Exact wave propagation analysis of lattice structures based on the dynamic stiffness method and the Wittrick–Williams algorithm

Abstract

This paper proposes two significant developments of the Wittrick–Williams (W–W) algorithm for an exact wave propagation analysis of lattice structures based on analytical dynamic stiffness (DS) model for each unit cell of the structures. Based on Bloch’s theorem, the combination of both the DS and the W–W algorithm makes the wave propagation analysis exact and efficient in contrast to existing methods such as the finite element method (FEM). Any number or order of natural frequencies can be computed within any desired accuracy from a very small-size DS matrix; and the W–W algorithm ensures that no natural frequency of the structure is missed in the computation. The proposed method is then applied to analyze the band gap characteristics and mode shapes of hexagonal honeycomb lattice structures and the results are validated and contrasted against the FE results. The effects of different primitive unit cell configurations on band diagrams and iso-frequency contours are thoroughly investigated. It is demonstrated that the proposed method gives exact eigenvalues and eigenmodes with the advantage of at least two orders of magnitude in computational efficiency over other methods. This research provides a powerful, reliable analysis and design tool for the wave propagations of lattice structures.