An exact solution to compute the band gap in phononic crystals

• Published in: Computational materials science Vol. 122; pp. 72 - 85
• Main Authors: Li, Eric, He, Z.C., Wang, Gang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2016
• Subjects: Alpha finite element method (αFEM); Band gap; Computation; Crystals; Exact solutions; Finite element method; Finite element method (FEM); Mathematical analysis; Mathematical models; Phononic crystals; Wave propagation; Phononic crystals; Finite element method (FEM); Band gap; Alpha finite element method (αFEM)
• ISSN: 0927-0256; 1879-0801
• DOI: 10.1016/j.commatsci.2016.05.004

An alpha finite element method (αFEM) is formulated to study the propagation of elastic waves in phononic crystals. With an optimal α value in αFEM model, the exact solution can be obtained. [Display omitted] 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.