An analysis of flexural wave band gaps of locally resonant beams with continuum beam resonators

Locally-resonant (LR) phononic meta-materials and structures have a potential for wide band-gaps of elastic wave attenuation in low frequency range. In this paper, we investigate a use of continuum beam resonators suspended periodically on an Euler–Bernoulli beam. In a mathematical analysis based on Floquet–Bloch’s theorem, we describe the dispersive characteristics of flexural wave attenuation. Our results show richer dispersion properties in the LR structures with periodically attached continuum resonators of distributed degrees of freedom than those with the conventional force-only resonators. In particular, we identify the appearance of a wide composite band gap of local resonance and Bragg-scattering types and its potentials for low-frequency applications.