Tunable elastic metamaterials using rotatable coupled dual-beam resonators

Abstract

We present the theoretical background, finite element and spectral element analyses, and experimental validation of a new class of tunable elastic metamaterials which leverage coupled dual-beam resonators that cancel in-phase bending vibration of each beam section. For a metamaterial with an array of rotatable single-beam resonators, we first show that the orthogonal bending modes of each resonator merely cause the shrinkage of one bandgap and the expansion of the other with changing resonator angle. Then, by simply rotating the coupled dual beams while keeping the joint tip mass stationary, we demonstrate that the bandgap of the host elastic metamaterial with an array of coupled dual-beam resonators can be continuously tuned over a wide range of frequencies. While canceling the undesired lateral bending motions, we enable tunable elastic metamaterials through altering the moment of inertia of the beam-type resonator attachments. Continuous bandgap tuning over a broad frequency range is validated experimentally, yielding a 42% change in the starting frequency of the bandgap as the coupled dual-beam resonators are rotated from 0° to 90°. Although passive tuning is considered in our work, active components can be incorporated in the proposed design to enable adaptive tuning as well as time-varying behavior.