Closed-form bandgap design formulas for beam-type metastructures

Abstract

Metastructures have received increasing attention because of their unique bandgap behavior that can be utilized to control vibration and noise of mechanical structures. This work is aimed to develop efficient formulas for bandgap estimation and design of flexural beam-type metastructures containing a periodic array of single-frequency force resonators. First, closed-form formulas are developed for a fast yet accurate estimation of the lowest two bandgaps, which may be formed by local resonance (LR) mechanism or Bragg scattering (BS) mechanism. Such formulas are shown to be more general than existing well-known closed-form formulas, which are only applicable to the case of deep-subwavelength LR-type bandgap. Second, closed-form formulas are proposed for a straightforward design of two particular cases of improved bandgaps compared with typical deep-subwavelength LR-type bandgap. One particular case is an ultra-wide near-coupled pseudo bandgap formed by strong interaction of the LR and BS mechanisms. Another particular case is an LR-type bandgap possessing significant attenuation performance at its bandgap center, and also having a broader effective width than the typical deep-subwavelength LR-type bandgap. Moreover, the broad applicability of the developed closed-form formulas is numerically verified by addressing bandgap design problems associated with simple and advanced multi-scale beam-type metastructures.