Self-adapting band gaps in rotating elastic metamaterials

Abstract

Rotation in mechanical systems can drastically change their vibrational response. For example, it can enable new properties, such as break time-reversal symmetry and induce non-reciprocity in acoustic metamaterials, due to Coriolis forces and gyroscopic effects. Rotation can also be highly detrimental: for example, synchronous vibrations occur in rotating mechanical components and can be extremely damaging when they coincide with system resonances. In addition, centrifugal forces from rotation significantly affect the dynamics of rotating systems, through stress stiffening and spin softening, however their effects on acoustic and elastic metamaterials have rarely been explored. Here, we demonstrate that centrifugal forces in rotating elastic metamaterials enable band gaps that “self-adapt” to synchronous vibrations, attenuating these vibrations over a broadband frequency range. Specifically, this talk presents a reduced order model that captures stress stiffening effects on the band gaps of a rotating elastic metamaterial. The resonators are beams with tip masses oriented perpendicular to the rotational axis, such that stress stiffening causes their resonant frequency to be linearly proportional to the rotational speed. The reduced order models are validated by full finite element simulations of a 3D elastic metamaterial whose band gap self-adapts to synchronous vibrations that are linearly proportional to rotational speed.