Locally resonant metamaterials have attracted lots of research interests for the application of vibration suppression which is a fundamental problem but remains as a challenge. Beam structure is a widely used in engineering. The transverse wave propagation in a beam is through the transmission of the shear force and bending moment. Most design of metamaterials in the existing literature use translational vibration resonators for inducing reaction force to prevent the transmission of the shear force, hence the wave propagation. This paper studies a metamaterial beam consisting of torsional vibration resonators. The reaction moments generated by the torsional resonators are expected to neutralize the bending moment in the beam, thus preventing the wave propagation. In order to effectively design such kind of metamaterials, an approach to calculate the dispersion relation for predicting band gaps is required. The existence of torsional vibration resonators leads to the moment discontinuity conditions which can not be directly taken into account using the Euler beam theory. By employing the Timoshenko beam theory, a novel method for band structure analysis is developed through a modal analysis based on the assumption of infinite number of resonators. The explicit expressions of the lower and upper bounds of the band gap are derived. The traditional transfer matrix method (TMM) is used to verify the proposed method. A discussion on the advantages of the proposed method as compared to the TMM is provided.


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

Division / Sponsors: 
Aerospace Division

Paper Proceedings: https://asmedigitalcollection.asme.org/SMASIS/SMASIS2020/volume/84027

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