In-plane wave propagation analysis for waveguide design of hexagonal lattice with Koch snowflake

In this study, the band structure and directional characteristics of the hexagonal lattice with Koch snowflake are investigated. The finite element method and Bloch theorem are used to analyze the wave propagation in hexagonal lattice with Koch snowflake for different fractal orders. The effects of the geometric parameters on band structures are discussed in detail. The group velocities at given frequencies are calculated for analyzing the directional characteristics of the wave propagation. The dynamic responses of the periodic lattice are investigated via numerical simulation to confirm the directional features. The vibration experiments are conducted to verify the existence of band gap and vibration suppression performances of the structures, which are used to design the waveguide in the lattices. The results demonstrate that the hexagonal lattice with Koch snowflake for different fractal orders can tune the elastic wave behaviors in a specific way. As the fractal order increases, multiple band gaps appear and the band structure has self-similarity in the low-frequency range. The directional characteristics of wave propagation in the hexagonal lattice with Koch snowflake can be used to further expand the vibration attenuation range. The results also show the potential importance and feasibility of using the hexagonal lattice with Koch snowflake for vibration isolation and control using the hexagonal lattice with Koch snowflake.