Wave and vibration attenuation analyzes of 2-D phononic crystals using the scaled boundary finite element method

Resumo

This study uses the scaled boundary finite element method (SBFEM) to study the wave propagation and vibration in a 2-D phononic crystal (PnC). The SBFEM is a general semi-analytical method where a problem domain is divided into subdomains satisfying the scaling requirement. It offers the advantages of the finite element method (FEM) and the boundary element method (BEM), avoiding some drawbacks and making it very attractive for PnC applications. In this investigation, the SBFEM is formulated using the Bloch-Floquet theory to model the periodic 2-D PnC unit cells. The 2-D PnC is composed by square inclusions distributed in a matrix with square lattice. The SBFEM results are computed in the form of dispersion diagram and forced response of the 2-D PnC. The dispersion diagram obtained by the SBFEM is validated with those obtained by the FEM and plane wave expansion (PWE) method. The unit cell wave attenuation (i.e., the imaginary part of wave number multiplied by the unit cell length) is also computed by using the extended plane wave expansion (EPWE) approach.