Interaction of Bragg scattering bandgaps and local resonators in mono-coupled periodic structures

Abstract

Periodic structures have gained attention in the research community since they show attenuation zones in their frequency response, called bandgaps. In this paper, the interactions of two mechanisms of bandgap formation in mono-coupled periodic structures are examined, i.e., Bragg scattering and local resonators. With reference to longitudinal elastic waves, an analytical study is carried out to describe in detail the formation of bandgaps. Local resonators are implemented via piezoelectric inserts shunted with a resonating electrical circuit for which a non-traditional model is needed since the study concerns higher frequencies with respect to those of the subwavelength regime. Design maps and tuning formulas are developed not only for the case of infinite structures, but also for the finite case, highlighting the role of the number of unit cells and that of resonances in the attenuation zones. Among the possible tuning strategies of local resonators, it is shown that the mutual influence between elastic and electric parameters is able to produce a wider attenuation zone, bridging Bragg scattering bandgaps thanks to the effect of local resonators. The analytical findings of this paper are validated with numerical results in an example application.