Band Structures Analysis Method of Two-Dimensional Phononic Crystals Using Wavelet-Based Elements

Liu, Mao; Xiang, Jiawei; Zhong, Yongteng

doi:10.3390/cryst7110328

Cited by 13 publications

(4 citation statements)

References 45 publications

(26 reference statements)

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“…As far as the materials are concerned, a number of studies investigated the effects induced by the contrast in Young's modulus, Poisson's ratio, and the density between the matrix and inclusions in the case of a binary composite [5,6]. On the other hand, as far as the topology is concerned, which indeed represents one of the most-important features affecting the band gap properties, research has been conducted at the unit cell level, focusing on the lattice parameters to attain an optimal design [7][8][9] through topology and parametric optimization techniques [10][11][12][13]. For instance, in [14,15], an optimization method was proposed on the basis of a closed-form estimation of the band gap width and of the starting frequency as a function of a number of key geometric parameters; such an approach resulted in being useful in obtaining the optimal bang gap and the material design, to achieve better properties.…”

Section: Introductionmentioning

confidence: 99%

Truss Metamaterials: Multi-Physics Modeling for Band GapTuning

Calegaro,

Mariani

2023

Machines

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Periodic elastic metamaterials (EMMs) display the capability to forbid the transmission of elastic waves for certain frequency ranges, leading to band gaps. If topology optimization strategies are exploited to tune the band gaps of EMMs, the said band gaps cannot be modified in real-time. This limitation can be overcome by allowing for active materials in the design of EMMs. In this work, a hyperelastic piezoelectric composite was considered to assess the coupled effects of material and geometric nonlinearities on the behavior of sculptured microstructures featuring a three-dimensional periodicity. Specifically, it was assumed that the composite material is obtained by embedding piezo nanoparticles into a soft polymeric matrix. In this way, piezoelectricity and instability-induced pattern transformation could be fully exploited to actively tune the band gaps. A thermodynamically consistent multi-physics model for the active composite material is discussed and implemented in a general-purpose finite-element code. The reported results of the simulations showed how the band gaps are affected by the aforementioned nonlinearities and by a feature of the architected periodic cell linked to its topology.

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Section: Introductionmentioning

confidence: 99%

Truss Metamaterials: Multi-Physics Modeling for Band GapTuning

Calegaro,

Mariani

2023

Machines

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“…Li et al [ 36 ] studied the propagation characteristics of Lamb waves on a 1D radial phononic crystal plate with periodic corrugations and discussed the effects of geometric parameters on band gaps. Liu et al [ 37 ] obtained the band structure of 2D square lattices using plane elastic elements based on a B-spline wavelet on the interval and compared it with traditional FEM, which provided good results. Xiang et al [ 38 ] proposed a 2D surround multi-scattering phononic crystal structure and calculated the band gap and transmission characteristics, which is helpful in the research and design of acoustic functional materials.…”

Section: Introductionmentioning

confidence: 99%

Vibration Band Gap Characteristics of Two-Dimensional Periodic Double-Wall Grillages

Wang

Yao

et al. 2021

Materials

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In this article, the wave finite element method (WFEM) is used to calculate the band gap characteristics of two-dimensional (2D) periodic double-wall grillages (DwGs), which are verified by the grillage model vibration measurement experiment and finite element calculation. To obtain the band gap characteristics of periodic DwGs, the finite element calculation model is established according to the lattice and energy band theory and the characteristic equation of the periodic unit cell under the given wave vector condition is solved based on Bloch theorem. Then, the frequency transfer functions of finite-length manufactured and finite element models are obtained to verify the band gap characteristics of periodic DwGs. Finally, the effects of material parameters and structural forms on band gap characteristics and transfer functions are analyzed, which can provide a reference for engineering structure vibration and noise reduction design.

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“…Sainidou et al calculated the frequency band structure of an infinite PC structure, which consists of a stack of identical slices parallel to a given surface [23]. Liu et al developed a wavelet-based FEM to calculate BGs and the corresponding transmission characteristics of 2D PC structures [24]. He also presented an array of periodic coating on a thin plate, which were investigated by FEM simulations and experiments [25].…”

Section: Introductionmentioning

confidence: 99%

Band Gaps and Transmission Characteristics Analysis on a Two-Dimensional Multiple-Scatter Phononic Crystal Structure

Xiang

2020

Materials

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In this paper, a novel wrap-around multi-scattering phononic crystal (PC) structure is proposed. Band gaps (BGs) and transmission characteristics of the present structure are calculated using finite element method (FEM). Through the calculations of single-scattering prototype, three complete BGs which are exhibited at low frequency and the fourth wide BG at high frequency are discovered. The transmission features and resonant spectra represented by frequency response function (FRF) shows that apparent resonance directly cause the four specific BGs. By keeping the total area of scatterers unchanged, 2 × 2, 3 × 3 and 4 × 4 scatterers are designed to obtain the change rule of BGs. Furthermore, the size ratio of 2 × 2 scatterers, the number of connection beams are investigated to obtain the regular pattern of acoustic energy transmission and attenuation. The present investigation of multiple-scatter PC structure will provide a solid support on the future design of acoustical functional materials.

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Band Structures Analysis Method of Two-Dimensional Phononic Crystals Using Wavelet-Based Elements

Cited by 13 publications

References 45 publications

Truss Metamaterials: Multi-Physics Modeling for Band GapTuning

Truss Metamaterials: Multi-Physics Modeling for Band GapTuning

Vibration Band Gap Characteristics of Two-Dimensional Periodic Double-Wall Grillages

Band Gaps and Transmission Characteristics Analysis on a Two-Dimensional Multiple-Scatter Phononic Crystal Structure

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