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...

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Bibliographic Details
Published in:Mathematical and computational applications 2021-03, Vol.26 (1), p.2
Main Authors: Fu, Zhuo-Jia, Li, Lu-Feng, Yin, De-Shun, Yuan, Li-Li
Format: Article
Language:English
Subjects:
Accuracy
band structures
Boundary conditions
Collocation
Crystal lattices
Efficiency
Eigenvalues
Elastic analysis
Elastic waves
Exact solutions
Finite element method
Mathematical analysis
Methods
Nodes
Numerical analysis
phononic crystals
Propagation
Simulation
Solvers
T-complete function
transmission spectra
Two dimensional analysis
Wave propagation
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Summary: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.
ISSN:2297-8747
1300-686X
2297-8747
DOI:10.3390/mca26010002