Elastodynamic analysis of two-dimensional periodic structures having a defect

Abstract

This paper presents a numerical method for two-dimensional solid phononic crystals having a defect. This problem is divided into two domains of the finite defective region and the surrounding periodic medium. The analysis method is then constructed by combining the finite element equation of the irregular region with the impedance matrix representing the external field. The impedance matrix is derived by analyzing a series of harmonic excitation problems of a periodic field given by the surrounding array. These solutions are obtained by the aid of Floquet transform. The developed method is applied to wave propagations through a defective field imbedded in a square lattice of circular holes. Modes trapped in the disturbed region are also analyzed for a composite material possessing a dispersion structure with a wide bandgap.