Band Gap Formation in Metamaterial Beam With Torsional Local Resonators for Vibration Suppression

Locally resonant metamaterials have attracted lots of research interests for the application of vibration suppression which is a fundamental problem but remains a big challenge in the engineering field. The transverse wave propagation in a beam is through the transmission of the shear force and bending moment. Most designs of metamaterials in the existing literature exploit translational local resonators to induce reaction force to prevent the transmission of the shear force, hence the wave propagation. This paper studies a metamaterial beam attached with torsional local resonators. The reaction moments generated by the torsional resonators are expected to neutralize the bending moment in the beam, thus preventing the wave propagation. The existence of torsional resonators leads to the moment discontinuity conditions which cannot be directly taken into account using the Euler beam theory. Based on the Timoshenko beam theory, the band structure analysis is developed through a modal analysis based on the infinite periodic local resonator structure. The numerical results reveal that the locally resonant frequency corresponds to the upper bound of the band gap. Both infinitely long and finitely long beams are also modeled using finite element method. The transmittance is calculated to verify the band structure analysis.