Study on bandgap and directional wave propagation of a two-dimensional lattice with a nested core

Abstract

Abstract This paper proposes a two-dimensional lattice structure with a nested core. The bandgap distribution and the anisotropy of the phase velocity and group velocity were studied based on Bloch’s theorem and the finite element method. The effects of the eccentric ratio ( e ) and the rotation angle ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> </mml:math> ) of the dual-phase structure on the bandgap distribution were investigated, and the anisotropy was studied via phase velocity and group velocity. The structure of e = 0.3 displayed the maximum total bandgap width. As <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> </mml:math> increased, the total bandgap widths of structures of different e all obviously increased and the low-frequency bandgap properties were improved. The phase velocity and group velocity of e = 0 displayed strong anisotropy, and the anisotropy was adjusted by tuning <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> </mml:math> . Furthermore, the group velocity of the eighth mode displayed high-directional wave propagation. For practical applications, a single-phase structure was proposed and analyzed. Through additive manufacturing technology, the single-phase structure was prepared and tested by a low amplitude test setup. The experimental results displayed good agreement with the numerical results, which demonstrated high directional propagation. This finding may pave the way for practical applications of the proposed lattice metamaterial in terms of wave filtering.