Phononic Crystals and Elastic Mechanical Metamaterials have shown unusual light and mechanical wave manipulating properties. These novel structures are composites of two or more linear elastic materials and have been extensively used in energy harvesting, vibration control and attenuation. They show vibration energy propagation inhibition over a specific range of frequencies. These are called phononic band gaps, whose presence essentially signifies the reduction of the flow of phonons in the form of elastic wave energy. Phononic crystals are generally constructed with some periodicity in geometry or boundary. They are also lightweight with a choice of tailoring their mechanical and dynamic properties. Some three-dimensional recently developed phononic crystals with Acoustic Black Holes (ABH) show flexural wave energy inside a structure.
The present study has investigated a metamaterial beam with coupled ABH, bending and torsional resonators for broadband flexural-torsional vibration isolation. The main aim is to design and analyse the metamaterial beam for simultaneous attenuation of flexural and torsional vibration waves using the Finite Element Method (FEM) and Bloch-Floquet theorem. Dispersion bandgaps of a single unit cell with infinite periodicity assumption are studied using Bloch-Floquet reduction in COMSOL Multiphysics software.
Initially, an ABH engraved plate is studied, and a low-frequency bandgap around 3 kHz is observed. With the addition of a torsional resonator, new bandgaps are formed. Introducing a cylindrical bending resonator broadens the existing bandgaps to a greater extent with the evolution of high-frequency bandgaps.
Transmissibility analysis of a metamaterial beam with the above unit cells is performed using FEM. The frequency responses closely corroborate the bandgaps observed in dispersion curves, thereby validating the unit cell analysis. It is observed that coupled ABH, bending and torsional resonators create the opportunity to widen and introduce new bandgaps compared to the uncoupled structures. These metamaterial beams with the coupled systems can aid in vibration isolation and frequency filtering of structures subjected to bending and torsional impact loads.