A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals

In this paper, we introduce a novel localized collocation solver for two-dimensional (2D) phononic crystal analysis. In the proposed collocation solver, the displacement at each node is expressed as a linear combination of T-complete functions in each stencil support and the sparse linear system is obtained by satisfying the considered governing equation at interior nodes and boundary conditions at boundary nodes. As compared with finite element method (FEM) results and the analytical solutions, the efficiency and accuracy of the proposed localized collocation solver are verified under a benchmark example. Then, the proposed method is applied to 2D phononic crystals with various lattice forms and scatterer shapes, where the related band structures, transmission spectra, and displacement amplitude distributions are calculated as compared with the FEM.

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A meshfree local RBF collocation method for anti-plane transverse elastic wave propagation analysis in 2D phononic crystals

Journal of Computational Physics ◽

10.1016/j.jcp.2015.10.020 ◽

2016 ◽

Vol 305 ◽

pp. 997-1014 ◽

Cited By ~ 40

Author(s):

Hui Zheng ◽

Chuanzeng Zhang ◽

Yuesheng Wang ◽

Jan Sladek ◽

Vladimir Sladek

Keyword(s):

Wave Propagation ◽

Elastic Wave ◽

Collocation Method ◽

Phononic Crystals ◽

Elastic Wave Propagation ◽

Propagation Analysis ◽

Plane Transverse

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Research on the large band gaps in multilayer radial phononic crystal structure

Modern Physics Letters B ◽

10.1142/s0217984916501098 ◽

2016 ◽

Vol 30 (10) ◽

pp. 1650108 ◽

Cited By ~ 1

Author(s):

Nansha Gao ◽

Jiu Hui Wu ◽

Dong Guan

Keyword(s):

Crystal Structure ◽

Finite Element Method ◽

Phononic Crystal ◽

Phononic Crystals ◽

Band Gaps ◽

Transmission Spectra ◽

Intermediate Mass ◽

Displacement Fields ◽

Vibration Coupling ◽

Single Material

In this paper, we study the band gaps (BGs) of new proposed radial phononic crystal (RPC) structure composed of multilayer sections. The band structure, transmission spectra and eigenmode displacement fields of the multilayer RPC are calculated by using finite element method (FEM). Due to the vibration coupling effects between thin circular plate and intermediate mass, the RPC structure can exhibit large BGs, which can be effectively shifted by changing the different geometry values. This study shows that multilayer RPC can unfold larger and lower BGs than traditional phononic crystals (PCs) and RPC can be composed of single material.

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Wave bandgap formation and its evolution in two-dimensional phononic crystals composed of rubber matrix with periodic steel quarter-cylinders

International Journal of Modern Physics B ◽

10.1142/s0217979218500376 ◽

2018 ◽

Vol 32 (04) ◽

pp. 1850037 ◽

Cited By ~ 1

Author(s):

Peng Li ◽

Guan Wang ◽

Dong Luo ◽

Xiaoshan Cao

Keyword(s):

Finite Element Method ◽

Phononic Crystal ◽

Phononic Crystals ◽

Rubber Matrix ◽

Two Dimensional ◽

The Finite Element Method ◽

Defect States ◽

Low Frequencies ◽

High Frequencies ◽

Inner Region

The band structure of a two-dimensional phononic crystal, which is composed of four homogenous steel quarter-cylinders immersed in rubber matrix, is investigated and compared with the traditional steel/rubber crystal by the finite element method (FEM). It is revealed that the frequency can then be tuned by changing the distance between adjacent quarter-cylinders. When the distance is relatively small, the integrality of scatterers makes the inner region inside them almost motionless, so that they can be viewed as a whole at high-frequencies. In the case of relatively larger distance, the interaction between each quarter-cylinder and rubber will introduce some new bandgaps at relatively low-frequencies. Lastly, the point defect states induced by the four quarter-cylinders are revealed. These results will be helpful in fabricating devices, such as vibration insulators and acoustic/elastic filters, whose band frequencies can be manipulated artificially.

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TUNABLE BAND STRUCTURES OF 2D MULTI-ATOM ARCHIMEDEAN-LIKE PHONONIC CRYSTALS

International Journal of Computational Materials Science and Engineering ◽

10.1142/s2047684112500169 ◽

2012 ◽

Vol 01 (02) ◽

pp. 1250016 ◽

Cited By ~ 2

Author(s):

Y. L. XU ◽

C. Q. CHEN ◽

X. G. TIAN

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Phononic Crystal ◽

Phononic Crystals ◽

Band Gaps ◽

Two Dimensional ◽

Primitive Cell ◽

The Finite Element Method ◽

Band Structures ◽

Solid System

Two dimensional multi-atom Archimedean-like phononic crystals (MAPCs) can be obtained by adding "atoms" at suitable positions in primitive cells of traditional simple lattices. Band structures of solid-solid and solid-air MAPCs are computed by the finite element method in conjunction with the Bloch theory. For the solid-solid system, our results show that the MAPCs can be suitably designed to split and shift band gaps of the corresponding traditional simple phononic crystal (i.e., with only one scatterer inside a primitive cell). For the solid-air system, the MAPCs have more and wider band gaps than the corresponding traditional simple phononic crystal. Numerical calculations for both solid-solid and solid-air MAPCs show that the band gap of traditional simple phononic crystal can be tuned by appropriately adding "atoms" into its primitive cell.

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Optimization of Phononic Crystals for the Simultaneous Attenuation of Out-of-Plane and In-Plane Waves

Volume 8: Mechanics of Solids, Structures and Fluids; Vibration, Acoustics and Wave Propagation ◽

10.1115/imece2011-65665 ◽

2011 ◽

Cited By ~ 4

Author(s):

Osama R. Bilal ◽

Mahmoud I. Hussein

Keyword(s):

Genetic Algorithm ◽

Phononic Crystal ◽

Plane Waves ◽

Phononic Crystals ◽

Gap Size ◽

Two Dimensional ◽

Dispersion Characteristics ◽

Out Of Plane ◽

Optimization Methodology ◽

Application Specific

The topological distribution of the material phases inside the unit cell composing a phononic crystal has a significant effect on its dispersion characteristics. This topology can be engineered to produce application-specific requirements. In this paper, a specialized genetic-algorithm-based topology optimization methodology for the design of two-dimensional phononic crystals is presented. Specifically the target is the opening and maximization of band gap size for (i) out-of-plane waves, (ii) in-plane waves and (iii) both out-of-plane and in-plane waves simultaneously. The methodology as well as the resulting designs are presented.

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Locally resonant effective phononic crystals for subwavelength vibration control of torsional cylindrical waves

Journal of Vibration and Acoustics ◽

10.1115/1.4052748 ◽

2021 ◽

pp. 1-30

Author(s):

Ignacio Arretche ◽

Kathryn Matlack

Keyword(s):

Wave Propagation ◽

Plane Wave ◽

Effective Properties ◽

Equations Of Motion ◽

Phononic Crystal ◽

Phononic Crystals ◽

Unit Cell ◽

Periodic Coefficients ◽

Bloch Theorem ◽

Plane Wave Propagation

Abstract Locally resonant materials allow for wave propagation control in the sub-wavelength regime. Even though these materials do not need periodicity, they are usually designed as periodic systems since this allows for the application of the Bloch theorem and analysis of the entire system based on a single unit cell. However, geometries that are invariant to translation result in equations of motion with periodic coefficients only if we assume plane wave propagation. When wave fronts are cylindrical or spherical, a system realized through tessellation of a unit cell does not result in periodic coefficients and the Bloch theorem cannot be applied. Therefore, most studies of periodic locally resonant systems are limited to plane wave propagation. In this paper, we address this limitation by introducing a locally resonant effective phononic crystal composed of a radially-varying matrix with attached torsional resonators. This material is not geometrically periodic but exhibits effective periodicity, i.e. its equations of motion are invariant to radial translations, allowing the Bloch theorem to be applied to radially propagating torsional waves. We show that this material can be analyzed under the already developed framework for metamaterials. To show the importance of using an effectively periodic system, we compare its behavior to a system that is not effectively periodic but has geometric periodicity. We show considerable differences in transmission as well as in the negative effective properties of these two systems. Locally resonant effective phononic crystals open possibilities for subwavelength elastic wave control in the near field of sources.

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Dual Photonic–Phononic Crystal Slot Nanobeam with Gradient Cavity for Liquid Sensing

Crystals ◽

10.3390/cryst10050421 ◽

2020 ◽

Vol 10 (5) ◽

pp. 421 ◽

Cited By ~ 1

Author(s):

Nan-Nong Huang ◽

Yi-Cheng Chung ◽

Hsiao-Ting Chiu ◽

Jin-Chen Hsu ◽

Yu-Feng Lin ◽

...

Keyword(s):

Finite Element Method ◽

Acoustic Waves ◽

Phononic Crystal ◽

Phononic Crystals ◽

The Finite Element Method ◽

Concentrate Energy ◽

Abrupt Changes ◽

Analyte Solution ◽

Liquid Sensing ◽

Sensing Performance

A dual photonic–phononic crystal slot nanobeam with a gradient cavity for liquid sensing is proposed and analyzed using the finite-element method. Based on the photonic and phononic crystals with mode bandgaps, both optical and acoustic waves can be confined within the slot and holes to enhance interactions between sound/light and analyte solution. The incorporation of a gradient cavity can further concentrate energy in the cavity and reduce energy loss by avoiding abrupt changes in lattices. The newly designed sensor is aimed at determining both the refractive index and sound velocity of the analyte solution by utilizing optical and acoustic waves. The effect of the cavity gradient on the optical sensing performance of the nanobeam is thoroughly examined. By optimizing the design of the gradient cavity, the photonic–phononic sensor has significant sensing performances on the test of glucose solutions. The currently proposed device provides both optical and acoustic detections. The analyte can be cross-examined, which consequently will reduce the sample sensing uncertainty and increase the sensing precision.

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Surface Effects on Bandgaps of Transverse Waves Propagating in Two Dimensional Phononic Crystals with Nanosized Holes

Materials Science Forum ◽

10.4028/www.scientific.net/msf.675-677.611 ◽

2011 ◽

Vol 675-677 ◽

pp. 611-614 ◽

Cited By ~ 7

Author(s):

Ni Zhen ◽

Yue Sheng Wang

Keyword(s):

Laplace Equation ◽

Surface Effect ◽

Phononic Crystal ◽

Surface Effects ◽

Phononic Crystals ◽

Square Lattice ◽

Two Dimensional ◽

Transverse Waves ◽

Circular Holes

In this paper, a method based on the displacement-traction map is developed to calculate the bandgaps of transverse waves propagating in a 2D phononic crystal composed of nanosized circular holes in a square lattice. The Young-Laplace equation is employed to take into account of the surface effects of the nanosized holes. Detailed calculations are performed for the system with nanosized circular holes in an aluminum host with or without the surface effect. The result shows that all bands descend with the first bandgap becoming wider due to the existence of the surface effects.

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