Realization of an ultrawide stop band in a 2-D elastic metamaterial with topologically optimized inertial amplification mechanisms

Abstract

The aim of this study is to design a two-dimensional solid structure with embedded inertial amplification mechanisms that shows an ultrawide stop band (band gap) at low frequencies. First of all, a unique compliant inertial amplification mechanism is suggested. The compliant (flexure) hinge connections are designed and the topology of the beams in the unit cell mechanism are optimized to achieve the maximum possible stop band width. Then, a two-dimensional periodic structure is formed by using this topologically optimized inertial amplification mechanism. Thereafter, the formed periodic structure is manufactured. Experimental and finite element analyses show that an ultrawide stop band between 29 Hz and 590 Hz is obtained for both longitudinal and transverse excitations. This outcome reveals a phononic gap whose upper and lower limits have a ratio that exceeds 20 (i.e., arithmetic mean normalized bandwidth of 181% or geometric mean normalized bandwidth of 429%). This much bandwidth has not been achieved in the literature for two dimensions, so far.