Mathematical modeling and analysis of a meta-plate for very low-frequency band gap

Wang, Kai; Zhou, Jiaxi; Cai, Changqi; Xu, Daolin; Ouyang, Huajiang

doi:10.1016/j.apm.2019.04.033

Cited by 70 publications

(18 citation statements)

References 37 publications

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“…According to the Galerkin method, the transverse displacement of the faceplates at this point (21) where m and n are the order of the eigenfunction, p(t) is generalized coordinate vector, ξ (x, y) is the displacement shape function which is assumed to satisfy the fully free boundary condition [42] and it is given by…”

Section: Dynamic Model Of Finite Sized Meta-plate With Mbs Resonatorsmentioning

confidence: 99%

“…Wang et al [42] designed a metamaterial plate with high-static-low-dynamic-stiffness resonators and explored the nonlinear frequency response of meta-plate under the excitation with different amplitudes. Fang et al [43] presented the chaotic band-gaps of nonlinear acoustic metamaterials and achieved the ultralow-and ultrabroadband wave suppressions.…”

Section: Introductionmentioning

confidence: 99%

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Tunable Nonlinear Band Gaps in a Sandwich-Like Meta-Plate

Xue

Wang

et al. 2021

Preprint

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This paper aims to explore the actual working mechanism of sandwich-like meta-plates by periodically attaching nonlinear mass-beam-spring (MBS) resonators for low-frequency wave absorption. The nonlinear MBS resonator consists of a mass, a cantilever beam and a spring that can provide negative stiffness in the transverse vibration of the resonator, and its stiffness is tunable by changing the parameters of the spring. Considering the nonlinear stiffness of the resonator, the energy method is applied to obtain the dispersion relation of the sandwich-like meta-plate and the band-gap bounds related to the amplitude of resonator is derived by dispersion analysis. For the finite sized sandwich-like meta-plate with the fully free boundary condition subjected to external excitations, its dynamic equation is also established by the Galerkin method. The frequency response analysis of the meta-plate is carried out by the numerical simulation, whose band-gap range demonstrates good agreement with the theoretical one. Results show that the band-gap range of the present meta-plate is tunable by the design of the structural parameters of the MBS resonator. Furthermore, by analyzing the vibration suppression of the finite sized meta-plate, it can be observed that the nonlinearity of resonators can widen the wave attenuation range of meta-plate.

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Section: Dynamic Model Of Finite Sized Meta-plate With Mbs Resonatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tunable Nonlinear Band Gaps in a Sandwich-Like Meta-Plate

Xue

Wang

et al. 2021

Preprint

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show abstract

“…Nouh et al [12,13] presented the vibration characteristic of metamaterial beams and plates manufactured out of assemblies of periodic elements with built-in local resonances. Wang et al [14] proposed a meta-plate model by periodically attaching high-static-low-dynamic-stiffness resonators onto the thin plate to attenuate very low-frequency flexural waves. To broaden the bandwidths, many researchers investigated the band gaps in periodic structures with multiple local resonators.…”

Section: Introductionmentioning

confidence: 99%

Low-Frequency Vibration and Radiation Performance of a Locally Resonant Plate Attached with Periodic Multiple Resonators

2020

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The low-frequency vibration and radiation performance of a locally resonant (LR) plate with periodic multiple resonators is studied in this paper, with both infinite and finite structure properties examined. For the finite cases, taking the LR plate attached with two periodic arrays of resonators as an example, the forced vibration response and the radiation efficiency are theoretically derived by adopting a general model with elastic boundary conditions. Through a comparison with the band structures calculated by the plane-wave-expansion method, it shows that the band gaps in the infinite LR plate are in good agreement with the vibration-attenuation bands in the finite LR plate, no matter what boundary conditions are applied to the latter. In contrast to the vibration reduction in the band gaps, the radiation efficiency of the finite LR plate is sharply increased in the band-gap frequency ranges. Furthermore, the acoustic power radiated from the finite LR plate can be seriously affected by its boundary conditions. For the LR plate with greater constraints, the acoustic power is reduced in the band-gap frequency ranges, while that from the one with fully free boundary conditions is increased. When further considering the damping loss factors of the resonators, the attenuation performance can be improved for both the vibration and radiation of the LR plate.

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“…Besides the mentioned methods, other methods such as the Adomian decomposition (Hajhosseini and Ebrahimi, 2019), the transfer matrix (Guo et al, 2018), the lumped-mass (Wang et al, 2004), the plane wave expansion (Wang et al, 2019), the lattice dynamics (Chang et al, 2018), the multiple scattering (Psarobas et al, 2000), the wave finite element (Nobrega et al, 2016), and the finite-difference time-domain methods (Sun and Wu, 2007) were also used to study the vibration bandgap properties of different periodic structures. Each method has some advantages and some disadvantages.…”

Section: Introductionmentioning

confidence: 99%

Analysis of complete vibration bandgaps in a new periodic lattice model using the differential quadrature method

Hajhosseini

2020

Journal of Vibration and Control

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In this study, a new periodic lattice model with special vibration-absorbing properties is introduced. This periodic structure consists of the connected beam elements with circular cross-sections. Four models with different sets of cross-sectional radii are considered for this periodic lattice. The theoretical equations of longitudinal, torsional, and transverse vibrations of beams are solved using the combination of generalized differential quadrature and generalized differential quadrature rule methods to calculate the first three complete bandgaps. Investigating the effects of geometrical parameters on the bandgaps shows that all bands are close to each other for specific values of the cross-sectional radii. Having close bandgaps means that this periodic structure has a relatively wide bandgap in total. Furthermore, this wide band can move to low-frequency ranges by changing the lattice thickness. Absorbing both in-plane and out-of-plane vibrations over a wide bandgap at low-frequency ranges makes this periodic lattice a good vibration absorber. Verification of the analytical method using ANSYS software shows that the combination of generalized differential quadrature and generalized differential quadrature rule methods can be used for vibration analysis of two- or three-dimensional structures such as frames and trusses with high accuracy.

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Mathematical modeling and analysis of a meta-plate for very low-frequency band gap

Cited by 70 publications

References 37 publications

Tunable Nonlinear Band Gaps in a Sandwich-Like Meta-Plate

Tunable Nonlinear Band Gaps in a Sandwich-Like Meta-Plate

Low-Frequency Vibration and Radiation Performance of a Locally Resonant Plate Attached with Periodic Multiple Resonators

Analysis of complete vibration bandgaps in a new periodic lattice model using the differential quadrature method

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