Band structure analysis for 2D acoustic phononic structure using isogeometric boundary element method

Gao, Haifeng; Chen, Leilei; Lian, Haojie; Zheng, Changjun; Xu, Huidong; Matsumoto, Toshiro

doi:10.1016/j.advengsoft.2020.102888

Cited by 11 publications

(11 citation statements)

References 44 publications

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“…One of the methods to determine the band structures is to calculate the angular frequency with the given Bloch wave vector, [22][23][24][25][26] and the other is to calculate the Bloch wave vector by sweeping the angular frequency. 27,28 However, the integral equations established are based on the fundamental solutions dependent on angular frequency for dynamics in all these studies. Therefore, it suffers from nonlinear eigenvalue problems when the angular frequency is taken as the solved parameter, which needs to be solved by combining special methods such as the block Sakurai-Sugiura method.…”

Section: Introductionmentioning

confidence: 99%

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

Wei

Xiang

Zhu

et al. 2023

Numerical Meth Engineering

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A novel method of combination of wavelet‐based boundary element method (WBEM) with frequency‐independent fundamental solutions is proposed to determine the band structures of fluid–solid phononic crystals (PCs) with square and triangular lattices. Integral equations established are based on the frequency‐independent fundamental solutions, which can avoid nonlinear eigenvalue problems and reduce computing time. Domain integral terms arising from the use of frequency‐independent fundamental solutions are handled with the radial integration method (RIM) and dual reciprocity method (DRM), respectively. The results show the lower precision in high frequency domain of using RIM to handle domain integral terms than that of using DRM, which can be solved by increasing Gauss point. The B‐spline wavelet on the interval and wavelet coefficients are applied to approximate the physical boundary conditions. It is proved that coupling conditions between matrix and scatterers and Bloch theorem are also applicable to wavelet coefficients. Some small matrix entries generated by wavelet vanishing moment characteristics are truncated by the provided matrix compression technique, and the influence of compressed matrices on the results is studied. Furthermore, the final Eigen equations constructed are modified to avoid numerical instability. Some examples are provided to demonstrate the accuracy and efficiency of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

Wei

Xiang

Zhu

et al. 2023

Numerical Meth Engineering

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“…The core concept of the IGABEM is to employ basis functions used in Computer-Aided Design (CAD) for geometric modeling to solve boundary integral equation that are transformed from the partial differential equations. As such, IGABEM enables numerical simulation to be conducted from CAD directly which avoids the cumbersome meshing procedure and retains geometric accuracy [13][14][15]. Unlike isogeometric finite element analysis, a volume parameterization is not needed in IGABEM, because both BEM and CAD are boundaryrepresented.…”

Section: Introductionmentioning

confidence: 99%

Noise Pollution Reduction through a Novel Optimization Procedure in Passive Control Methods

Lian¹,

Chen²,

Lin³

et al. 2022

Computer Modeling in Engineering &Amp; Sciences

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This paper proposes a novel optimization framework in passive control techniques to reduce noise pollution. The geometries of the structures are represented by Catmull-Clark subdivision surfaces, which are able to build gap-free Computer-Aided Design models and meanwhile tackle the extraordinary points that are commonly encountered in geometric modelling. The acoustic fields are simulated using the isogeometric boundary element method, and a density-based topology optimization is conducted to optimize distribution of sound-absorbing materials adhered to structural surfaces. The approach enables one to perform acoustic optimization from Computer-Aided Design models directly without needing meshing and volume parameterization, thereby avoiding the geometric errors and time-consuming preprocessing steps in conventional simulation and optimization methods. The effectiveness of the present method is demonstrated by three dimensional numerical examples.

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“…IGA is a widely used numerical technique to solve eigenvalue problems (see, e.g., [8][9][10][11][12][13][14][15][16][17]). Recently, the application of rIGA in eigenanalysis has been also investigated in [6,18].…”

Section: Introductionmentioning

confidence: 99%

Refined isogeometric analysis of quadratic eigenvalue problems

Hashemian

García

Pardo

et al. 2022

Computer Methods in Applied Mechanics and Engineering

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Band structure analysis for 2D acoustic phononic structure using isogeometric boundary element method

Cited by 11 publications

References 44 publications

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

Noise Pollution Reduction through a Novel Optimization Procedure in Passive Control Methods

Refined isogeometric analysis of quadratic eigenvalue problems

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