Dynamics of Thin-Walled Metamaterial Beam with Local Resonators

A thin-walled beam with local resonators metamaterial for vibration wave attenuation is studied using a numerical method. The main objective is to analyse the dynamic behaviours of the thin-walled metamaterial beam and to design a local resonator for attenuating the vibration waves. The unit cell of the metamaterial beam is studied to predict the vibration waves in an infinite beam. It is investigated using Bloch’s theorem and finite element method. The related result shows two bandgaps in which flexural and torsional waves can both be attenuated at the same time. It is obtained near the 1700 and 2200 Hz frequencies. It is validated by studying a finite metamaterial beam using transmissibility analysis. The six-unit cells are considered to investigate the flexural, torsional, and coupled flexural and torsional waves in a beam. Vibration transmission is reduced in the same frequency range as the band gap in the single cell analysis. The finite metamaterial is simulated with a different number of single cells to observe the effect on vibration transmissibility. The impact of the resonator mass and stiffness on the band gap is also examined for coupled flexural and torsional vibration waves. It will help to identify the best-suited design of a local resonator for the particular application. The metamaterial characteristics can suppress the vibration waves in the thin-walled beam by utilizing the local resonators.