Dispersion Analysis of Plane Wave Propagation in Lattice-Based Mechanical Metamaterial for Vibration Suppression

Abstract

Phononic crystals based on lattice structures provide important wave dispersion characteristics as band structures, showing excellent compatibility with additive manufacturing. Although the lattice structures have shown the potential for vibration suppression, a design guideline to control the frequency range of the bandgap has not been well established. This paper studies the dispersion characteristics of plane wave propagation in lattice-based mechanical metamaterials to realize effective vibration suppression for potential aerospace applications. Triangular and hexagonal periodic lattice structures are mainly studied in this paper. The influence of different geometric parameters on the bandgap characteristics is investigated. A finite element approach with Floquet–Bloch’s principles is implemented to effectively evaluate the dispersion characteristics of waves in lattice structures, which is validated numerically and experimentally with a 3D-printed lattice plate. Based on numerical studies with the developed analysis framework, the influences of the geometric parameters of lattice plate structures on dispersion characteristics can mainly be categorized into three patterns: change in specific branches related to in-plane or out-of-plane vibrations, upward/downward shift in frequency range, and drastic change in dispersion characteristics. The results obtained from the study provide insight into the design of band structures to realize vibration suppression at specific frequencies for engineering applications.