Dispersion analysis of the hourglass-shaped periodic shell lattice structure

Abstract

A novel hourglass-shaped lattice metamaterial with broadband and multiband characteristics is studied here. Its unique shape helps to evolve customizable stiffness profiles, which makes it succeed in significantly magnifying the vibration attenuation capability. The general concept of a locally resonant phononic crystal is used to design the proposed metamaterial with a wide bandgap. The concept utilizes elastic wave resonances to form constructive or destructive interference, which creates ranges of frequencies at which waves are either allowed to propagate (pass bands) or blocked in one (stop bands) or multiple directions (complete band gaps (BGs)). The bandgap depends on the geometric configuration and material of the unit cell, stiffness properties of the periodic structure as well as host matrix of the resonating mass, which has been exploited in designing the metamaterial. The unit cell is designed with the hourglass lattice integrated with a cubic resonating mass at the center which helps to induce ultrawide bandgaps with effective mechanical properties. A detailed bandgap analysis has been performed for a spherical and parabolic hourglass-based matrix with various parametric combinations. After numerical simulation, additive layer manufacturing (3D printing) and experimental testing are carried out to evaluate the system and reveal the underlying physics responsible for their unique dynamic behavior.