Band structure calculation of 2D fluid/solid and solid/fluid phononic crystal using a modified smoothed finite element method with fluid–solid interaction

Abstract

Recently, a novel modified smoothed finite element method (M-SFEM) is proposed to calculate the band structures of two-dimensional (2D) in-plane elastic waves in phononic crystals (PCs) by the authors. In present work, the proposed algorithm is extended to analyze the band structures of 2D phononic crystals (PCs) with fluid/structure interaction (FSI). In order to study the phononic crystals (PCs) with FSI, this method extends the gradient smoothing technique to soften the stiffness matrix of fluid domain and solid domain. Meanwhile, according to the generalized integration rules, this method simply shifts these integration points of elements to an unconventional location in the mass matrix. In addition, different Bloch boundary conditions, viz. fluid/solid and solid/fluid, including the square and triangular lattice using M-SFEM are also investigated in the computation of PCs with FSI. Several PCs models with FSI are studied to verify the high accuracy of the M-SFEM in the analysis of band structures. In order to emerge the superiority of the proposed method, the results of finite element method (integration points on conventional location), modified finite element method (integration points on unconventional location), smoothed finite element method are all presented. Numerical analysis shows that the M-SFEM can be used to predict the band structures in PCs with FSI, and can obtained more precise results as compared to FEM and SFEM.