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.
Highlights
The complex geometries and materials developed in biological systems possess unique mechanical properties
The number of iterations of the lattice metamaterials with Koch fractals has a significant effect on the band structure
The band structures and group velocities of lattice metamaterials composed of Koch fractals with different iteration numbers are studied
Summary
The complex geometries and materials developed in biological systems possess unique mechanical properties. [10,11,12] Their unique vibrational properties, including band gaps and directional wave propagation characteristics, are the main outstanding features. In this study, inspired by the Koch fractal topology, lattice metamaterials with different numbers of iterations were designed to study the wave propagation characteristics, as the Koch fractal can potentially tune the band gap and directional wave propagation. The effect of Koch fractal on wave propagation was studied in terms of the band gap of desired frequency position by adjusting the geometric parameters of the Koch fractal. 3, the band structures and group velocities of lattice metamaterials with different Koch fractal iterations are presented, and the results are verified by finite element simulations.
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