Coupled flexural and torsional vibration attenuation with locally resonant metamaterials

Abstract

A metamaterial beam with coupled bending and torsional resonators for broadband flexural–torsional vibration suppression is studied. The main objective is to design and analyse the metamaterial beam for simultaneous attenuation of flexural and torsional vibration waves using FEM and the Bloch-Floquet theorem. The bandgaps of the single unit cell with an infinite periodic structure assumption are studied using Bloch-Floquet reduction with a commercial multi-physics program. Initially, the beam with a bending resonator is examined, and a high-frequency broadband vibration frequency bandgap above 10 kHz is observed. With the addition of a torsional resonator, the existing bending bandgaps are widened, and further new bandgaps are formed. Transmissibility analysis of a metamaterial beam with the above unit cells is performed using the finite element method. The FRFs show similar bandgaps observed in the dispersion curves, thereby validating unit cell analysis. It is observed that coupled bending and torsional resonators create the opportunity to widen and introduce new bandgaps compared to uncoupled resonators. These metamaterial beams with bending and coupled resonators can aid in vibration isolation and frequency filtering of structures subjected to bending and torsional impact loads.