A generic theoretical approach for estimating bandgap bounds of metamaterial beams

Abstract

The bandgap phenomenon in metamaterials has attracted much research interest for controlling structural vibrations. To tailor the bandgap for applications in a specific frequency range, analytical tools for bandgap bound estimations are critically important. This work presents a generic theoretical approach for fast estimation of the bandgap bounds. Starting from the lattice metamaterial systems, we develop the procedure and provide the analytical bound expressions based on a hypothesis of extreme points in the band structure of metamaterial systems. The proposed approach for the lattice system is verified by the results of transmittance analysis. Subsequently, to explore the fidelity of the proposed approach on continuous metamaterial systems, three typical metamaterial beams (metabeams) have been investigated: a metabeam with mechanical local resonators, a piezoelectric metabeam with shunt resonant circuits, and a hybrid metabeam. Finite element analysis is performed to verify the theoretical expressions of bandgap bounds derived using the proposed approach. With the verified bound expressions, bandgap tailoring and optimization are further investigated. In summary, the developed theoretical approach is generic and offers a promising technique for bandgap estimation of metamaterial systems integrated with various types of resonators.