Formation and coupling of band gaps in a locally resonant elastic system comprising a string with attached resonators

A uniform string with periodically attached spring-mass resonators represents a simple locally resonant continuous elastic system whose band gap mechanisms are basic to more general and complicated problems. In this Letter, analytical models with explicit formulations are provided to understand the band gap mechanisms of such a system. Some interesting phenomena are demonstrated and discussed, such as asymmetric/symmetric attenuation behavior within a resonance gap, and the realization of a super-wide gap due to exact coupling between Bragg and resonance gaps. In addition, some approximate formulas for the evaluation of low frequency resonance gaps are derived using an approach different from existing investigations. (C) 2011 Elsevier B.V. All rights reserved.