Elastic Wave Propagation in Lattice Metamaterials with Koch Fractal
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ISSN 1860-2134
Elastic Wave Propagation in Lattice Metamaterials with Koch Fractal Pengcheng Zhao1,2
Kai Zhang1,2
Zichen Deng1,2
1
( School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China) (2 MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an 710072, China)
Received 4 March 2020; revision received 5 June 2020; Accepted 9 June 2020 c The Author(s) 2020
ABSTRACT In this study, the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave propagation. The analytical models of lattice metamaterials are established using the finite element method, and the dispersion relation is solved using the Bloch’s theorem. The band structures of the lattice metamaterials with different numbers of iterations are studied, and the group velocities at a selected frequency are calculated to analyze the directional wave propagation characteristics. Furthermore, dynamic responses of the finite structures are calculated using commercial finite element software to verify the band gaps and directional wave propagation behaviors in the lattice metamaterials. The results show that multiple and low band gaps are present in the lattice materials with various geometric parameters of the Koch fractal, and the position of the lowest band gap decreases as the number of iterations increases. The results indicate the potential applications of lattice metamaterials with Koch fractals for vibration isolation and multi-functional design.
KEY WORDS Elastic wave propagation, Lattice metamaterial, Koch fractal, Band gap, Group velocity
1. Introduction The complex geometries and materials developed in biological systems possess unique mechanical properties. These systems have inspired the development of bioprinting and metamaterial manufacturing and have attracted widespread attention in engineering fields [1–3]. Through centuries of evolution and optimization, nature provides an excellent source of inspiration for metamaterials, which has inspired scholars to design and explore multi-functional metamaterials. Lattice metamaterials are emerging as popular research subjects. This has been greatly promoted by additive manufacturing technology. Lattice metamaterials are obtained using artificially designed unit cells in periodic arrays in one, two, or three dimensions. They have great potential for practical applications, such as vibration filtering [4], creating materials with adjustable Poisson’s ratios [5], and waveguide design [6–9]. Lattice metamaterials exhibit unique mechanical, thermal, and vibrational properties, which have been the subject of numerous analytical, numerical, and experimental studies
Corresponding author. E-mail: [email protected]
ACTA MECHANICA SOLIDA SINICA
[10–12]. In particular, their unique vibrational properties, including band gaps and directional wave propagation characteristics, are the main outstanding feature
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