Energy dissipation enhancement of flexural metamaterial beams with inerter and rotational deformation

Elastic metamaterials with locally resonant components exhibit unique band-gap behavior that can be applied to control wave propagation in flexural beams. Previous studies mainly emphasized the utilization of transversal deformations of flexural beams. A novel metamaterial configuration is presented in this work; in particular, to obtain a wide band gap in low-frequency ranges with reduced expenses in associated mass, inerter-based resonators and cantilevered deformations caused by the rotation of flexural beams are combined. The study is performed by using an analytical approach based on the finite element (FE) method and the Floquet-Bloch theorem. Both the wavenumber-frequency and the damping ratio-frequency relationships and relevant band structures are set. These two types of band structures are further considered for the investigation of the effects of various system parameters on the band-gap behavior and wave attenuation performance in the whole frequency range. Finally, the effectiveness of the proposed concept is validated by means of numerical examples.