Bandgap merging with double-negative metabeam

Abstract

We theoretically investigate the bandgap formation in an Euler–Bernoulli beam-based metastructure with periodically attached double negative 3-dof local resonators. The idiosyncratic physical phenomena found in mechanical metamaterials, such as negative stiffness and mass, are introduced in the attached local resonator to design the double negative metabeam. The transfer matrix method with the Bloch–Floquet formulation is implemented in a unit cell of the double negative metabeam. The complex band structure describes the existence of various locally resonant attenuation bandgaps on the frequency spectrum. Further system analysis is conducted to illustrate the merging of the negative stiffness and mass controlled locally resonant bandgaps. A significant increase of 164% is found in the attenuation bandwidth due to the merging of locally resonant bandgaps.