Centrifugal forces enable band gaps that self-adapt to synchronous vibrations in rotating elastic metamaterial

•Stress-stiffening in local resonances of rotating acoustic metamaterials can be captured using a stress stiffening function.•Rotating acoustic metamaterials with beam-tip-mass resonators support band gaps that depend linearly on the rotational speed.•Resonator parameters can be chosen such that band gaps of the metamaterial self-adjust to the synchronous vibration frequency, resulting in attenuation over a wide range of frequencies and thus rotational speeds.