Design of Stretch-Dominated Metamaterials Avoiding Bandgap Resonance

Bandgap resonance is the significant structural response caused by the dynamic loads within the bandgap of a metamaterial. This phenomenon is undesirable because it undermines the vibration isolation performance of the metamaterial. The sufficient condition to avoid bandgap resonance is derived for stretch-dominated metamaterials, which are modelled as pin-jointed bar structures. Specifically, the metamaterials should exhibit spatial inversion symmetry and be subjected to certain boundary conditions. For metamaterials that satisfy this sufficient condition, the expected bandgaps can be obtained by adjusting the node coordinates and the element cross-sectional areas of the unit cell under symmetry constraint. A two-dimensional example is presented to validate the proposed sufficient condition and the corresponding design method.