Design of Stretch-Dominated Metamaterials Avoiding Bandgap Resonance

Mechanical metamaterials subjected to dynamic loads within their bandgaps can still experience significant undesired structural responses, which are referred to as bandgap resonances. This paper proposes a design method for stretch-dominated metamaterials to avoid such a phenomenon. The metamaterials are modeled as pin-jointed bar structures, and the sufficient condition for preventing their bandgap resonances is derived: they must exhibit spatial inversion symmetry and satisfy certain boundary conditions. A matrix-form perturbation expression of the bandgap is then provided to generate expected bandgaps by adjusting the node coordinates and element cross-sectional areas of the unit cells under symmetry constraint. As an example, a two-dimensional metamaterial is designed to achieve an expected bandgap of 600–1000 Hz. The frequency-response analyses show that the sufficient condition ensures the suppression of bandgap resonances.