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

Liu, X., Lu, Z., Adhikari, S. , Li, Y. L. & Banerjee, J. R. (2022). Exact wave propagation analysis of lattice structures based on the dynamic stiffness method and the Wittrick–Williams algorithm. Mechanical Systems and Signal Processing, 174, 109044. doi: 10.1016/j.ymssp.2022.109044

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.

Publication Type: Article
Additional Information: © 2022. This article has been published in Mechanical Systems and Signal Processing by Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: Wave propagation, Band gap, Dynamic stiffness method, Wittrick–Williams algorithm, Dispersion relations
Subjects: Q Science > QC Physics
T Technology > TA Engineering (General). Civil engineering (General)
T Technology > TJ Mechanical engineering and machinery
Departments: School of Mathematics, Computer Science & Engineering > Engineering > Mechanical Engineering & Aeronautics
[img] Text - Accepted Version
This document is not freely accessible until 5 April 2023 due to copyright restrictions.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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