Study on bandgap and directional wave propagation of a two-dimensional lattice with a nested core

Hou, Jiahong; Zhang, Zhijun; Li, Dong

doi:10.1088/1361-6463/ac47c0

Cited by 9 publications

(12 citation statements)

References 63 publications

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“…Due to the periodicity of the lattice structure, Bloch's theorem is used in the theoretical calculations. [ 14 ] The displacement of any point in a periodic structure can be given by this theorem, as shown in Equation (1).

{boldu}_{q} = {\begin{matrix} u_{x} \\ u_{y} \end{matrix}} {= v}_{q} e^{i (k \cdot r ‐ ω t)} = {\begin{matrix} v_{x} \\ v_{y} \end{matrix}} e^{{i (k}_{normalx} {x + k}_{y} y ‐ ω t)}

where

{boldv}_{q}

is the displacement magnitude vector, with the same periodicity as the structure; k is the wavevector,

{k = (k}_{x} {, k}_{y})

; r is the coordinate,

r = (x, y)

; ω is the circular frequency; and t is the time.…”

Section: Design and Methodsmentioning

confidence: 99%

“…Due to the periodicity of the lattice structure, Bloch's theorem is used in the theoretical calculations. [14] The displacement of any point in a periodic structure can be given by this theorem, as shown in Equation (1).…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…[ 6 ] Due to the unique bandgap properties of acoustic metamaterials, they have been extensively studied over the past two decades. [ 7–17 ]…”

Section: Introductionmentioning

confidence: 99%

“…[6] Due to the unique bandgap properties of acoustic metamaterials, they have been extensively studied over the past two decades. [7][8][9][10][11][12][13][14][15][16][17] In recent years, many researchers have studied acoustic metamaterials from the perspective of hierarchical structures. The hierarchical structures have excellent wave attenuation characteristics during elastic wave transmission.…”

Section: Introductionmentioning

confidence: 99%

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Wave Propagation Properties of a Spider‐Web‐Like Hierarchical Acoustic Metamaterial

Ruan

Liu

2022

Physica Status Solidi (b)

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Herein, a hierarchical acoustic metamaterial with a spider‐web‐like structure is proposed based on bionics theory. The wave propagation behaviors of the hierarchical structures are studied and discussed with the finite‐element method and Bloch theorem. The effects of the basic shape of the hierarchical structure, the levels (n), and the ambient temperature on the distribution of the bandgap are analyzed, respectively. The results show that the quadrilateral hierarchical structure has better bandgap properties than the same level's octagonal and hexagonal hierarchical structures. The level of the hierarchical structure has a significant effect on the distribution of the low‐frequency bandgap. When the level of the structure is 15, the lowest opening frequency is 99.875 Hz. When the temperature variable is introduced, the temperature‐induced deformation can significantly change the range of the first bandgap of the hierarchical structure. These findings can provide new ideas for the design of acoustic metamaterials.

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{boldu}_{q} = {\begin{matrix} u_{x} \\ u_{y} \end{matrix}} {= v}_{q} e^{i (k \cdot r ‐ ω t)} = {\begin{matrix} v_{x} \\ v_{y} \end{matrix}} e^{{i (k}_{normalx} {x + k}_{y} y ‐ ω t)}

where

{boldv}_{q}

is the displacement magnitude vector, with the same periodicity as the structure; k is the wavevector,

{k = (k}_{x} {, k}_{y})

; r is the coordinate,

r = (x, y)

; ω is the circular frequency; and t is the time.…”

Section: Design and Methodsmentioning

confidence: 99%

“…Due to the periodicity of the lattice structure, Bloch's theorem is used in the theoretical calculations. [14] The displacement of any point in a periodic structure can be given by this theorem, as shown in Equation (1).…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…[ 6 ] Due to the unique bandgap properties of acoustic metamaterials, they have been extensively studied over the past two decades. [ 7–17 ]…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Wave Propagation Properties of a Spider‐Web‐Like Hierarchical Acoustic Metamaterial

Ruan

Liu

2022

Physica Status Solidi (b)

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“…They have been widely applied in the design of compression components of many industrial and aircraft structures, and have the tremendous potential for multi-functional applications. 1 Among many sandwich structures, lightweight sandwich structures, such as metamaterial filling structures like honeycomb and foam, 2,3,4,5,6,7,8,9,10,11,12,13,14,15 are attracting greater attention because of their high bending stiffness and weight ratio. 16,17 Many researches have shown that PBCs of CSPs may be much higher than buckling loads.…”

Section: Introductionmentioning

confidence: 99%

Effects of parameters on postbuckling failure of composite sandwich panels loaded axially: Function form and applications

Bao-zong

2023

Jnl of Sandwich Structures & Materials

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Based on the refined first-order shear theory (simplified zig-zag model), using quasi-conforming finite element method with path-following and switching approach, the postbuckling behaviors and postbuckling bearing capacity (PBC) of composite sandwich panels (CSPs) axially loaded were studied and discussed in detail. To utilize the carrying potential of CSPs in postbuckling, the effects of the key parameters on postbuckling behaviors of the CSPs were analyzed by finite element method. The numerical results show that the PBC of CSPs increases with the increase of face sheets thickness, core thickness and core shear modulus, but it is insensitive to the change of the side length ratio. The enhancement of core shear strength can increase the PBC of CSPs and change the failure mode, but it is found there is a threshold value, beyond which, the PBC will no longer or slightly increases with the increase of core shear strength. The failure of CSPs is mainly determined by the tensile strength in the direction perpendicular to the fiber. Finally, a parameter selection optimization approach is proposed to effectively improve the PBC of CSPs under axial compression.

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Study on Bandgap Property of Three‐Dimensional Star‐Like Double‐Arrow Lattice

Hou

et al. 2023

Physica Status Solidi (b)

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Herein, a three‐dimensional star‐like double‐arrow lattice is proposed, which is inspired by the double‐arrow structure. Based on Bloch's theorem and finite element method, the calculation program is made up and the band structures are calculated. The calculation results demonstrate that the bandgap property of the double‐arrow lattice is improved compared with that of a cross lattice. The parametric study is carried out and geometric parameters have strong effects on the bandgap property. As the angle between the external edge and symmetric line increases, the total bandgap width increases apparently, and the opening frequency of low‐order bandgap decreases. This phenomenon reflects that the low‐frequency bandgap property is improved. Via the isosurface of phase velocity and group velocity, the anisotropy is investigated. Strong anisotropy and energy focus appear, which can be used to design waveguides.

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Study on bandgap and directional wave propagation of a two-dimensional lattice with a nested core

Cited by 9 publications

References 63 publications

Wave Propagation Properties of a Spider‐Web‐Like Hierarchical Acoustic Metamaterial

Wave Propagation Properties of a Spider‐Web‐Like Hierarchical Acoustic Metamaterial

Effects of parameters on postbuckling failure of composite sandwich panels loaded axially: Function form and applications

Study on Bandgap Property of Three‐Dimensional Star‐Like Double‐Arrow Lattice

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