Three-dimensional ultra-wide elastic metamaterial with inertial amplification mechanisms having optimized flexure hinges

The aim of this paper is to obtain an ultra-wide low-frequency stop band in three dimensions by using inertial amplification mechanisms. A two-stage remote center flexure mechanism design is introduced that allows 3D assembly of inertial amplification mechanisms while enabling ends of the inertial amplification mechanisms to bend in two orthogonal axes so that broadband excitations coming from all directions can be impeded. Cross flexure and split flat flexure hinges that restrain undesired torsional, in-plane and out-of-plane bending modes of the inertial amplification mechanisms are utilized for the first time in order to maximize the stop band frequency range. An octahedron and 3D arrays of octahedrons are generated with the use of these mechanisms. By making design improvements and topological changes on the mechanisms forming the octahedron, the stop band of the octahedron is widened. Finally, the bandwidth is maximized by optimizing the thicknesses of the flexures in the inertial amplification mechanisms. Eventually, a 3D elastic metamaterial with an ultra-wide band gap between 33.7 Hz and 457.5 Hz is obtained, yielding arithmetic mean normalized bandwidth of 172.6%.