Broadband wave attenuation in locally resonant periodic flexural beams with force-moment resonators

We investigate flexural wave propagation in Euler-Bernoulli beams with periodically suspended 2-DOF forcemoment resonators. We use the transfer matrix method for a unit cell in the beam in conjunction with Bloch's theorem, to define the dispersion curves and frequency band structure. Our analysis shows that the uncoupled force-moment resonators generate rich attenuation properties that are not observed in the conventional locally resonant structures with suspended forceonly (or moment-only) vibrators. As a prime focus, we identify a Bragg-like band gap below the resonance frequency of the resonator and its coupling with the resonance gap, giving rise to a potentially super-wide attenuation gap that can be tuned for any low frequency range. The analysis presented can be extended to other types of phononic meta-materials and structures of multi-degrees of freedom (and distributed) resonators, which may exhibit more practically significant wave attenuation characteristics.