Flexural wave bandgap and vibration reduction of a metabeam with 2DOF resonators

A metabeam is designed by attaching periodic two-degree-of-freedom (2DOF) local resonators to a thin homogeneous beam. The 2DOF resonator is realized by a double-ended thin beam mounted with mass blocks at its two tips. Explicit formula is derived for the prediction of bandgaps in the metabeam. Analytical predictions show that the proposed metabeam can exhibits two local resonance band gaps below the Bragg frequency and a Bragg scattering band gap around the Bragg frequency. We further conduct an experimental measurement of the vibration transmissibility across a finite metabeam specimen with a periodic array of 10 local resonators. Significant vibration reduction is observed within the predicted band-gap frequency range, which confirms the validity of the design and modeling of the metabeam with 2DOF resonators.