Asymmetric bandgaps for bidirectional vibration suppression in metamaterial beams

Abstract This paper proposes a finite-length metamaterial beam (FLMB) based on local resonance, featuring two distinct bandgaps. The impact of forward and backward wave propagation on the dispersion characteristics of the proposed FLMB is investigated using numerical methods alongside experimental validation. Transfer matrix method (TMM) models incorporating the influence of wave propagation direction are developed to predict the band structure and frequency response functions. Experimental results align well with both TMM and finite element method simulations. Collectively, they demonstrate that the stop-band under forward wave propagation is continuous and broad, whereas the stop-band under backward wave propagation is segmented. This directional difference originates from the reversal in interaction moments between the primary beam and local resonators. Analysis of the TMM-derived band structure reveals that forward and backward transport properties are predominantly governed by the suppression capability concerning evanescent waves. These asymmetric transport properties become markedly distinct for a limited number of unitcells but converge as the number approaches infinity. The effects of resonator parameters on the FLMB’s asymmetric bandgaps characteristics are also discussed.