have similar unit cell structure.

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Studies of band gaps in flexural vibrations of a locally resonant beam with novel multi-oscillator configuration

Cited by 32 publications

References 40 publications

On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

Reverberation-Ray Matrix Analysis and Interpretation of Bending Waves in Bi-Coupled Periodic Multi-Component Beams

Reduced order derivation of the two-dimensional band structure of a mixed-mode resonator array

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