An accurate and efficient method based on the dynamic stiffness matrix for analyzing wave propagation in defective lattice structures

Abstract

In this study, we present an efficient and accurate method for analyzing wave propagation in lattice structures with periodic defects, which are composed of three-dimensional (3D) unit cells arranged infinitely in two or three directions, with defects existing periodically along the directions of the arrangement. The unit cell is composed of 3D beams, and the dynamic stiffness formulation of the 3D beam is developed by combining the Timoshenko-Ehrenfest, Rayleigh-Love and torsion theories. Based on the dynamic stiffness matrix, any number or order of natural frequencies of defective lattice structures can be calculated accurately and efficiently using the Wittrick-Williams algorithm. By combining it with the Bloch theorem, the proposed method can be used to calculate the dispersion curves of lattice structures with periodic defects. The accuracy and efficiency of the proposed method are demonstrated through numerical examples. Additionally, the effects of periodic defects in the lattice structures on the bandgap are analyzed.