Abstract
In this paper, an alpha finite element method (αFEM) is formulated to study the propagation of elastic waves in periodic crystals. Using the simple triangular elements, the αFEM with optimal α value can always provide the exact solutions in the prediction of the band gap of phononic crystals. In addition, the upper and lower solutions are always observed in the computation of the band gap of phononic crystals with the adjustment of α value. The performance of αFEM is compared with standard finite element method (FEM) with different types of mass matrix formulation. The numerical examples have strongly demonstrated that the αFEM has given more accuracy prediction in the analysis of phononic crystals compared with standard FEM.
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