Abstract
A wavelet-based finite element method (WFEM) is developed to calculate the elastic band structures of two-dimensional phononic crystals (2DPCs), which are composed of square lattices of solid cuboids in a solid matrix. In a unit cell, a new model of band-gap calculation of 2DPCs is constructed using plane elastomechanical elements based on a B-spline wavelet on the interval (BSWI). Substituting the periodic boundary conditions (BCs) and interface conditions, a linear eigenvalue problem dependent on the Bloch wave vector is derived. Numerical examples show that the proposed method performs well for band structure problems when compared with those calculated by traditional FEM. This study also illustrates that filling fractions, material parameters, and incline angles of a 2DPC structure can cause band-gap width and location changes.
Highlights
On small scales, periodic compositions of structure with different material properties are termed phononic crystals (PCs) [1]
A wavelet-based finite element method (WFEM) is developed to calculate the elastic band structures of two-dimensional phononic crystals (2DPCs), which are composed of square lattices of solid cuboids in a solid matrix
2DPCs is constructed using plane elastomechanical elements based on a B-spline wavelet on the interval (BSWI)
Summary
Periodic compositions of structure with different material properties are termed phononic crystals (PCs) [1]. In the search for complete band-gaps, many mathematical models are constructed to calculate band-gaps (BGs) of two-dimensional phononic crystals (2DPCs), such as the plane-wave expansion method (PWE) [6,7,8], multiple scattering theory (MST) [9], finite difference time-domain method (FDTD) [10,11], lumped mass method (LM) [12], wavelet method [13,14], boundary element method (BEM) [15,16,17], etc. It should be pointed out that FEM performs well for band-gap calculations of 2DPCs as compared with many time-domain methods. Developing a new band-gap calculation model of 2DPCs based on wavelet-based FEM is significant. A new numerical formulation is introduced for computing the band structures of
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